Le Song

NeurIPS Conference 2025 Conference Paper

Dimensional Collapse in VQVAEs: Evidence and Remedies

• Jiayou Zhang
• Yifan Shen
• Guangyi Chen
• Le Song
• Eric Xing

Vector-Quantized Variational Autoencoders (VQVAEs) have enabled strong performance in generative modeling by mapping continuous data to learnable codes. In this work, we identify a surprising yet consistent phenomenon that we term \emph{dimensional collapse}: despite using high-dimensional embeddings, VQVAEs tend to compress their representations into a much smaller subspace, typically only 4 to 10 dimensions. We provide an in-depth analysis of this phenomenon and reveal its relation to model performance and learning dynamics. Interestingly, VQVAEs naturally gravitate toward this low-dimensional regime, and enforcing higher-dimensional usage (e. g. , via rank regularization) could lead to degraded performance. To overcome this low-dimensionality limitation, we propose \textbf{Divide-and-Conquer VQ (DCVQ)}, which partitions the latent space into multiple low-dimensional subspaces, each quantized independently. By design, each subspace respects the model’s preference for low dimensionality, while their combination expands the overall capacity. Our results show that DCVQ overcomes the inherent dimensional bottleneck and achieves improved reconstruction quality across image datasets.

NeurIPS Conference 2025 Conference Paper

Protein Inverse Folding From Structure Feedback

• Junde Xu
• Zijun Gao
• Xinyi Zhou
• Xingyi Cheng
• Le Song
• Guangyong Chen
• Pheng-Ann Heng
• Jiezhong Qiu

The inverse folding problem, aiming to design amino acid sequences that fold into desired three-dimensional structures, is pivotal for various biotechnological applications. Here, we introduce a novel approach leveraging Direct Preference Optimization (DPO) to fine-tune an inverse folding model using feedback from a protein folding model. Given a target protein structure, we begin by sampling candidate sequences from the inverse‐folding model, then predict the three‐dimensional structure of each sequence with the folding model to generate pairwise structural‐preference labels. These labels are used to fine‐tune the inverse‐folding model under the DPO objective. Our results on the CATH 4. 2 test set demonstrate that DPO fine-tuning not only improves sequence recovery of baseline models but also leads to a significant improvement in average TM-Score from 0. 77 to 0. 81, indicating enhanced structure similarity. Furthermore, iterative application of our DPO-based method on challenging protein structures yields substantial gains, with an average TM-Score increase of 79. 5\% with regard to the baseline model. This work establishes a promising direction for enhancing protein sequence design ability from structure feedback by effectively utilizing preference optimization.

NeurIPS Conference 2025 Conference Paper

Pruning Spurious Subgraphs for Graph Out-of-Distribution Generalization

• Tianjun Yao
• Haoxuan Li
• Yongqiang Chen
• Tongliang Liu
• Le Song
• Eric Xing
• Zhiqiang Shen

Graph Neural Networks (GNNs) often encounter significant performance degradation under distribution shifts between training and test data, hindering their applicability in real-world scenarios. Recent studies have proposed various methods to address the out-of-distribution (OOD) generalization challenge, with many methods in the graph domain focusing on directly identifying an invariant subgraph that is predictive of the target label. However, we argue that identifying the edges from the invariant subgraph directly is challenging and error-prone, especially when some spurious edges exhibit strong correlations with the targets. In this paper, we propose $\texttt{PrunE}$, the first pruning-based graph OOD method that eliminates spurious edges to improve OOD generalizability. By pruning spurious edges, $\texttt{PrunE}$ retains the invariant subgraph more comprehensively, which is critical for OOD generalization. Specifically, $\texttt{PrunE}$ employs two regularization terms to prune spurious edges: 1) _graph size constraint_ to exclude uninformative spurious edges, and 2) _$\epsilon$-probability alignment_ to further suppress the occurrence of spurious edges. Through theoretical analysis and extensive experiments, we show that $\texttt{PrunE}$ achieves superior OOD performance and outperforms previous state-of-the-art methods significantly.

ICLR Conference 2025 Conference Paper

Size-Generalizable RNA Structure Evaluation by Exploring Hierarchical Geometries

• Zongzhao Li
• Jiacheng Cen
• Wenbing Huang 0001
• Taifeng Wang
• Le Song

Understanding the 3D structure of RNA is essential for deciphering its function and developing RNA-based therapeutics. Geometric Graph Neural Networks (GeoGNNs) that conform to the $\mathrm{E}(3)$-symmetry have advanced RNA structure evaluation, a crucial step toward RNA structure prediction. However, existing GeoGNNs are still defective in two aspects: 1. inefficient or incapable of capturing the full geometries of RNA; 2. limited generalization ability when the size of RNA significantly differs between training and test datasets. In this paper, we propose EquiRNA, a novel equivariant GNN model by exploring the three-level hierarchical geometries of RNA. At its core, EquiRNA effectively addresses the size generalization challenge by reusing the representation of nucleotide, the common building block shared across RNAs of varying sizes. Moreover, by adopting a scalarization-based equivariant GNN as the backbone, our model maintains directional information while offering higher computational efficiency compared to existing GeoGNNs. Additionally, we propose a size-insensitive $K$-nearest neighbor sampling strategy to enhance the model's robustness to RNA size shifts. We test our approach on our created benchmark as well as an existing dataset. The results show that our method significantly outperforms other state-of-the-art methods, providing a robust baseline for RNA 3D structure modeling and evaluation.

NeurIPS Conference 2024 Conference Paper

MSAGPT: Neural Prompting Protein Structure Prediction via MSA Generative Pre-Training

• Bo Chen
• Zhilei Bei
• Xingyi Cheng
• Pan Li
• Jie Tang
• Le Song

Multiple Sequence Alignment (MSA) plays a pivotal role in unveiling the evolutionary trajectories of protein families. The accuracy of protein structure predictions is often compromised for protein sequences that lack sufficient homologous information to construct high-quality MSA. Although various methods have been proposed to generate high-quality MSA under these conditions, they fall short in comprehensively capturing the intricate co-evolutionary patterns within MSA or require guidance from external oracle models. Here we introduce MSAGPT, a novel approach to prompt protein structure predictions via MSA generative pre-training in a low-MSA regime. MSAGPT employs a simple yet effective 2D evolutionary positional encoding scheme to model the complex evolutionary patterns. Endowed by this, the flexible 1D MSA decoding framework facilitates zero- or few-shot learning. Moreover, we demonstrate leveraging the feedback from AlphaFold2 (AF2) can further enhance the model’s capacity via Rejective Fine-tuning (RFT) and Reinforcement Learning from AF2 Feedback (RLAF). Extensive experiments confirm the efficacy of MSAGPT in generating faithful and informative MSA (up to +8. 5% TM-Score on few-shot scenarios). The transfer learning also demonstrates its great potential for the wide range of tasks resorting to the quality of MSA.

ICLR Conference 2024 Conference Paper

Optimistic Bayesian Optimization with Unknown Constraints

• Quoc Phong Nguyen
• Wan Theng Ruth Chew
• Le Song
• Bryan Kian Hsiang Low
• Patrick Jaillet

Though some research efforts have been dedicated to constrained Bayesian optimization (BO), there remains a notable absence of a principled approach with a theoretical performance guarantee in the decoupled setting. Such a setting involves independent evaluations of the objective function and constraints at different inputs, and is hence a relaxation of the commonly-studied coupled setting where functions must be evaluated together. As a result, the decoupled setting requires an adaptive selection between evaluating either the objective function or a constraint, in addition to selecting an input (in the coupled setting). This paper presents a novel constrained BO algorithm with a provable performance guarantee that can address the above relaxed setting. Specifically, it considers the fundamental trade-off between exploration and exploitation in constrained BO, and, interestingly, affords a noteworthy connection to active learning. The performance of our proposed algorithms is also empirically evaluated using several synthetic and real-world optimization problems.

NeurIPS Conference 2024 Conference Paper

Training Compute-Optimal Protein Language Models

• Xingyi Cheng
• Bo Chen
• Pan Li
• Jing Gong
• Jie Tang
• Le Song

We explore optimally training protein language models, an area of significant interest in biological research where guidance on best practices is limited. Most models are trained with extensive compute resources until performance gains plateau, focusing primarily on increasing model sizes rather than optimizing the efficient compute frontier that balances performance and compute budgets. Our investigation is grounded in a massive dataset consisting of 939 million protein sequences. We trained over 300 models ranging from 3. 5 million to 10. 7 billion parameters on 5 to 200 billion unique tokens, to investigate the relations between model sizes, training token numbers, and objectives. First, we observed the effect of diminishing returns for the Causal Language Model (CLM) and that of overfitting for Masked Language Model (MLM) when repeating the commonly used Uniref database. To address this, we included metagenomic protein sequences in the training set to increase the diversity and avoid the plateau or overfitting effects. Second, we obtained the scaling laws of CLM and MLM on Transformer, tailored to the specific characteristics of protein sequence data. Third, we observe a transfer scaling phenomenon from CLM to MLM, further demonstrating the effectiveness of transfer through scaling behaviors based on estimated Effectively Transferred Tokens. Finally, to validate our scaling laws, we compare the large-scale versions of ESM-2 and PROGEN2 on downstream tasks, encompassing evaluations of protein generation as well as structure- and function-related tasks, all within less or equivalent pre-training compute budgets.

ECAI Conference 2023 Conference Paper

An Empirical Study of Retrieval-Enhanced Graph Neural Networks

• Dingmin Wang
• Shengchao Liu
• Hanchen Wang 0002
• Bernardo Cuenca Grau
• Linfeng Song
• Jian Tang 0005
• Le Song
• Qi Liu 0049

Graph Neural Networks (GNNs) are effective tools for graph representation learning. Most GNNs rely on a recursive neighborhood aggregation scheme, named message passing, thereby their theoretical expressive power is limited to the first-order Weisfeiler-Lehman test (1-WL). An effective approach to this challenge is to explicitly retrieve some annotated examples used to enhance GNN models. While retrieval-enhanced models have been proved to be effective in many language and vision domains, it remains an open question how effective retrieval-enhanced GNNs are when applied to graph datasets. Motivated by this, we want to explore how the retrieval idea can help augment the useful information learned in the graph neural networks, and we design a retrieval-enhanced scheme called GRAPHRETRIEVAL, which is agnostic to the choice of graph neural network models. In GRAPHRETRIEVAL, for each input graph, similar graphs together with their ground-true labels are retrieved from an existing database. Thus they can act as a potential enhancement to complete various graph property predictive tasks. We conduct comprehensive experiments over 13 datasets, and we observe that GRAPHRETRIEVAL is able to reach substantial improvements over existing GNNs. Moreover, our empirical study also illustrates that retrieval enhancement is a promising remedy for alleviating the long-tailed label distribution problem.

NeurIPS Conference 2023 Conference Paper

Injecting Multimodal Information into Rigid Protein Docking via Bi-level Optimization

• Ruijia Wang
• YiWu Sun
• Yujie Luo
• Shaochuan Li
• Cheng Yang
• Xingyi Cheng
• Hui Li
• Chuan Shi

The structure of protein-protein complexes is critical for understanding binding dynamics, biological mechanisms, and intervention strategies. Rigid protein docking, a fundamental problem in this field, aims to predict the 3D structure of complexes from their unbound states without conformational changes. In this scenario, we have access to two types of valuable information: sequence-modal information, such as coevolutionary data obtained from multiple sequence alignments, and structure-modal information, including the 3D conformations of rigid structures. However, existing docking methods typically utilize single-modal information, resulting in suboptimal predictions. In this paper, we propose xTrimoBiDock (or BiDock for short), a novel rigid docking model that effectively integrates sequence- and structure-modal information through bi-level optimization. Specifically, a cross-modal transformer combines multimodal information to predict an inter-protein distance map. To achieve rigid docking, the roto-translation transformation is optimized to align the docked pose with the predicted distance map. In order to tackle this bi-level optimization problem, we unroll the gradient descent of the inner loop and further derive a better initialization for roto-translation transformation based on spectral estimation. Compared to baselines, BiDock achieves a promising result of a maximum 234% relative improvement in challenging antibody-antigen docking problem.

NeurIPS Conference 2023 Conference Paper

xTrimoGene: An Efficient and Scalable Representation Learner for Single-Cell RNA-Seq Data

• Jing Gong
• Minsheng Hao
• Xingyi Cheng
• Xin Zeng
• Chiming Liu
• Jianzhu Ma
• Xuegong Zhang
• Taifeng Wang

Advances in high-throughput sequencing technology have led to significant progress in measuring gene expressions at the single-cell level. The amount of publicly available single-cell RNA-seq (scRNA-seq) data is already surpassing 50M records for humans with each record measuring 20, 000 genes. This highlights the need for unsupervised representation learning to fully ingest these data, yet classical transformer architectures are prohibitive to train on such data in terms of both computation and memory. To address this challenge, we propose a novel asymmetric encoder-decoder transformer for scRNA-seq data, called xTrimoGene$^\alpha$ (or xTrimoGene for short), which leverages the sparse characteristic of the data to scale up the pre-training. This scalable design of xTrimoGene reduces FLOPs by one to two orders of magnitude compared to classical transformers while maintaining high accuracy, enabling us to train the largest transformer models over the largest scRNA-seq dataset today. Our experiments also show that the performance of xTrimoGene improves as we scale up the model sizes, and it also leads to SOTA performance over various downstream tasks, such as cell type annotation, perturb-seq effect prediction, and drug combination prediction. xTrimoGene model is now available for use as a service via the following link: https: //api. biomap. com/xTrimoGene/apply.

ICLR Conference 2022 Conference Paper

Explaining Point Processes by Learning Interpretable Temporal Logic Rules

• Shuang Li 0002
• Mingquan Feng
• Lu Wang 0029
• Abdelmajid Essofi
• Yufeng Cao
• Junchi Yan
• Le Song

We propose a principled method to learn a set of human-readable logic rules to explain temporal point processes. We assume that the generative mechanisms underlying the temporal point processes are governed by a set of first-order temporal logic rules, as a compact representation of domain knowledge. Our method formulates the rule discovery process from noisy event data as a maximum likelihood problem, and designs an efficient and tractable branch-and-price algorithm to progressively search for new rules and expand existing rules. The proposed algorithm alternates between the rule generation stage and the rule evaluation stage, and uncovers the most important collection of logic rules within a fixed time limit for both synthetic and real event data. In a real healthcare application, we also had human experts (i.e., doctors) verify the learned temporal logic rules and provide further improvements. These expert-revised interpretable rules lead to a point process model which outperforms previous state-of-the-arts for symptom prediction, both in their occurrence times and types.

ICLR Conference 2022 Conference Paper

GNN is a Counter? Revisiting GNN for Question Answering

• Kuan Wang
• Yuyu Zhang
• Diyi Yang
• Le Song
• Tao Qin

Question Answering (QA) has been a long-standing research topic in AI and NLP fields, and a wealth of studies has been conducted to attempt to equip QA systems with human-level reasoning capability. To approximate the complicated human reasoning process, state-of-the-art QA systems commonly use pre-trained language models (LMs) to access knowledge encoded in LMs together with elaborately designed modules based on Graph Neural Networks (GNNs) to perform reasoning over knowledge graphs (KGs). However, many problems remain open regarding the reasoning functionality of these GNN-based modules. Can these GNN-based modules really perform a complex reasoning process? Are they under- or over-complicated for QA? To open the black box of GNN and investigate these problems, we dissect state-of-the-art GNN modules for QA and analyze their reasoning capability. We discover that even a very simple graph neural counter can outperform all the existing GNN modules on CommonsenseQA and OpenBookQA, two popular QA benchmark datasets which heavily rely on knowledge-aware reasoning. Our work reveals that existing knowledge-aware GNN modules may only carry out some simple reasoning such as counting. It remains a challenging open problem to build comprehensive reasoning modules for knowledge-powered QA.

ICLR Conference 2022 Conference Paper

Provable Learning-based Algorithm For Sparse Recovery

• Xinshi Chen
• Haoran Sun
• Le Song

Recovering sparse parameters from observational data is a fundamental problem in machine learning with wide applications. Many classic algorithms can solve this problem with theoretical guarantees, but their performances rely on choosing the correct hyperparameters. Besides, hand-designed algorithms do not fully exploit the particular problem distribution of interest. In this work, we propose a deep learning method for algorithm learning called PLISA (Provable Learning-based Iterative Sparse recovery Algorithm). PLISA is designed by unrolling a classic path-following algorithm for sparse recovery, with some components being more flexible and learnable. We theoretically show the improved recovery accuracy achievable by PLISA. Furthermore, we analyze the empirical Rademacher complexity of PLISA to characterize its generalization ability to solve new problems outside the training set. This paper contains novel theoretical contributions to the area of learning-based algorithms in the sense that (i) PLISA is generically applicable to a broad class of sparse estimation problems, (ii) generalization analysis has received less attention so far, and (iii) our analysis makes novel connections between the generalization ability and algorithmic properties such as stability and convergence of the unrolled algorithm, which leads to a tighter bound that can explain the empirical observations. The techniques could potentially be applied to analyze other learning-based algorithms in the literature.

ICLR Conference 2022 Conference Paper

Spanning Tree-based Graph Generation for Molecules

• Sungsoo Ahn
• Binghong Chen
• Tianzhe Wang
• Le Song

In this paper, we explore the problem of generating molecules using deep neural networks, which has recently gained much interest in chemistry. To this end, we propose a spanning tree-based graph generation (STGG) framework based on formulating molecular graph generation as a construction of a spanning tree and the residual edges. Such a formulation exploits the sparsity of molecular graphs and allows using compact tree-constructive operations to define the molecular graph connectivity. Based on the intermediate graph structure of the construction process, our framework can constrain its generation to molecular graphs that satisfy the chemical valence rules. We also newly design a Transformer architecture with tree-based relative positional encodings for realizing the tree construction procedure. Experiments on QM9, ZINC250k, and MOSES benchmarks verify the effectiveness of the proposed framework in metrics such as validity, Frechet ChemNet distance, and fragment similarity. We also demonstrate the usefulness of STGG in maximizing penalized LogP value of molecules.

NeurIPS Conference 2022 Conference Paper

Uncovering the Structural Fairness in Graph Contrastive Learning

• Ruijia Wang
• Xiao Wang
• Chuan Shi
• Le Song

Recent studies show that graph convolutional network (GCN) often performs worse for low-degree nodes, exhibiting the so-called structural unfairness for graphs with long-tailed degree distributions prevalent in the real world. Graph contrastive learning (GCL), which marries the power of GCN and contrastive learning, has emerged as a promising self-supervised approach for learning node representations. How does GCL behave in terms of structural fairness? Surprisingly, we find that representations obtained by GCL methods are already fairer to degree bias than those learned by GCN. We theoretically show that this fairness stems from intra-community concentration and inter-community scatter properties of GCL, resulting in a much clear community structure to drive low-degree nodes away from the community boundary. Based on our theoretical analysis, we further devise a novel graph augmentation method, called GRAph contrastive learning for DEgree bias (GRADE), which applies different strategies to low- and high-degree nodes. Extensive experiments on various benchmarks and evaluation protocols validate the effectiveness of the proposed method.

NeurIPS Conference 2021 Conference Paper

A Biased Graph Neural Network Sampler with Near-Optimal Regret

• Qingru Zhang
• David Wipf
• Quan Gan
• Le Song

Graph neural networks (GNN) have recently emerged as a vehicle for applying deep network architectures to graph and relational data. However, given the increasing size of industrial datasets, in many practical situations, the message passing computations required for sharing information across GNN layers are no longer scalable. Although various sampling methods have been introduced to approximate full-graph training within a tractable budget, there remain unresolved complications such as high variances and limited theoretical guarantees. To address these issues, we build upon existing work and treat GNN neighbor sampling as a multi-armed bandit problem but with a newly-designed reward function that introduces some degree of bias designed to reduce variance and avoid unstable, possibly-unbounded pay outs. And unlike prior bandit-GNN use cases, the resulting policy leads to near-optimal regret while accounting for the GNN training dynamics introduced by SGD. From a practical standpoint, this translates into lower variance estimates and competitive or superior test accuracy across several benchmarks.

IROS Conference 2021 Conference Paper

A General Framework for Lifelong Localization and Mapping in Changing Environment

• Min Zhao
• Xin Guo
• Le Song
• Baoxing Qin
• Xuesong Shi
• Gim Hee Lee
• Guanghui Sun

The environment of most real-world scenarios such as malls and supermarkets changes at all times. A pre-built map that does not account for these changes becomes out-of-date easily. Therefore, it is necessary to have an up-to-date model of the environment to facilitate long-term operation of a robot. To this end, this paper presents a general lifelong simultaneous localization and mapping (SLAM) framework. Our framework uses a multiple session map representation, and exploits an efficient map updating strategy that includes map building, pose graph refinement and sparsification. To mitigate the unbounded increase of memory usage, we propose a map-trimming method based on the Chow-Liu maximum-mutual-information spanning tree. The proposed SLAM framework has been comprehensively validated by over a month of robot deployment in real supermarket environment. Furthermore, we release the dataset collected from the indoor and outdoor changing environment with the hope to accelerate lifelong SLAM research in the community. Our dataset is available at https://github.com/sanduan168/lifelong-SLAM-dataset.

NeurIPS Conference 2021 Conference Paper

Locality Sensitive Teaching

• Zhaozhuo Xu
• Beidi Chen
• Chaojian Li
• Weiyang Liu
• Le Song
• Yingyan Lin
• Anshumali Shrivastava

The emergence of the Internet-of-Things (IoT) sheds light on applying the machine teaching (MT) algorithms for online personalized education on home devices. This direction becomes more promising during the COVID-19 pandemic when in-person education becomes infeasible. However, as one of the most influential and practical MT paradigms, iterative machine teaching (IMT) is prohibited on IoT devices due to its inefficient and unscalable algorithms. IMT is a paradigm where a teacher feeds examples iteratively and intelligently based on the learner's status. In each iteration, current IMT algorithms greedily traverse the whole training set to find an example for the learner, which is computationally expensive in practice. We propose a novel teaching framework, Locality Sensitive Teaching (LST), based on locality sensitive sampling, to overcome these challenges. LST has provable near-constant time complexity, which is exponentially better than the existing baseline. With at most 425. 12x speedups and 99. 76% energy savings over IMT, LST is the first algorithm that enables energy and time efficient machine teaching on IoT devices. Owing to LST's substantial efficiency and scalability, it is readily applicable in real-world education scenarios.

ICLR Conference 2021 Conference Paper

Molecule Optimization by Explainable Evolution

• Binghong Chen
• Tianzhe Wang
• Chengtao Li
• Hanjun Dai
• Le Song

Optimizing molecules for desired properties is a fundamental yet challenging task in chemistry, material science, and drug discovery. This paper develops a novel algorithm for optimizing molecular properties via an Expectation-Maximization (EM) like explainable evolutionary process. The algorithm is designed to mimic human experts in the process of searching for desirable molecules and alternate between two stages: the first stage on explainable local search which identifies rationales, i.e., critical subgraph patterns accounting for desired molecular properties, and the second stage on molecule completion which explores the larger space of molecules containing good rationales. We test our approach against various baselines on a real-world multi-property optimization task where each method is given the same number of queries to the property oracle. We show that our evolution-by-explanation algorithm is 79% better than the best baseline in terms of a generic metric combining aspects such as success rate, novelty, and diversity. Human expert evaluation on optimized molecules shows that 60% of top molecules obtained from our methods are deemed successful.

NeurIPS Conference 2021 Conference Paper

Multi-task Learning of Order-Consistent Causal Graphs

• Xinshi Chen
• Haoran Sun
• Caleb Ellington
• Eric Xing
• Le Song

We consider the problem of discovering $K$ related Gaussian directed acyclic graphs (DAGs), where the involved graph structures share a consistent causal order and sparse unions of supports. Under the multi-task learning setting, we propose a $l_1/l_2$-regularized maximum likelihood estimator (MLE) for learning $K$ linear structural equation models. We theoretically show that the joint estimator, by leveraging data across related tasks, can achieve a better sample complexity for recovering the causal order (or topological order) than separate estimations. Moreover, the joint estimator is able to recover non-identifiable DAGs, by estimating them together with some identifiable DAGs. Lastly, our analysis also shows the consistency of union support recovery of the structures. To allow practical implementation, we design a continuous optimization problem whose optimizer is the same as the joint estimator and can be approximated efficiently by an iterative algorithm. We validate the theoretical analysis and the effectiveness of the joint estimator in experiments.

NeurIPS Conference 2021 Conference Paper

RoMA: Robust Model Adaptation for Offline Model-based Optimization

• Sihyun Yu
• Sungsoo Ahn
• Le Song
• Jinwoo Shin

We consider the problem of searching an input maximizing a black-box objective function given a static dataset of input-output queries. A popular approach to solving this problem is maintaining a proxy model, e. g. , a deep neural network (DNN), that approximates the true objective function. Here, the main challenge is how to avoid adversarially optimized inputs during the search, i. e. , the inputs where the DNN highly overestimates the true objective function. To handle the issue, we propose a new framework, coined robust model adaptation (RoMA), based on gradient-based optimization of inputs over the DNN. Specifically, it consists of two steps: (a) a pre-training strategy to robustly train the proxy model and (b) a novel adaptation procedure of the proxy model to have robust estimates for a specific set of candidate solutions. At a high level, our scheme utilizes the local smoothness prior to overcome the brittleness of the DNN. Experiments under various tasks show the effectiveness of RoMA compared with previous methods, obtaining state-of-the-art results, e. g. , RoMA outperforms all at 4 out of 6 tasks and achieves runner-up results at the remaining tasks.

NeurIPS Conference 2021 Conference Paper

Scallop: From Probabilistic Deductive Databases to Scalable Differentiable Reasoning

• Jiani Huang
• Ziyang Li
• Binghong Chen
• Karan Samel
• Mayur Naik
• Le Song
• Xujie Si

Deep learning and symbolic reasoning are complementary techniques for an intelligent system. However, principled combinations of these techniques have limited scalability, rendering them ill-suited for real-world applications. We propose Scallop, a system that builds upon probabilistic deductive databases, to bridge this gap. The key insight underlying Scallop is a provenance framework that introduces a tunable parameter to specify the level of reasoning granularity. Scallop thereby i) generalizes exact probabilistic reasoning, ii) asymptotically reduces computational cost, and iii) provides relative accuracy guarantees. On a suite of tasks that involve mathematical and logical reasoning, Scallop scales significantly better without sacrificing accuracy compared to DeepProbLog, a principled neural logic programming approach. We also create and evaluate on a real-world Visual Question Answering (VQA) benchmark that requires multi-hop reasoning. Scallop outperforms two VQA-tailored models, a Neural Module Networks based and a transformer based model, by 12. 42% and 21. 66% respectively.

AAAI Conference 2020 Conference Paper

Accelerating Primal Solution Findings for Mixed Integer Programs Based on Solution Prediction

• Jian-Ya Ding
• Chao Zhang
• Lei Shen
• Shengyin Li
• Bing Wang
• Yinghui Xu
• Le Song

Mixed Integer Programming (MIP) is one of the most widely used modeling techniques for combinatorial optimization problems. In many applications, a similar MIP model is solved on a regular basis, maintaining remarkable similarities in model structures and solution appearances but differing in formulation coefficients. This offers the opportunity for machine learning methods to explore the correlations between model structures and the resulting solution values. To address this issue, we propose to represent a MIP instance using a tripartite graph, based on which a Graph Convolutional Network (GCN) is constructed to predict solution values for binary variables. The predicted solutions are used to generate a local branching type cut which can be either treated as a global (invalid) inequality in the formulation resulting in a heuristic approach to solve the MIP, or as a root branching rule resulting in an exact approach. Computational evaluations on 8 distinct types of MIP problems show that the proposed framework improves the primal solution finding performance significantly on a state-of-the-art open-source MIP solver.

ICRA Conference 2020 Conference Paper

Are We Ready for Service Robots? The OpenLORIS-Scene Datasets for Lifelong SLAM

• Xuesong Shi
• Dongjiang Li
• Pengpeng Zhao 0005
• Qinbin Tian
• Yuxin Tian
• Qiwei Long
• Chunhao Zhu
• Jingwei Song

Service robots should be able to operate autonomously in dynamic and daily changing environments over an extended period of time. While Simultaneous Localization And Mapping (SLAM) is one of the most fundamental problems for robotic autonomy, most existing SLAM works are evaluated with data sequences that are recorded in a short period of time. In real-world deployment, there can be out-of-sight scene changes caused by both natural factors and human activities. For example, in home scenarios, most objects may be movable, replaceable or deformable, and the visual features of the same place may be significantly different in some successive days. Such out-of-sight dynamics pose great challenges to the robustness of pose estimation, and hence a robot’s long-term deployment and operation. To differentiate the forementioned problem from the conventional works which are usually evaluated in a static setting in a single run, the term lifelong SLAM is used here to address SLAM problems in an ever-changing environment over a long period of time. To accelerate lifelong SLAM research, we release the OpenLORIS-Scene datasets. The data are collected in real-world indoor scenes, for multiple times in each place to include scene changes in real life. We also design benchmarking metrics for lifelong SLAM, with which the robustness and accuracy of pose estimation are evaluated separately. The datasets and benchmark are available online at lifelong-robotic-vision.github.io/dataset/scene.

NeurIPS Conference 2020 Conference Paper

Bandit Samplers for Training Graph Neural Networks

• Ziqi Liu
• Zhengwei Wu
• Zhiqiang Zhang
• Jun Zhou
• Shuang Yang
• Le Song
• Yuan Qi

Several sampling algorithms with variance reduction have been proposed for accelerating the training of Graph Convolution Networks (GCNs). However, due to the intractable computation of optimal sampling distribution, these sampling algorithms are suboptimal for GCNs and are not applicable to more general graph neural networks (GNNs) where the message aggregator contains learned weights rather than fixed weights, such as Graph Attention Networks (GAT). The fundamental reason is that the embeddings of the neighbors or learned weights involved in the optimal sampling distribution are \emph{changing} during the training and \emph{not known a priori}, but only \emph{partially observed} when sampled, thus making the derivation of an optimal variance reduced samplers non-trivial. In this paper, we formulate the optimization of the sampling variance as an adversary bandit problem, where the rewards are related to the node embeddings and learned weights, and can vary constantly. Thus a good sampler needs to acquire variance information about more neighbors (exploration) while at the same time optimizing the immediate sampling variance (exploit). We theoretically show that our algorithm asymptotically approaches the optimal variance within a factor of 3. We show the efficiency and effectiveness of our approach on multiple datasets.

AAAI Conference 2020 Conference Paper

Cost-Effective Incentive Allocation via Structured Counterfactual Inference

• Romain Lopez
• Chenchen Li
• Xiang Yan
• Junwu Xiong
• Michael Jordan
• Yuan Qi
• Le Song

We address a practical problem ubiquitous in modern marketing campaigns, in which a central agent tries to learn a policy for allocating strategic financial incentives to customers and observes only bandit feedback. In contrast to traditional policy optimization frameworks, we take into account the additional reward structure and budget constraints common in this setting, and develop a new two-step method for solving this constrained counterfactual policy optimization problem. Our method first casts the reward estimation problem as a domain adaptation problem with supplementary structure, and then subsequently uses the estimators for optimizing the policy with constraints. We also establish theoretical error bounds for our estimation procedure and we empirically show that the approach leads to significant improvement on both synthetic and real datasets.

ICLR Conference 2020 Conference Paper

Double Neural Counterfactual Regret Minimization

• Hui Li 0061
• Kailiang Hu
• Shaohua Zhang
• Yuan (Alan) Qi
• Le Song

Counterfactual regret minimization (CFR) is a fundamental and effective technique for solving Imperfect Information Games (IIG). However, the original CFR algorithm only works for discrete states and action spaces, and the resulting strategy is maintained as a tabular representation. Such tabular representation limits the method from being directly applied to large games. In this paper, we propose a double neural representation for the IIGs, where one neural network represents the cumulative regret, and the other represents the average strategy. Such neural representations allow us to avoid manual game abstraction and carry out end-to-end optimization. To make the learning efficient, we also developed several novel techniques including a robust sampling method and a mini-batch Monte Carlo Counterfactual Regret Minimization (MCCFR) method, which may be of independent interests. Empirically, on games tractable to tabular approaches, neural strategies trained with our algorithm converge comparably to their tabular counterparts, and significantly outperform those based on deep reinforcement learning. On extremely large games with billions of decision nodes, our approach achieved strong performance while using hundreds of times less memory than the tabular CFR. On head-to-head matches of hands-up no-limit texas hold'em, our neural agent beat the strong agent ABS-CFR by $9.8\pm4.1$ chips per game. It's a successful application of neural CFR in large games.

ICLR Conference 2020 Conference Paper

Efficient Probabilistic Logic Reasoning with Graph Neural Networks

• Yuyu Zhang
• Xinshi Chen
• Yuan Yang
• Arun Ramamurthy
• Bo Li
• Yuan (Alan) Qi
• Le Song

Markov Logic Networks (MLNs), which elegantly combine logic rules and probabilistic graphical models, can be used to address many knowledge graph problems. However, inference in MLN is computationally intensive, making the industrial-scale application of MLN very difficult. In recent years, graph neural networks (GNNs) have emerged as efficient and effective tools for large-scale graph problems. Nevertheless, GNNs do not explicitly incorporate prior logic rules into the models, and may require many labeled examples for a target task. In this paper, we explore the combination of MLNs and GNNs, and use graph neural networks for variational inference in MLN. We propose a GNN variant, named ExpressGNN, which strikes a nice balance between the representation power and the simplicity of the model. Our extensive experiments on several benchmark datasets demonstrate that ExpressGNN leads to effective and efficient probabilistic logic reasoning.

ICLR Conference 2020 Conference Paper

GLAD: Learning Sparse Graph Recovery

• Harsh Shrivastava 0001
• Xinshi Chen
• Binghong Chen
• Guanghui Lan
• Srinivas Aluru
• Han Liu 0001
• Le Song

Recovering sparse conditional independence graphs from data is a fundamental problem in machine learning with wide applications. A popular formulation of the problem is an $\ell_1$ regularized maximum likelihood estimation. Many convex optimization algorithms have been designed to solve this formulation to recover the graph structure. Recently, there is a surge of interest to learn algorithms directly based on data, and in this case, learn to map empirical covariance to the sparse precision matrix. However, it is a challenging task in this case, since the symmetric positive definiteness (SPD) and sparsity of the matrix are not easy to enforce in learned algorithms, and a direct mapping from data to precision matrix may contain many parameters. We propose a deep learning architecture, GLAD, which uses an Alternating Minimization (AM) algorithm as our model inductive bias, and learns the model parameters via supervised learning. We show that GLAD learns a very compact and effective model for recovering sparse graphs from data.

ICLR Conference 2020 Conference Paper

Hoppity: Learning Graph Transformations to Detect and Fix Bugs in Programs

• Elizabeth Dinella
• Hanjun Dai
• Ziyang Li 0002
• Mayur Naik
• Le Song
• Ke Wang 0022

We present a learning-based approach to detect and fix a broad range of bugs in Javascript programs. We frame the problem in terms of learning a sequence of graph transformations: given a buggy program modeled by a graph structure, our model makes a sequence of predictions including the position of bug nodes and corresponding graph edits to produce a fix. Unlike previous works that use deep neural networks, our approach targets bugs that are more complex and semantic in nature (i.e.~bugs that require adding or deleting statements to fix). We have realized our approach in a tool called HOPPITY. By training on 290,715 Javascript code change commits on Github, HOPPITY correctly detects and fixes bugs in 9,490 out of 36,361 programs in an end-to-end fashion. Given the bug location and type of the fix, HOPPITY also outperforms the baseline approach by a wide margin.

ICLR Conference 2020 Conference Paper

Learn to Explain Efficiently via Neural Logic Inductive Learning

• Yuan Yang
• Le Song

The capability of making interpretable and self-explanatory decisions is essential for developing responsible machine learning systems. In this work, we study the learning to explain the problem in the scope of inductive logic programming (ILP). We propose Neural Logic Inductive Learning (NLIL), an efficient differentiable ILP framework that learns first-order logic rules that can explain the patterns in the data. In experiments, compared with the state-of-the-art models, we find NLIL is able to search for rules that are x10 times longer while remaining x3 times faster. We also show that NLIL can scale to large image datasets, i.e. Visual Genome, with 1M entities.

ICLR Conference 2020 Conference Paper

Learning to Plan in High Dimensions via Neural Exploration-Exploitation Trees

• Binghong Chen
• Bo Dai 0001
• Qinjie Lin
• Guo Ye
• Han Liu 0001
• Le Song

We propose a meta path planning algorithm named \emph{Neural Exploration-Exploitation Trees~(NEXT)} for learning from prior experience for solving new path planning problems in high dimensional continuous state and action spaces. Compared to more classical sampling-based methods like RRT, our approach achieves much better sample efficiency in high-dimensions and can benefit from prior experience of planning in similar environments. More specifically, NEXT exploits a novel neural architecture which can learn promising search directions from problem structures. The learned prior is then integrated into a UCB-type algorithm to achieve an online balance between \emph{exploration} and \emph{exploitation} when solving a new problem. We conduct thorough experiments to show that NEXT accomplishes new planning problems with more compact search trees and significantly outperforms state-of-the-art methods on several benchmarks.

ICML Conference 2020 Conference Paper

Learning To Stop While Learning To Predict

• Xinshi Chen
• Hanjun Dai
• Yu Li 0006
• Xin Gao 0001
• Le Song

There is a recent surge of interest in designing deep architectures based on the update steps in traditional algorithms, or learning neural networks to improve and replace traditional algorithms. While traditional algorithms have certain stopping criteria for outputting results at different iterations, many algorithm-inspired deep models are restricted to a “fixed-depth” for all inputs. Similar to algorithms, the optimal depth of a deep architecture may be different for different input instances, either to avoid “over-thinking”, or because we want to compute less for operations converged already. In this paper, we tackle this varying depth problem using a steerable architecture, where a feed-forward deep model and a variational stopping policy are learned together to sequentially determine the optimal number of layers for each input instance. Training such architecture is very challenging. We provide a variational Bayes perspective and design a novel and effective training procedure which decomposes the task into an oracle model learning stage and an imitation stage. Experimentally, we show that the learned deep model along with the stopping policy improves the performances on a diverse set of tasks, including learning sparse recovery, few-shot meta learning, and computer vision tasks.

ICML Conference 2020 Conference Paper

Retro*: Learning Retrosynthetic Planning with Neural Guided A* Search

• Binghong Chen
• Chengtao Li
• Hanjun Dai
• Le Song

Retrosynthetic planning is a critical task in organic chemistry which identifies a series of reactions that can lead to the synthesis of a target product. The vast number of possible chemical transformations makes the size of the search space very big, and retrosynthetic planning is challenging even for experienced chemists. However, existing methods either require expensive return estimation by rollout with high variance, or optimize for search speed rather than the quality. In this paper, we propose Retro*, a neural-based A*-like algorithm that finds high-quality synthetic routes efficiently. It maintains the search as an AND-OR tree, and learns a neural search bias with off-policy data. Then guided by this neural network, it performs best-first search efficiently during new planning episodes. Experiments on benchmark USPTO datasets show that, our proposed method outperforms existing state-of-the-art with respect to both the success rate and solution quality, while being more efficient at the same time.

ICLR Conference 2020 Conference Paper

RNA Secondary Structure Prediction By Learning Unrolled Algorithms

• Xinshi Chen
• Yu Li 0006
• Ramzan Umarov
• Xin Gao 0001
• Le Song

In this paper, we propose an end-to-end deep learning model, called E2Efold, for RNA secondary structure prediction which can effectively take into account the inherent constraints in the problem. The key idea of E2Efold is to directly predict the RNA base-pairing matrix, and use an unrolled algorithm for constrained programming as the template for deep architectures to enforce constraints. With comprehensive experiments on benchmark datasets, we demonstrate the superior performance of E2Efold: it predicts significantly better structures compared to previous SOTA (especially for pseudoknotted structures), while being as efficient as the fastest algorithms in terms of inference time.

ICML Conference 2020 Conference Paper

Temporal Logic Point Processes

• Shuang Li 0002
• Lu Wang 0008
• Ruizhi Zhang
• Xiaofu Chang
• Xuqin Liu
• Yao Xie 0002
• Yuan (Alan) Qi
• Le Song

We propose a modeling framework for event data and aim to answer questions such as \emph{when} and \emph{why} the next event would happen. Our proposed model excels in small data regime with the ability to incorporate domain knowledge in terms of logic rules. We model the dynamics of the event starts and ends via intensity function with the structures informed by a set of first-order temporal logic rules. Using the softened representation of temporal relations, and a weighted combination of logic rules, our probabilistic model can deal with uncertainty in events. Furthermore, many well-known point processes (e. g. , Hawkes process, self-correcting point process) can be interpreted as special cases of our model given simple temporal logic rules. Our model, therefore, riches the family of point processes. We derive a maximum likelihood estimation procedure for our model and show that it can lead to accurate predictions when data are sparse and domain knowledge is critical.

NeurIPS Conference 2020 Conference Paper

The Devil is in the Detail: A Framework for Macroscopic Prediction via Microscopic Models

• Yingxiang Yang
• Negar Kiyavash
• Le Song
• Niao He

Macroscopic data aggregated from microscopic events are pervasive in machine learning, such as country-level COVID-19 infection statistics based on city-level data. Yet, many existing approaches for predicting macroscopic behavior only use aggregated data, leaving a large amount of fine-grained microscopic information unused. In this paper, we propose a principled optimization framework for macroscopic prediction by fitting microscopic models based on conditional stochastic optimization. The framework leverages both macroscopic and microscopic information, and adapts to individual microscopic models involved in the aggregation. In addition, we propose efficient learning algorithms with convergence guarantees. In our experiments, we show that the proposed learning framework clearly outperforms other plug-in supervised learning approaches in real-world applications, including the prediction of daily infections of COVID-19 and medicare claims.

NeurIPS Conference 2020 Conference Paper

Understanding Deep Architecture with Reasoning Layer

• Xinshi Chen
• Yufei Zhang
• Christoph Reisinger
• Le Song

Recently, there is a surge of interest in combining deep learning models with reasoning in order to handle more sophisticated learning tasks. In many cases, a reasoning task can be solved by an iterative algorithm. This algorithm is often unrolled, truncated, and used as a specialized layer in the deep architecture, which can be trained end-to-end with other neural components. Although such hybrid deep architectures have led to many empirical successes, theoretical understandings of such architectures, especially the interplay between algorithm layers and other neural layers, remains largely unexplored. In this paper, we take an initial step toward an understanding of such hybrid deep architectures by showing that properties of the algorithm layers, such as convergence, stability and sensitivity, are intimately related to the approximation and generalization abilities of the end-to-end model. Furthermore, our analysis matches nicely with experimental observations under various conditions, suggesting that our theory can provide useful guidelines for designing deep architectures with reasoning layers.

NeurIPS Conference 2019 Conference Paper

Exponential Family Estimation via Adversarial Dynamics Embedding

• Bo Dai
• Zhen Liu
• Hanjun Dai
• Niao He
• Arthur Gretton
• Le Song
• Dale Schuurmans

We present an efficient algorithm for maximum likelihood estimation (MLE) of exponential family models, with a general parametrization of the energy function that includes neural networks. We exploit the primal-dual view of the MLE with a kinetics augmented model to obtain an estimate associated with an adversarial dual sampler. To represent this sampler, we introduce a novel neural architecture, dynamics embedding, that generalizes Hamiltonian Monte-Carlo (HMC). The proposed approach inherits the flexibility of HMC while enabling tractable entropy estimation for the augmented model. By learning both a dual sampler and the primal model simultaneously, and sharing parameters between them, we obviate the requirement to design a separate sampling procedure once the model has been trained, leading to more effective learning. We show that many existing estimators, such as contrastive divergence, pseudo/composite-likelihood, score matching, minimum Stein discrepancy estimator, non-local contrastive objectives, noise-contrastive estimation, and minimum probability flow, are special cases of the proposed approach, each expressed by a different (fixed) dual sampler. An empirical investigation shows that adapting the sampler during MLE can significantly improve on state-of-the-art estimators.

ICML Conference 2019 Conference Paper

Generative Adversarial User Model for Reinforcement Learning Based Recommendation System

• Xinshi Chen
• Shuang Li 0002
• Hui Li 0061
• Shaohua Jiang
• Yuan (Alan) Qi
• Le Song

There are great interests as well as many challenges in applying reinforcement learning (RL) to recommendation systems. In this setting, an online user is the environment; neither the reward function nor the environment dynamics are clearly defined, making the application of RL challenging. In this paper, we propose a novel model-based reinforcement learning framework for recommendation systems, where we develop a generative adversarial network to imitate user behavior dynamics and learn her reward function. Using this user model as the simulation environment, we develop a novel Cascading DQN algorithm to obtain a combinatorial recommendation policy which can handle a large number of candidate items efficiently. In our experiments with real data, we show this generative adversarial user model can better explain user behavior than alternatives, and the RL policy based on this model can lead to a better long-term reward for the user and higher click rate for the system.

AAAI Conference 2019 Conference Paper

GeniePath: Graph Neural Networks with Adaptive Receptive Paths

• Ziqi Liu
• Chaochao Chen
• Longfei Li
• Jun Zhou
• Xiaolong Li
• Le Song
• Yuan Qi

In this paper, we propose a new online feature selection algorithm for streaming data. We aim to focus on the following two problems which remain unaddressed in literature. First, most existing online feature selection algorithms merely utilize the first-order information of the data streams, regardless of the fact that second-order information explores the correlations between features and significantly improves the performance. Second, most online feature selection algorithms are based on the balanced data presumption, which is not true in many real-world applications. For example, in fraud detection, the number of positive examples are much less than negative examples because most cases are not fraud. The balanced assumption will make the selected features biased towards the majority class and fail to detect the fraud cases. We propose an Adaptive Sparse Confidence-Weighted (ASCW) algorithm to solve the aforementioned two problems. We first introduce an `0-norm constraint into the second-order confidence-weighted (CW) learning for feature selection. Then the original loss is substituted with a cost-sensitive loss function to address the imbalanced data issue. Furthermore, our algorithm maintains multiple sparse CW learner with the corresponding cost vector to dynamically select an optimal cost. We theoretically enhance the theory of sparse CW learning and analyze the performance behavior in F-measure. Empirical studies show the superior performance over the stateof-the-art online learning methods in the online-batch setting.

IJCAI Conference 2019 Conference Paper

Large Scale Evolving Graphs with Burst Detection

• Yifeng Zhao
• Xiangwei Wang
• Hongxia Yang
• Le Song
• Jie Tang

Analyzing large-scale evolving graphs are crucial for understanding the dynamic and evolutionary nature of social networks. Most existing works focus on discovering repeated and consistent temporal patterns, however, such patterns cannot fully explain the complexity observed in dynamic networks. For example, in recommendation scenarios, users sometimes purchase products on a whim during a window shopping. Thus, in this paper, we design and implement a novel framework called BurstGraph which can capture both recurrent and consistent patterns, and especially unexpected bursty network changes. The performance of the proposed algorithm is demonstrated on both a simulated dataset and a world-leading E-Commerce company dataset, showing that they are able to discriminate recurrent events from extremely bursty events in terms of action propensity.

AAAI Conference 2019 Conference Paper

Latent Dirichlet Allocation for Internet Price War

• Chenchen Li
• Xiang Yan
• Xiaotie Deng
• Yuan Qi
• Wei Chu
• Le Song
• Junlong Qiao
• Jianshan He

Current Internet market makers are facing an intense competitive environment, where personalized price reductions or discounted coupons are provided by their peers to attract more customers. Much investment is spent to catch up with each other’s competitors but participants in such a price cut war are often incapable of winning due to their lack of information about others’ strategies or customers’ preference. We formalize the problem as a stochastic game with imperfect and incomplete information and develop a variant of Latent Dirichlet Allocation (LDA) to infer latent variables under the current market environment, which represents preferences of customers and strategies of competitors. Tests on simulated experiments and an open dataset for real data show that, by subsuming all available market information of the market maker’s competitors, our model exhibits a significant improvement for understanding the market environment and finding the best response strategies in the Internet price war. Our work marks the first successful learning method to infer latent information in the environment of price war by the LDA modeling, and sets an example for related competitive applications to follow.

NeurIPS Conference 2019 Conference Paper

Meta Architecture Search

• Albert Shaw
• Wei Wei
• Weiyang Liu
• Le Song
• Bo Dai

Neural Architecture Search (NAS) has been quite successful in constructing state-of-the-art models on a variety of tasks. Unfortunately, the computational cost can make it difficult to scale. In this paper, we make the first attempt to study Meta Architecture Search which aims at learning a task-agnostic representation that can be used to speed up the process of architecture search on a large number of tasks. We propose the Bayesian Meta Architecture SEarch (BASE) framework which takes advantage of a Bayesian formulation of the architecture search problem to learn over an entire set of tasks simultaneously. We show that on Imagenet classification, we can find a model that achieves 25. 7% top-1 error and 8. 1% top-5 error by adapting the architecture in less than an hour from an 8 GPU days pretrained meta-network. By learning a good prior for NAS, our method dramatically decreases the required computation cost while achieving comparable performance to current state-of-the-art methods - even finding competitive models for unseen datasets with very quick adaptation. We believe our framework will open up new possibilities for efficient and massively scalable architecture search research across multiple tasks.

NeurIPS Conference 2019 Conference Paper

Neural Similarity Learning

• Weiyang Liu
• Zhen Liu
• James Rehg
• Le Song

Inner product-based convolution has been the founding stone of convolutional neural networks (CNNs), enabling end-to-end learning of visual representation. By generalizing inner product with a bilinear matrix, we propose the neural similarity which serves as a learnable parametric similarity measure for CNNs. Neural similarity naturally generalizes the convolution and enhances flexibility. Further, we consider the neural similarity learning (NSL) in order to learn the neural similarity adaptively from training data. Specifically, we propose two different ways of learning the neural similarity: static NSL and dynamic NSL. Interestingly, dynamic neural similarity makes the CNN become a dynamic inference network. By regularizing the bilinear matrix, NSL can be viewed as learning the shape of kernel and the similarity measure simultaneously. We further justify the effectiveness of NSL with a theoretical viewpoint. Most importantly, NSL shows promising performance in visual recognition and few-shot learning, validating the superiority of NSL over the inner product-based convolution counterparts.

ICML Conference 2019 Conference Paper

Particle Flow Bayes' Rule

• Xinshi Chen
• Hanjun Dai
• Le Song

We present a particle flow realization of Bayes’ rule, where an ODE-based neural operator is used to transport particles from a prior to its posterior after a new observation. We prove that such an ODE operator exists. Its neural parameterization can be trained in a meta-learning framework, allowing this operator to reason about the effect of an individual observation on the posterior, and thus generalize across different priors, observations and to sequential Bayesian inference. We demonstrated the generalization ability of our particle flow Bayes operator in several canonical and high dimensional examples.

NeurIPS Conference 2019 Conference Paper

Retrosynthesis Prediction with Conditional Graph Logic Network

• Hanjun Dai
• Chengtao Li
• Connor Coley
• Bo Dai
• Le Song

Retrosynthesis is one of the fundamental problems in organic chemistry. The task is to identify reactants that can be used to synthesize a specified product molecule. Recently, computer-aided retrosynthesis is finding renewed interest from both chemistry and computer science communities. Most existing approaches rely on template-based models that define subgraph matching rules, but whether or not a chemical reaction can proceed is not defined by hard decision rules. In this work, we propose a new approach to this task using the Conditional Graph Logic Network, a conditional graphical model built upon graph neural networks that learns when rules from reaction templates should be applied, implicitly considering whether the resulting reaction would be both chemically feasible and strategic. We also propose an efficient hierarchical sampling to alleviate the computation cost. While achieving a significant improvement of 8. 2% over current state-of-the-art methods on the benchmark dataset, our model also offers interpretations for the prediction.

NeurIPS Conference 2019 Conference Paper

Value Propagation for Decentralized Networked Deep Multi-agent Reinforcement Learning

• Chao Qu
• Shie Mannor
• Huan Xu
• Yuan Qi
• Le Song
• Junwu Xiong

We consider the networked multi-agent reinforcement learning (MARL) problem in a fully decentralized setting, where agents learn to coordinate to achieve joint success. This problem is widely encountered in many areas including traffic control, distributed control, and smart grids. We assume each agent is located at a node of a communication network and can exchange information only with its neighbors. Using softmax temporal consistency, we derive a primal-dual decentralized optimization method and obtain a principled and data-efficient iterative algorithm named {\em value propagation}. We prove a non-asymptotic convergence rate of $\mathcal{O}(1/T)$ with nonlinear function approximation. To the best of our knowledge, it is the first MARL algorithm with a convergence guarantee in the control, off-policy, non-linear function approximation, fully decentralized setting.

ICML Conference 2018 Conference Paper

Adversarial Attack on Graph Structured Data

• Hanjun Dai
• Hui Li
• Tian Tian 0001
• Xin Huang
• Lin Wang
• Jun Zhu 0001
• Le Song

Deep learning on graph structures has shown exciting results in various applications. However, few attentions have been paid to the robustness of such models, in contrast to numerous research work for image or text adversarial attack and defense. In this paper, we focus on the adversarial attacks that fool deep learning models by modifying the combinatorial structure of data. We first propose a reinforcement learning based attack method that learns the generalizable attack policy, while only requiring prediction labels from the target classifier. We further propose attack methods based on genetic algorithms and gradient descent in the scenario where additional prediction confidence or gradients are available. We use both synthetic and real-world data to show that, a family of Graph Neural Network models are vulnerable to these attacks, in both graph-level and node-level classification tasks. We also show such attacks can be used to diagnose the learned classifiers.

NeurIPS Conference 2018 Conference Paper

Coupled Variational Bayes via Optimization Embedding

• Bo Dai
• Hanjun Dai
• Niao He
• Weiyang Liu
• Zhen Liu
• Jianshu Chen
• Lin Xiao
• Le Song

Variational inference plays a vital role in learning graphical models, especially on large-scale datasets. Much of its success depends on a proper choice of auxiliary distribution class for posterior approximation. However, how to pursue an auxiliary distribution class that achieves both good approximation ability and computation efficiency remains a core challenge. In this paper, we proposed coupled variational Bayes which exploits the primal-dual view of the ELBO with the variational distribution class generated by an optimization procedure, which is termed optimization embedding. This flexible function class couples the variational distribution with the original parameters in the graphical models, allowing end-to-end learning of the graphical models by back-propagation through the variational distribution. Theoretically, we establish an interesting connection to gradient flow and demonstrate the extreme flexibility of this implicit distribution family in the limit sense. Empirically, we demonstrate the effectiveness of the proposed method on multiple graphical models with either continuous or discrete latent variables comparing to state-of-the-art methods.

AAAI Conference 2018 Conference Paper

Deep Semi-Random Features for Nonlinear Function Approximation

• Kenji Kawaguchi
• Bo Xie
• Le Song

We propose semi-random features for nonlinear function approximation. The flexibility of semi-random feature lies between the fully adjustable units in deep learning and the random features used in kernel methods. For one hidden layer models with semi-random features, we prove with no unrealistic assumptions that the model classes contain an arbitrarily good function as the width increases (universality), and despite non-convexity, we can find such a good function (optimization theory) that generalizes to unseen new data (generalization bound). For deep models, with no unrealistic assumptions, we prove universal approximation ability, a lower bound on approximation error, a partial optimization guarantee, and a generalization bound. Depending on the problems, the generalization bound of deep semi-random features can be exponentially better than the known bounds of deep ReLU nets; our generalization error bound can be independent of the depth, the number of trainable weights as well as the input dimensionality. In experiments, we show that semi-random features can match the performance of neural networks by using slightly more units, and it outperforms random features by using significantly fewer units. Moreover, we introduce a new implicit ensemble method by using semi-random features.

AAAI Conference 2018 Conference Paper

Learning Conditional Generative Models for Temporal Point Processes

• Shuai Xiao
• Hongteng Xu
• Junchi Yan
• Mehrdad Farajtabar
• Xiaokang Yang
• Le Song
• Hongyuan Zha

Estimating the future event sequence conditioned on current observations is a long-standing and challenging task in temporal analysis. On one hand for many real-world problems the underlying dynamics can be very complex and often unknown. This renders the traditional parametric point process models often fail to fit the data for their limited capacity. On the other hand, long-term prediction suffers from the problem of bias exposure where the error accumulates and propagates to future prediction. Our new model builds upon the sequence to sequence (seq2seq) prediction network. Compared with parametric point process models, its modeling capacity is higher and has better flexibility for fitting real-world data. The main novelty of the paper is to mitigate the second challenge by introducing the likelihood-free loss based on Wasserstein distance between point processes, besides negative maximum likelihood loss used in the traditional seq2seq model. Wasserstein distance, unlike KL divergence i. e. MLE loss, is sensitive to the underlying geometry between samples and can robustly enforce close geometry structure between them. This technique is proven able to improve the vanilla seq2seq model by a notable margin on various tasks.

NeurIPS Conference 2018 Conference Paper

Learning Loop Invariants for Program Verification

• Xujie Si
• Hanjun Dai
• Mukund Raghothaman
• Mayur Naik
• Le Song

A fundamental problem in program verification concerns inferring loop invariants. The problem is undecidable and even practical instances are challenging. Inspired by how human experts construct loop invariants, we propose a reasoning framework Code2Inv that constructs the solution by multi-step decision making and querying an external program graph memory block. By training with reinforcement learning, Code2Inv captures rich program features and avoids the need for ground truth solutions as supervision. Compared to previous learning tasks in domains with graph-structured data, it addresses unique challenges, such as a binary objective function and an extremely sparse reward that is given by an automated theorem prover only after the complete loop invariant is proposed. We evaluate Code2Inv on a suite of 133 benchmark problems and compare it to three state-of-the-art systems. It solves 106 problems compared to 73 by a stochastic search-based system, 77 by a heuristic search-based system, and 100 by a decision tree learning-based system. Moreover, the strategy learned can be generalized to new programs: compared to solving new instances from scratch, the pre-trained agent is more sample efficient in finding solutions.

ICML Conference 2018 Conference Paper

Learning Steady-States of Iterative Algorithms over Graphs

• Hanjun Dai
• Zornitsa Kozareva
• Bo Dai 0001
• Alexander J. Smola
• Le Song

Many graph analytics problems can be solved via iterative algorithms where the solutions are often characterized by a set of steady-state conditions. Different algorithms respect to different set of fixed point constraints, so instead of using these traditional algorithms, can we learn an algorithm which can obtain the same steady-state solutions automatically from examples, in an effective and scalable way? How to represent the meta learner for such algorithm and how to carry out the learning? In this paper, we propose an embedding representation for iterative algorithms over graphs, and design a learning method which alternates between updating the embeddings and projecting them onto the steady-state constraints. We demonstrate the effectiveness of our framework using a few commonly used graph algorithms, and show that in some cases, the learned algorithm can handle graphs with more than 100, 000, 000 nodes in a single machine.

NeurIPS Conference 2018 Conference Paper

Learning Temporal Point Processes via Reinforcement Learning

• Shuang Li
• Shuai Xiao
• Shixiang Zhu
• Nan Du
• Yao Xie
• Le Song

Social goods, such as healthcare, smart city, and information networks, often produce ordered event data in continuous time. The generative processes of these event data can be very complex, requiring flexible models to capture their dynamics. Temporal point processes offer an elegant framework for modeling event data without discretizing the time. However, the existing maximum-likelihood-estimation (MLE) learning paradigm requires hand-crafting the intensity function beforehand and cannot directly monitor the goodness-of-fit of the estimated model in the process of training. To alleviate the risk of model-misspecification in MLE, we propose to generate samples from the generative model and monitor the quality of the samples in the process of training until the samples and the real data are indistinguishable. We take inspiration from reinforcement learning (RL) and treat the generation of each event as the action taken by a stochastic policy. We parameterize the policy as a flexible recurrent neural network and gradually improve the policy to mimic the observed event distribution. Since the reward function is unknown in this setting, we uncover an analytic and nonparametric form of the reward function using an inverse reinforcement learning formulation. This new RL framework allows us to derive an efficient policy gradient algorithm for learning flexible point process models, and we show that it performs well in both synthetic and real data.

ICML Conference 2018 Conference Paper

Learning to Explain: An Information-Theoretic Perspective on Model Interpretation

• Jianbo Chen
• Le Song
• Martin J. Wainwright
• Michael I. Jordan

We introduce instancewise feature selection as a methodology for model interpretation. Our method is based on learning a function to extract a subset of features that are most informative for each given example. This feature selector is trained to maximize the mutual information between selected features and the response variable, where the conditional distribution of the response variable given the input is the model to be explained. We develop an efficient variational approximation to the mutual information, and show the effectiveness of our method on a variety of synthetic and real data sets using both quantitative metrics and human evaluation.

NeurIPS Conference 2018 Conference Paper

Learning towards Minimum Hyperspherical Energy

• Weiyang Liu
• Rongmei Lin
• Zhen Liu
• Lixin Liu
• Zhiding Yu
• Bo Dai
• Le Song

Neural networks are a powerful class of nonlinear functions that can be trained end-to-end on various applications. While the over-parametrization nature in many neural networks renders the ability to fit complex functions and the strong representation power to handle challenging tasks, it also leads to highly correlated neurons that can hurt the generalization ability and incur unnecessary computation cost. As a result, how to regularize the network to avoid undesired representation redundancy becomes an important issue. To this end, we draw inspiration from a well-known problem in physics -- Thomson problem, where one seeks to find a state that distributes N electrons on a unit sphere as evenly as possible with minimum potential energy. In light of this intuition, we reduce the redundancy regularization problem to generic energy minimization, and propose a minimum hyperspherical energy (MHE) objective as generic regularization for neural networks. We also propose a few novel variants of MHE, and provide some insights from a theoretical point of view. Finally, we apply neural networks with MHE regularization to several challenging tasks. Extensive experiments demonstrate the effectiveness of our intuition, by showing the superior performance with MHE regularization.

ICML Conference 2018 Conference Paper

SBEED: Convergent Reinforcement Learning with Nonlinear Function Approximation

• Bo Dai 0001
• Albert E. Shaw
• Lihong Li 0001
• Lin Xiao
• Niao He
• Zhen Liu 0019
• Jianshu Chen
• Le Song

When function approximation is used, solving the Bellman optimality equation with stability guarantees has remained a major open problem in reinforcement learning for decades. The fundamental difficulty is that the Bellman operator may become an expansion in general, resulting in oscillating and even divergent behavior of popular algorithms like Q-learning. In this paper, we revisit the Bellman equation, and reformulate it into a novel primal-dual optimization problem using Nesterov’s smoothing technique and the Legendre-Fenchel transformation. We then develop a new algorithm, called Smoothed Bellman Error Embedding, to solve this optimization problem where any differentiable function class may be used. We provide what we believe to be the first convergence guarantee for general nonlinear function approximation, and analyze the algorithm’s sample complexity. Empirically, our algorithm compares favorably to state-of-the-art baselines in several benchmark control problems.

ICML Conference 2018 Conference Paper

Stochastic Training of Graph Convolutional Networks with Variance Reduction

• Jianfei Chen 0001
• Jun Zhu 0001
• Le Song

Graph convolutional networks (GCNs) are powerful deep neural networks for graph-structured data. However, GCN computes the representation of a node recursively from its neighbors, making the receptive field size grow exponentially with the number of layers. Previous attempts on reducing the receptive field size by subsampling neighbors do not have convergence guarantee, and their receptive field size per node is still in the order of hundreds. In this paper, we develop control variate based algorithms with new theoretical guarantee to converge to a local optimum of GCN regardless of the neighbor sampling size. Empirical results show that our algorithms enjoy similar convergence rate and model quality with the exact algorithm using only two neighbors per node. The running time of our algorithms on a large Reddit dataset is only one seventh of previous neighbor sampling algorithms.

ICML Conference 2018 Conference Paper

Towards Black-box Iterative Machine Teaching

• Weiyang Liu
• Bo Dai 0001
• Xingguo Li
• Zhen Liu 0019
• James M. Rehg
• Le Song

In this paper, we make an important step towards the black-box machine teaching by considering the cross-space machine teaching, where the teacher and the learner use different feature representations and the teacher can not fully observe the learner’s model. In such scenario, we study how the teacher is still able to teach the learner to achieve faster convergence rate than the traditional passive learning. We propose an active teacher model that can actively query the learner (i. e. , make the learner take exams) for estimating the learner’s status and provably guide the learner to achieve faster convergence. The sample complexities for both teaching and query are provided. In the experiments, we compare the proposed active teacher with the omniscient teacher and verify the effectiveness of the active teacher model.

AAAI Conference 2018 Conference Paper

Variational Reasoning for Question Answering With Knowledge Graph

• Yuyu Zhang
• Hanjun Dai
• Zornitsa Kozareva
• Alexander Smola
• Le Song

Knowledge graph (KG) is known to be helpful for the task of question answering (QA), since it provides well-structured relational information between entities, and allows one to further infer indirect facts. However, it is challenging to build QA systems which can learn to reason over knowledge graphs based on question-answer pairs alone. First, when people ask questions, their expressions are noisy (for example, typos in texts, or variations in pronunciations), which is non-trivial for the QA system to match those mentioned entities to the knowledge graph. Second, many questions require multi-hop logic reasoning over the knowledge graph to retrieve the answers. To address these challenges, we propose a novel and unified deep learning architecture, and an end-to-end variational learning algorithm which can handle noise in questions, and learn multi-hop reasoning simultaneously. Our method achieves state-of-the-art performance on a recent benchmark dataset in the literature. We also derive a series of new benchmark datasets, including questions for multi-hop reasoning, questions paraphrased by neural translation model, and questions in human voice. Our method yields very promising results on all these challenging datasets.

JMLR Journal 2017 Journal Article

COEVOLVE: A Joint Point Process Model for Information Diffusion and Network Evolution

• Mehrdad Farajtabar
• Yichen Wang
• Manuel Gomez-Rodriguez
• Shuang Li
• Hongyuan Zha
• Le Song

Information diffusion in online social networks is affected by the underlying network topology, but it also has the power to change it. Online users are constantly creating new links when exposed to new information sources, and in turn these links are alternating the way information spreads. However, these two highly intertwined stochastic processes, information diffusion and network evolution, have been predominantly studied separately, ignoring their co-evolutionary dynamics. We propose a temporal point process model, Coevolve, for such joint dynamics, allowing the intensity of one process to be modulated by that of the other. This model allows us to efficiently simulate interleaved diffusion and network events, and generate traces obeying common diffusion and network patterns observed in real-world networks such as Twitter. Furthermore, we also develop a convex optimization framework to learn the parameters of the model from historical diffusion and network evolution traces. We experimented with both synthetic data and data gathered from Twitter, and show that our model provides a good fit to the data as well as more accurate predictions than alternatives. [abs] [ pdf ][ bib ] &copy JMLR 2017. ( edit, beta )

NeurIPS Conference 2017 Conference Paper

Deep Hyperspherical Learning

• Weiyang Liu
• Yan-Ming Zhang
• Xingguo Li
• Zhiding Yu
• Bo Dai
• Tuo Zhao
• Le Song

Convolution as inner product has been the founding basis of convolutional neural networks (CNNs) and the key to end-to-end visual representation learning. Benefiting from deeper architectures, recent CNNs have demonstrated increasingly strong representation abilities. Despite such improvement, the increased depth and larger parameter space have also led to challenges in properly training a network. In light of such challenges, we propose hyperspherical convolution (SphereConv), a novel learning framework that gives angular representations on hyperspheres. We introduce SphereNet, deep hyperspherical convolution networks that are distinct from conventional inner product based convolutional networks. In particular, SphereNet adopts SphereConv as its basic convolution operator and is supervised by generalized angular softmax loss - a natural loss formulation under SphereConv. We show that SphereNet can effectively encode discriminative representation and alleviate training difficulty, leading to easier optimization, faster convergence and comparable (even better) classification accuracy over convolutional counterparts. We also provide some theoretical insights for the advantages of learning on hyperspheres. In addition, we introduce the learnable SphereConv, i. e. , a natural improvement over prefixed SphereConv, and SphereNorm, i. e. , hyperspherical learning as a normalization method. Experiments have verified our conclusions.

ICML Conference 2017 Conference Paper

Fake News Mitigation via Point Process Based Intervention

• Mehrdad Farajtabar
• Jiachen Yang
• Xiaojing Ye
• Huan Xu
• Rakshit S. Trivedi
• Elias B. Khalil
• Shuang Li 0002
• Le Song

We propose the first multistage intervention framework that tackles fake news in social networks by combining reinforcement learning with a point process network activity model. The spread of fake news and mitigation events within the network is modeled by a multivariate Hawkes process with additional exogenous control terms. By choosing a feature representation of states, defining mitigation actions and constructing reward functions to measure the effectiveness of mitigation activities, we map the problem of fake news mitigation into the reinforcement learning framework. We develop a policy iteration method unique to the multivariate networked point process, with the goal of optimizing the actions for maximal reward under budget constraints. Our method shows promising performance in real-time intervention experiments on a Twitter network to mitigate a surrogate fake news campaign, and outperforms alternatives on synthetic datasets.

ICML Conference 2017 Conference Paper

Iterative Machine Teaching

• Weiyang Liu
• Bo Dai 0001
• Ahmad Humayun
• Charlene Tay
• Chen Yu 0001
• Linda B. Smith
• James M. Rehg
• Le Song

In this paper, we consider the problem of machine teaching, the inverse problem of machine learning. Different from traditional machine teaching which views the learners as batch algorithms, we study a new paradigm where the learner uses an iterative algorithm and a teacher can feed examples sequentially and intelligently based on the current performance of the learner. We show that the teaching complexity in the iterative case is very different from that in the batch case. Instead of constructing a minimal training set for learners, our iterative machine teaching focuses on achieving fast convergence in the learner model. Depending on the level of information the teacher has from the learner model, we design teaching algorithms which can provably reduce the number of teaching examples and achieve faster convergence than learning without teachers. We also validate our theoretical findings with extensive experiments on different data distribution and real image datasets.

ICML Conference 2017 Conference Paper

Know-Evolve: Deep Temporal Reasoning for Dynamic Knowledge Graphs

• Rakshit S. Trivedi
• Hanjun Dai
• Yichen Wang 0001
• Le Song

The availability of large scale event data with time stamps has given rise to dynamically evolving knowledge graphs that contain temporal information for each edge. Reasoning over time in such dynamic knowledge graphs is not yet well understood. To this end, we present Know-Evolve, a novel deep evolutionary knowledge network that learns non-linearly evolving entity representations over time. The occurrence of a fact (edge) is modeled as a multivariate point process whose intensity function is modulated by the score for that fact computed based on the learned entity embeddings. We demonstrate significantly improved performance over various relational learning approaches on two large scale real-world datasets. Further, our method effectively predicts occurrence or recurrence time of a fact which is novel compared to prior reasoning approaches in multi-relational setting.

NeurIPS Conference 2017 Conference Paper

Learning Combinatorial Optimization Algorithms over Graphs

• Elias Khalil
• Hanjun Dai
• Yuyu Zhang
• Bistra Dilkina
• Le Song

The design of good heuristics or approximation algorithms for NP-hard combinatorial optimization problems often requires significant specialized knowledge and trial-and-error. Can we automate this challenging, tedious process, and learn the algorithms instead? In many real-world applications, it is typically the case that the same optimization problem is solved again and again on a regular basis, maintaining the same problem structure but differing in the data. This provides an opportunity for learning heuristic algorithms that exploit the structure of such recurring problems. In this paper, we propose a unique combination of reinforcement learning and graph embedding to address this challenge. The learned greedy policy behaves like a meta-algorithm that incrementally constructs a solution, and the action is determined by the output of a graph embedding network capturing the current state of the solution. We show that our framework can be applied to a diverse range of optimization problems over graphs, and learns effective algorithms for the Minimum Vertex Cover, Maximum Cut and Traveling Salesman problems.

NeurIPS Conference 2017 Conference Paper

On the Complexity of Learning Neural Networks

• Le Song
• Santosh Vempala
• John Wilmes
• Bo Xie

The stunning empirical successes of neural networks currently lack rigorous theoretical explanation. What form would such an explanation take, in the face of existing complexity-theoretic lower bounds? A first step might be to show that data generated by neural networks with a single hidden layer, smooth activation functions and benign input distributions can be learned efficiently. We demonstrate here a comprehensive lower bound ruling out this possibility: for a wide class of activation functions (including all currently used), and inputs drawn from any logconcave distribution, there is a family of one-hidden-layer functions whose output is a sum gate that are hard to learn in a precise sense: any statistical query algorithm (which includes all known variants of stochastic gradient descent with any loss function) needs an exponential number of queries even using tolerance inversely proportional to the input dimensionality. Moreover, this hard family of functions is realizable with a small (sublinear in dimension) number of activation units in the single hidden layer. The lower bound is also robust to small perturbations of the true weights. Systematic experiments illustrate a phase transition in the training error as predicted by the analysis.

NeurIPS Conference 2017 Conference Paper

Predicting User Activity Level In Point Processes With Mass Transport Equation

• Yichen Wang
• Xiaojing Ye
• Hongyuan Zha
• Le Song

Point processes are powerful tools to model user activities and have a plethora of applications in social sciences. Predicting user activities based on point processes is a central problem. However, existing works are mostly problem specific, use heuristics, or simplify the stochastic nature of point processes. In this paper, we propose a framework that provides an unbiased estimator of the probability mass function of point processes. In particular, we design a key reformulation of the prediction problem, and further derive a differential-difference equation to compute a conditional probability mass function. Our framework is applicable to general point processes and prediction tasks, and achieves superb predictive and efficiency performance in diverse real-world applications compared to state-of-arts.

JMLR Journal 2017 Journal Article

Scalable Influence Maximization for Multiple Products in Continuous-Time Diffusion Networks

• Nan Du
• Yingyu Liang
• Maria-Florina Balcan
• Manuel Gomez-Rodriguez
• Hongyuan Zha
• Le Song

A typical viral marketing model identifies influential users in a social network to maximize a single product adoption assuming unlimited user attention, campaign budgets, and time. In reality, multiple products need campaigns, users have limited attention, convincing users incurs costs, and advertisers have limited budgets and expect the adoptions to be maximized soon. Facing these user, monetary, and timing constraints, we formulate the problem as a submodular maximization task in a continuous-time diffusion model under the intersection of one matroid and multiple knapsack constraints. We propose a randomized algorithm estimating the user influence (Partial results in the paper on influence estimation have been published in a conference paper: Nan Du, Le Song, Manuel Gomez-Rodriguez, and Hongyuan Zha. Scalable influence estimation in continuous time diffusion networks. In Advances in Neural Information Processing Systems 26, 2013.) in a network ($|\mathcal{V}|$ nodes, $|\mathcal{E}|$ edges) to an accuracy of $\epsilon$ with $n=\mathcal{O}(1/\epsilon^2)$ randomizations and $\tilde{\mathcal{O}}(n|\mathcal{E}|+n|\mathcal{V}|)$ computations. By exploiting the influence estimation algorithm as a subroutine, we develop an adaptive threshold greedy algorithm achieving an approximation factor $k_a/(2+2 k)$ of the optimal when $k_a$ out of the $k$ knapsack constraints are active. Extensive experiments on networks of millions of nodes demonstrate that the proposed algorithms achieve the state-of- the-art in terms of effectiveness and scalability. [abs] [ pdf ][ bib ] &copy JMLR 2017. ( edit, beta )

ICML Conference 2017 Conference Paper

Stochastic Generative Hashing

• Bo Dai 0001
• Ruiqi Guo
• Sanjiv Kumar
• Niao He
• Le Song

Learning-based binary hashing has become a powerful paradigm for fast search and retrieval in massive databases. However, due to the requirement of discrete outputs for the hash functions, learning such functions is known to be very challenging. In addition, the objective functions adopted by existing hashing techniques are mostly chosen heuristically. In this paper, we propose a novel generative approach to learn hash functions through Minimum Description Length principle such that the learned hash codes maximally compress the dataset and can also be used to regenerate the inputs. We also develop an efficient learning algorithm based on the stochastic distributional gradient, which avoids the notorious difficulty caused by binary output constraints, to jointly optimize the parameters of the hash function and the associated generative model. Extensive experiments on a variety of large-scale datasets show that the proposed method achieves better retrieval results than the existing state-of-the-art methods.

ICML Conference 2017 Conference Paper

Variational Policy for Guiding Point Processes

• Yichen Wang 0001
• Grady Williams
• Evangelos A. Theodorou
• Le Song

Temporal point processes have been widely applied to model event sequence data generated by online users. In this paper, we consider the problem of how to design the optimal control policy for point processes, such that the stochastic system driven by the point process is steered to a target state. In particular, we exploit the key insight to view the stochastic optimal control problem from the perspective of optimal measure and variational inference. We further propose a convex optimization framework and an efficient algorithm to update the policy adaptively to the current system state. Experiments on synthetic and real-world data show that our algorithm can steer the user activities much more accurately and efficiently than other stochastic control methods.

NeurIPS Conference 2017 Conference Paper

Wasserstein Learning of Deep Generative Point Process Models

• Shuai Xiao
• Mehrdad Farajtabar
• Xiaojing Ye
• Junchi Yan
• Le Song
• Hongyuan Zha

Point processes are becoming very popular in modeling asynchronous sequential data due to their sound mathematical foundation and strength in modeling a variety of real-world phenomena. Currently, they are often characterized via intensity function which limits model's expressiveness due to unrealistic assumptions on its parametric form used in practice. Furthermore, they are learned via maximum likelihood approach which is prone to failure in multi-modal distributions of sequences. In this paper, we propose an intensity-free approach for point processes modeling that transforms nuisance processes to a target one. Furthermore, we train the model using a likelihood-free leveraging Wasserstein distance between point processes. Experiments on various synthetic and real-world data substantiate the superiority of the proposed point process model over conventional ones.

NeurIPS Conference 2016 Conference Paper

Coevolutionary Latent Feature Processes for Continuous-Time User-Item Interactions

• Yichen Wang
• Nan Du
• Rakshit Trivedi
• Le Song

Matching users to the right items at the right time is a fundamental task in recommendation systems. As users interact with different items over time, users' and items' feature may evolve and co-evolve over time. Traditional models based on static latent features or discretizing time into epochs can become ineffective for capturing the fine-grained temporal dynamics in the user-item interactions. We propose a coevolutionary latent feature process model that accurately captures the coevolving nature of users' and items' feature. To learn parameters, we design an efficient convex optimization algorithm with a novel low rank space sharing constraints. Extensive experiments on diverse real-world datasets demonstrate significant improvements in user behavior prediction compared to state-of-the-arts.

ICML Conference 2016 Conference Paper

Discriminative Embeddings of Latent Variable Models for Structured Data

• Hanjun Dai
• Bo Dai 0001
• Le Song

Kernel classifiers and regressors designed for structured data, such as sequences, trees and graphs, have significantly advanced a number of interdisciplinary areas such as computational biology and drug design. Typically, kernels are designed beforehand for a data type which either exploit statistics of the structures or make use of probabilistic generative models, and then a discriminative classifier is learned based on the kernels via convex optimization. However, such an elegant two-stage approach also limited kernel methods from scaling up to millions of data points, and exploiting discriminative information to learn feature representations. We propose, structure2vec, an effective and scalable approach for structured data representation based on the idea of embedding latent variable models into feature spaces, and learning such feature spaces using discriminative information. Interestingly, structure2vec extracts features by performing a sequence of function mappings in a way similar to graphical model inference procedures, such as mean field and belief propagation. In applications involving millions of data points, we showed that structure2vec runs 2 times faster, produces models which are 10, 000 times smaller, while at the same time achieving the state-of-the-art predictive performance.

JMLR Journal 2016 Journal Article

Estimating Diffusion Networks: Recovery Conditions, Sample Complexity and Soft-thresholding Algorithm

• Manuel Gomez-Rodriguez
• Le Song
• Hadi Daneshm
• Bernhard Schölkopf

Information spreads across social and technological networks, but often the network structures are hidden from us and we only observe the traces left by the diffusion processes, called cascades. Can we recover the hidden network structures from these observed cascades? What kind of cascades and how many cascades do we need? Are there some network structures which are more difficult than others to recover? Can we design efficient inference algorithms with provable guarantees? Despite the increasing availability of cascade data and methods for inferring networks from these data, a thorough theoretical understanding of the above questions remains largely unexplored in the literature. In this paper, we investigate the network structure inference problem for a general family of continuous- time diffusion models using an $\ell_1$-regularized likelihood maximization framework. We show that, as long as the cascade sampling process satisfies a natural incoherence condition, our framework can recover the correct network structure with high probability if we observe $O(d^3 \log N)$ cascades, where $d$ is the maximum number of parents of a node and $N$ is the total number of nodes. Moreover, we develop a simple and efficient soft-thresholding network inference algorithm which demonstrate the match between our theoretical prediction and empirical results. In practice, this new algorithm also outperforms other alternatives in terms of the accuracy of recovering hidden diffusion networks. [abs] [ pdf ][ bib ] &copy JMLR 2016. ( edit, beta )

ICML Conference 2016 Conference Paper

Isotonic Hawkes Processes

• Yichen Wang 0001
• Bo Xie 0002
• Nan Du 0002
• Le Song

Hawkes processes are powerful tools for modeling the mutual-excitation phenomena commonly observed in event data from a variety of domains, such as social networks, quantitative finance and healthcare records. The intensity function of a Hawkes process is typically assumed to be linear in the sum of triggering kernels, rendering it inadequate to capture nonlinear effects present in real-world data. To address this shortcoming, we propose an Isotonic-Hawkes process whose intensity function is modulated by an additional nonlinear link function. We also developed a novel iterative algorithm which learns both the nonlinear link function and other parameters provably. We showed that Isotonic-Hawkes processes can fit a variety of nonlinear patterns which cannot be captured by conventional Hawkes processes, and achieve superior empirical performance in real world applications.

AAAI Conference 2016 Conference Paper

Learning to Branch in Mixed Integer Programming

• Elias Khalil
• Pierre Le Bodic
• Le Song
• George Nemhauser
• Bistra Dilkina

The design of strategies for branching in Mixed Integer Programming (MIP) is guided by cycles of parameter tuning and offline experimentation on an extremely heterogeneous testbed, using the average performance. Once devised, these strategies (and their parameter settings) are essentially input-agnostic. To address these issues, we propose a machine learning (ML) framework for variable branching in MIP. Our method observes the decisions made by Strong Branching (SB), a time-consuming strategy that produces small search trees, collecting features that characterize the candidate branching variables at each node of the tree. Based on the collected data, we learn an easy-to-evaluate surrogate function that mimics the SB strategy, by means of solving a learning-to-rank problem, common in ML. The learned ranking function is then used for branching. The learning is instance-specific, and is performed on-the-fly while executing a branch-and-bound search to solve the instance. Experiments on benchmark instances indicate that our method produces significantly smaller search trees than existing heuristics, and is competitive with a state-of-the-art commercial solver.

NeurIPS Conference 2016 Conference Paper

Multistage Campaigning in Social Networks

• Mehrdad Farajtabar
• Xiaojing Ye
• Sahar Harati
• Le Song
• Hongyuan Zha

We consider control problems for multi-stage campaigning over social networks. The dynamic programming framework is employed to balance the high present reward and large penalty on low future outcome in the presence of extensive uncertainties. In particular, we establish theoretical foundations of optimal campaigning over social networks where the user activities are modeled as a multivariate Hawkes process, and we derive a time dependent linear relation between the intensity of exogenous events and several commonly used objective functions of campaigning. We further develop a convex dynamic programming framework for determining the optimal intervention policy that prescribes the required level of external drive at each stage for the desired campaigning result. Experiments on both synthetic data and the real-world MemeTracker dataset show that our algorithm can steer the user activities for optimal campaigning much more accurately than baselines.

NeurIPS Conference 2015 Conference Paper

COEVOLVE: A Joint Point Process Model for Information Diffusion and Network Co-evolution

• Mehrdad Farajtabar
• Yichen Wang
• Manuel Gomez Rodriguez
• Shuang Li
• Hongyuan Zha
• Le Song

Information diffusion in online social networks is affected by the underlying network topology, but it also has the power to change it. Online users are constantly creating new links when exposed to new information sources, and in turn these links are alternating the way information spreads. However, these two highly intertwined stochastic processes, information diffusion and network evolution, have been predominantly studied separately, ignoring their co-evolutionary dynamics. We propose a temporal point process model, COEVOLVE, for such joint dynamics, allowing the intensity of one process to be modulated by that of the other. This model allows us to efficiently simulate interleaved diffusion and network events, and generate traces obeying common diffusion and network patterns observed in real-world networks. Furthermore, we also develop a convex optimization framework to learn the parameters of the model from historical diffusion and network evolution traces. We experimented with both synthetic data and data gathered from Twitter, and show that our model provides a good fit to the data as well as more accurate predictions than alternatives.

NeurIPS Conference 2015 Conference Paper

Efficient Learning of Continuous-Time Hidden Markov Models for Disease Progression

• Yu-Ying Liu
• Shuang Li
• Fuxin Li
• Le Song
• James Rehg

The Continuous-Time Hidden Markov Model (CT-HMM) is an attractive approach to modeling disease progression due to its ability to describe noisy observations arriving irregularly in time. However, the lack of an efficient parameter learning algorithm for CT-HMM restricts its use to very small models or requires unrealistic constraints on the state transitions. In this paper, we present the first complete characterization of efficient EM-based learning methods for CT-HMM models. We demonstrate that the learning problem consists of two challenges: the estimation of posterior state probabilities and the computation of end-state conditioned statistics. We solve the first challenge by reformulating the estimation problem in terms of an equivalent discrete time-inhomogeneous hidden Markov model. The second challenge is addressed by adapting three approaches from the continuous time Markov chain literature to the CT-HMM domain. We demonstrate the use of CT-HMMs with more than 100 states to visualize and predict disease progression using a glaucoma dataset and an Alzheimer's disease dataset.

UAI Conference 2015 Conference Paper

Learning Latent Variable Models by Improving Spectral Solutions with Exterior Point Method

• Amirreza Shaban
• Mehrdad Farajtabar
• Bo Xie 0002
• Le Song
• Byron Boots

Probabilistic latent-variable models are a fundamental tool in statistics and machine learning. Despite their widespread use, identifying the parameters of basic latent variable models continues to be an extremely challenging problem. Traditional maximum likelihood-based learning algorithms find valid parameters, but suffer from high computational cost, slow convergence, and local optima. In contrast, recently developed spectral algorithms are computationally efficient and provide strong statistical guarantees, but are not guaranteed to find valid parameters. In this work, we introduce a two-stage learning algorithm for latent variable models. We first use a spectral method of moments algorithm to find a solution that is close to the optimal solution but not necessarily in the valid set of model parameters. We then incrementally refine the solution via an exterior point method until a local optima that is arbitrarily near the valid set of parameters is found. We perform several experiments on synthetic and real-world data and show that our approach is more accurate than previous work, especially when training data is limited.

NeurIPS Conference 2015 Conference Paper

M-Statistic for Kernel Change-Point Detection

• Shuang Li
• Yao Xie
• Hanjun Dai
• Le Song

Detecting the emergence of an abrupt change-point is a classic problem in statistics and machine learning. Kernel-based nonparametric statistics have been proposed for this task which make fewer assumptions on the distributions than traditional parametric approach. However, none of the existing kernel statistics has provided a computationally efficient way to characterize the extremal behavior of the statistic. Such characterization is crucial for setting the detection threshold, to control the significance level in the offline case as well as the average run length in the online case. In this paper we propose two related computationally efficient M-statistics for kernel-based change-point detection when the amount of background data is large. A novel theoretical result of the paper is the characterization of the tail probability of these statistics using a new technique based on change-of-measure. Such characterization provides us accurate detection thresholds for both offline and online cases in computationally efficient manner, without the need to resort to the more expensive simulations such as bootstrapping. We show that our methods perform well in both synthetic and real world data.

NeurIPS Conference 2015 Conference Paper

Scale Up Nonlinear Component Analysis with Doubly Stochastic Gradients

• Bo Xie
• Yingyu Liang
• Le Song

Nonlinear component analysis such as kernel Principle Component Analysis (KPCA) and kernel Canonical Correlation Analysis (KCCA) are widely used in machine learning, statistics and data analysis, but they can not scale up to big datasets. Recent attempts have employed random feature approximations to convert the problem to the primal form for linear computational complexity. However, to obtain high quality solutions, the number of random features should be the same order of magnitude as the number of data points, making such approach not directly applicable to the regime with millions of data points. We propose a simple, computationally efficient, and memory friendly algorithm based on the ``doubly stochastic gradients'' to scale up a range of kernel nonlinear component analysis, such as kernel PCA, CCA and SVD. Despite the \emph{non-convex} nature of these problems, our method enjoys theoretical guarantees that it converges at the rate $\Otil(1/t)$ to the global optimum, even for the top $k$ eigen subspace. Unlike many alternatives, our algorithm does not require explicit orthogonalization, which is infeasible on big datasets. We demonstrate the effectiveness and scalability of our algorithm on large scale synthetic and real world datasets.

NeurIPS Conference 2015 Conference Paper

Time-Sensitive Recommendation From Recurrent User Activities

• Nan Du
• Yichen Wang
• Niao He
• Jimeng Sun
• Le Song

By making personalized suggestions, a recommender system is playing a crucial role in improving the engagement of users in modern web-services. However, most recommendation algorithms do not explicitly take into account the temporal behavior and the recurrent activities of users. Two central but less explored questions are how to recommend the most desirable item \emph{at the right moment}, and how to predict \emph{the next returning time} of a user to a service. To address these questions, we propose a novel framework which connects self-exciting point processes and low-rank models to capture the recurrent temporal patterns in a large collection of user-item consumption pairs. We show that the parameters of the model can be estimated via a convex optimization, and furthermore, we develop an efficient algorithm that maintains $O(1 / \epsilon)$ convergence rate, scales up to problems with millions of user-item pairs and thousands of millions of temporal events. Compared to other state-of-the-arts in both synthetic and real datasets, our model achieves superb predictive performance in the two time-sensitive recommendation questions. Finally, we point out that our formulation can incorporate other extra context information of users, such as profile, textual and spatial features.

NeurIPS Conference 2014 Conference Paper

Active Learning and Best-Response Dynamics

• Maria-Florina Balcan
• Christopher Berlind
• Avrim Blum
• Emma Cohen
• Kaushik Patnaik
• Le Song

We consider a setting in which low-power distributed sensors are each making highly noisy measurements of some unknown target function. A center wants to accurately learn this function by querying a small number of sensors, which ordinarily would be impossible due to the high noise rate. The question we address is whether local communication among sensors, together with natural best-response dynamics in an appropriately-defined game, can denoise the system without destroying the true signal and allow the center to succeed from only a small number of active queries. We prove positive (and negative) results on the denoising power of several natural dynamics, and also show experimentally that when combined with recent agnostic active learning algorithms, this process can achieve low error from very few queries, performing substantially better than active or passive learning without these denoising dynamics as well as passive learning with denoising.

ICML Conference 2014 Conference Paper

Estimating Diffusion Network Structures: Recovery Conditions, Sample Complexity & Soft-thresholding Algorithm

• Hadi Daneshmand
• Manuel Gomez Rodriguez
• Le Song
• Bernhard Schölkopf

Information spreads across social and technological networks, but often the network structures are hidden from us and we only observe the traces left by the diffusion processes, called cascades. Can we recover the hidden network structures from these observed cascades? What kind of cascades and how many cascades do we need? Are there some network structures which are more difficult than others to recover? Can we design efficient inference algorithms with provable guarantees? Despite the increasing availability of cascade data and methods for inferring networks from these data, a thorough theoretical understanding of the above questions remains largely unexplored in the literature. In this paper, we investigate the network structure inference problem for a general family of continuous-time diffusion models using an l1-regularized likelihood maximization framework. We show that, as long as the cascade sampling process satisfies a natural incoherence condition, our framework can recover the correct network structure with high probability if we observe O(d^3 log N) cascades, where d is the maximum number of parents of a node and N is the total number of nodes. Moreover, we develop a simple and efficient soft-thresholding inference algorithm, which we use to illustrate the consequences of our theoretical results, and show that our framework outperforms other alternatives in practice.

ICML Conference 2014 Conference Paper

Influence Function Learning in Information Diffusion Networks

• Nan Du 0002
• Yingyu Liang
• Maria-Florina Balcan
• Le Song

Can we learn the influence of a set of people in a social network from cascades of information diffusion? This question is often addressed by a two-stage approach: first learn a diffusion model, and then calculate the influence based on the learned model. Thus, the success of this approach relies heavily on the correctness of the diffusion model which is hard to verify for real world data. In this paper, we exploit the insight that the influence functions in many diffusion models are coverage functions, and propose a novel parameterization of such functions using a convex combination of random basis functions. Moreover, we propose an efficient maximum likelihood based algorithm to learn such functions directly from cascade data, and hence bypass the need to specify a particular diffusion model in advance. We provide both theoretical and empirical analysis for our approach, showing that the proposed approach can provably learn the influence function with low sample complexity, be robust to the unknown diffusion models, and significantly outperform existing approaches in both synthetic and real world data.

NeurIPS Conference 2014 Conference Paper

Learning Time-Varying Coverage Functions

• Nan Du
• Yingyu Liang
• Maria-Florina Balcan
• Le Song

Coverage functions are an important class of discrete functions that capture laws of diminishing returns. In this paper, we propose a new problem of learning time-varying coverage functions which arise naturally from applications in social network analysis, machine learning, and algorithmic game theory. We develop a novel parametrization of the time-varying coverage function by illustrating the connections with counting processes. We present an efficient algorithm to learn the parameters by maximum likelihood estimation, and provide a rigorous theoretic analysis of its sample complexity. Empirical experiments from information diffusion in social network analysis demonstrate that with few assumptions about the underlying diffusion process, our method performs significantly better than existing approaches on both synthetic and real world data.

ICML Conference 2014 Conference Paper

Least Squares Revisited: Scalable Approaches for Multi-class Prediction

• Alekh Agarwal
• Sham M. Kakade
• Nikos Karampatziakis
• Le Song
• Gregory Valiant

This work provides simple algorithms for multi-class (and multi-label) prediction in settings where both the number of examples n and the data dimension d are relatively large. These robust and parameter free algorithms are essentially iterative least-squares updates and very versatile both in theory and in practice. On the theoretical front, we present several variants with convergence guarantees. Owing to their effective use of second-order structure, these algorithms are substantially better than first-order methods in many practical scenarios. On the empirical side, we show how to scale our approach to high dimensional datasets, achieving dramatic computational speedups over popular optimization packages such as Liblinear and Vowpal Wabbit on standard datasets (MNIST and CIFAR-10), while attaining state-of-the-art accuracies.

ICML Conference 2014 Conference Paper

Nonparametric Estimation of Multi-View Latent Variable Models

• Le Song
• Anima Anandkumar
• Bo Dai 0001
• Bo Xie 0002

Spectral methods have greatly advanced the estimation of latent variable models, generating a sequence of novel and efficient algorithms with strong theoretical guarantees. However, current spectral algorithms are largely restricted to mixtures of discrete or Gaussian distributions. In this paper, we propose a kernel method for learning multi-view latent variable models, allowing each mixture component to be nonparametric and learned from data in an unsupervised fashion. The key idea of our method is to embed the joint distribution of a multi-view latent variable model into a reproducing kernel Hilbert space, and then the latent parameters are recovered using a robust tensor power method. We establish that the sample complexity for the proposed method is quadratic in the number of latent components and is a low order polynomial in the other relevant parameters. Thus, our nonparametric tensor approach to learning latent variable models enjoys good sample and computational efficiencies. As a special case of our framework, we also obtain a first unsupervised conditional density estimator of the kind with provable guarantees. In both synthetic and real world datasets, the nonparametric tensor power method compares favorably to EM algorithm and other spectral algorithms.

NeurIPS Conference 2014 Conference Paper

Scalable Kernel Methods via Doubly Stochastic Gradients

• Bo Dai
• Bo Xie
• Niao He
• Yingyu Liang
• Anant Raj
• Maria-Florina Balcan
• Le Song

The general perception is that kernel methods are not scalable, so neural nets become the choice for large-scale nonlinear learning problems. Have we tried hard enough for kernel methods? In this paper, we propose an approach that scales up kernel methods using a novel concept called ``doubly stochastic functional gradients''. Based on the fact that many kernel methods can be expressed as convex optimization problems, our approach solves the optimization problems by making two unbiased stochastic approximations to the functional gradient---one using random training points and another using random features associated with the kernel---and performing descent steps with this noisy functional gradient. Our algorithm is simple, need no commit to a preset number of random features, and allows the flexibility of the function class to grow as we see more incoming data in the streaming setting. We demonstrate that a function learned by this procedure after t iterations converges to the optimal function in the reproducing kernel Hilbert space in rate O(1/t), and achieves a generalization bound of O(1/\sqrt{t}). Our approach can readily scale kernel methods up to the regimes which are dominated by neural nets. We show competitive performances of our approach as compared to neural nets in datasets such as 2. 3 million energy materials from MolecularSpace, 8 million handwritten digits from MNIST, and 1 million photos from ImageNet using convolution features.

NeurIPS Conference 2014 Conference Paper

Shaping Social Activity by Incentivizing Users

• Mehrdad Farajtabar
• Nan Du
• Manuel Gomez Rodriguez
• Isabel Valera
• Hongyuan Zha
• Le Song

Events in an online social network can be categorized roughly into endogenous events, where users just respond to the actions of their neighbors within the network, or exogenous events, where users take actions due to drives external to the network. How much external drive should be provided to each user, such that the network activity can be steered towards a target state? In this paper, we model social events using multivariate Hawkes processes, which can capture both endogenous and exogenous event intensities, and derive a time dependent linear relation between the intensity of exogenous events and the overall network activity. Exploiting this connection, we develop a convex optimization framework for determining the required level of external drive in order for the network to reach a desired activity level. We experimented with event data gathered from Twitter, and show that our method can steer the activity of the network more accurately than alternatives.

ICML Conference 2013 Conference Paper

Hierarchical Tensor Decomposition of Latent Tree Graphical Models

• Le Song
• Mariya Ishteva
• Ankur P. Parikh
• Eric P. Xing
• Haesun Park

We approach the problem of estimating the parameters of a latent tree graphical model from a hierarchical tensor decomposition point of view. In this new view, the marginal probability table of the observed variables in a latent tree is treated as a tensor, and we show that: (i) the latent variables induce low rank structures in various matricizations of the tensor; (ii) this collection of low rank matricizations induce a hierarchical low rank decomposition of the tensor. Exploiting these properties, we derive an optimization problem for estimating the parameters of a latent tree graphical model, i. e. , hierarchical decomposion of a tensor which minimizes the Frobenius norm of the difference between the original tensor and its decomposition. When the latent tree graphical models are correctly specified, we show that a global optimum of the optimization problem can be obtained via a recursive decomposition algorithm. This algorithm recovers previous spectral algorithms for hidden Markov models (Hsu et al. , 2009; Foster et al. , 2012) and latent tree graphical models (Parikh et al. , 2011; Song et al. , 2011) as special cases, elucidating the global objective these algorithms are optimizing for. When the latent tree graphical models are misspecified, we derive a better decomposition based on our framework, and provide approximation guarantee for this new estimator. In both synthetic and real world data, this new estimator significantly improves over the-state-of-the-art.

JMLR Journal 2013 Journal Article

Kernel Bayes' Rule: Bayesian Inference with Positive Definite Kernels

• Kenji Fukumizu
• Le Song
• Arthur Gretton

A kernel method for realizing Bayes' rule is proposed, based on representations of probabilities in reproducing kernel Hilbert spaces. Probabilities are uniquely characterized by the mean of the canonical map to the RKHS. The prior and conditional probabilities are expressed in terms of RKHS functions of an empirical sample: no explicit parametric model is needed for these quantities. The posterior is likewise an RKHS mean of a weighted sample. The estimator for the expectation of a function of the posterior is derived, and rates of consistency are shown. Some representative applications of the kernel Bayes' rule are presented, including Bayesian computation without likelihood and filtering with a nonparametric state-space model. [abs] [ pdf ][ bib ] &copy JMLR 2013. ( edit, beta )

ICML Conference 2013 Conference Paper

Learning Triggering Kernels for Multi-dimensional Hawkes Processes

• Ke Zhou 0002
• Hongyuan Zha
• Le Song

How does the activity of one person affect that of another person? Does the strength of influence remain periodic or decay exponentially over time? In this paper, we study these critical questions in social network analysis quantitatively under the framework of multi-dimensional Hawkes processes. In particular, we focus on the nonparametric learning of the triggering kernels, and propose an algorithm \sf MMEL that combines the idea of decoupling the parameters through constructing a tight upper-bound of the objective function and application of Euler-Lagrange equations for optimization in infinite dimensional functional space. We show that the proposed method performs significantly better than alternatives in experiments on both synthetic and real world datasets.

NeurIPS Conference 2013 Conference Paper

Robust Low Rank Kernel Embeddings of Multivariate Distributions

• Le Song
• Bo Dai

Kernel embedding of distributions has led to many recent advances in machine learning. However, latent and low rank structures prevalent in real world distributions have rarely been taken into account in this setting. Furthermore, no prior work in kernel embedding literature has addressed the issue of robust embedding when the latent and low rank information are misspecified. In this paper, we propose a hierarchical low rank decomposition of kernels embeddings which can exploit such low rank structures in data while being robust to model misspecification. We also illustrate with empirical evidence that the estimated low rank embeddings lead to improved performance in density estimation.

NeurIPS Conference 2013 Conference Paper

Scalable Influence Estimation in Continuous-Time Diffusion Networks

• Nan Du
• Le Song
• Manuel Gomez Rodriguez
• Hongyuan Zha

If a piece of information is released from a media site, can it spread, in 1 month, to a million web pages? This influence estimation problem is very challenging since both the time-sensitive nature of the problem and the issue of scalability need to be addressed simultaneously. In this paper, we propose a randomized algorithm for influence estimation in continuous-time diffusion networks. Our algorithm can estimate the influence of every node in a network with $|\Vcal|$ nodes and $|\Ecal|$ edges to an accuracy of $\epsilon$ using $n=O(1/\epsilon^2)$ randomizations and up to logarithmic factors $O(n|\Ecal|+n|\Vcal|)$ computations. When used as a subroutine in a greedy influence maximization algorithm, our proposed method is guaranteed to find a set of nodes with an influence of at least $(1 - 1/e)\operatorname{OPT} - 2\epsilon$, where $\operatorname{OPT}$ is the optimal value. Experiments on both synthetic and real-world data show that the proposed method can easily scale up to networks of millions of nodes while significantly improves over previous state-of-the-arts in terms of the accuracy of the estimated influence and the quality of the selected nodes in maximizing the influence.

ICML Conference 2013 Conference Paper

Unfolding Latent Tree Structures using 4th Order Tensors

• Mariya Ishteva
• Haesun Park
• Le Song

Discovering the latent structure from many observed variables is an important yet challenging learning task. Existing approaches for discovering latent structures often require the unknown number of hidden states as an input. In this paper, we propose a quartet based approach which is agnostic to this number. The key contribution is a novel rank characterization of the tensor associated with the marginal distribution of a quartet. This characterization allows us to design a nuclear norm based test for resolving quartet relations. We then use the quartet test as a subroutine in a divide-and-conquer algorithm for recovering the latent tree structure. Under mild conditions, the algorithm is consistent and its error probability decays exponentially with increasing sample size. We demonstrate that the proposed approach compares favorably to alternatives. In a real world stock dataset, it also discovers meaningful groupings of variables, and produces a model that fits the data better.

UAI Conference 2012 Conference Paper

A Spectral Algorithm for Latent Junction Trees

• Ankur P. Parikh
• Le Song
• Mariya Ishteva
• Gabi Teodoru
• Eric P. Xing

Latent variable models are an elegant framework for capturing rich probabilistic dependencies in many applications. However, current approaches typically parametrize these models using conditional probability tables, and learning relies predominantly on local search heuristics such as Expectation Maximization. Using tensor algebra, we propose an alternative parameterization of latent variable models (where the model structures are junction trees) that still allows for computation of marginals among observed variables. While this novel representation leads to a moderate increase in the number of parameters for junction trees of low treewidth, it lets us design a local-minimum-free algorithm for learning this parameterization. The main computation of the algorithm involves only tensor operations and SVDs which can be orders of magnitude faster than EM algorithms for large datasets. To our knowledge, this is the first provably consistent parameter learning technique for a large class of low-treewidth latent graphical models beyond trees. We demonstrate the advantages of our method on synthetic and real datasets.

JMLR Journal 2012 Journal Article

Feature Selection via Dependence Maximization

• Le Song
• Alex Smola
• Arthur Gretton
• Justin Bedo
• Karsten Borgwardt

We introduce a framework for feature selection based on dependence maximization between the selected features and the labels of an estimation problem, using the Hilbert-Schmidt Independence Criterion. The key idea is that good features should be highly dependent on the labels. Our approach leads to a greedy procedure for feature selection. We show that a number of existing feature selectors are special cases of this framework. Experiments on both artificial and real-world data show that our feature selector works well in practice. [abs] [ pdf ][ bib ] &copy JMLR 2012. ( edit, beta )

NeurIPS Conference 2012 Conference Paper

Learning Networks of Heterogeneous Influence

• Nan Du
• Le Song
• Ming Yuan
• Alex Smola

Information, disease, and influence diffuse over networks of entities in both natural systems and human society. Analyzing these transmission networks plays an important role in understanding the diffusion processes and predicting events in the future. However, the underlying transmission networks are often hidden and incomplete, and we observe only the time stamps when cascades of events happen. In this paper, we attempt to address the challenging problem of uncovering the hidden network only from the cascades. The structure discovery problem is complicated by the fact that the influence among different entities in a network are heterogeneous, which can not be described by a simple parametric model. Therefore, we propose a kernel-based method which can capture a diverse range of different types of influence without any prior assumption. In both synthetic and real cascade data, we show that our model can better recover the underlying diffusion network and drastically improve the estimation of the influence functions between networked entities.

ICML Conference 2011 Conference Paper

A Spectral Algorithm for Latent Tree Graphical Models

• Ankur P. Parikh
• Le Song
• Eric P. Xing

Latent variable models are powerful tools for probabilistic modeling, and have been successfully applied to various domains, such as speech analysis and bioinformatics. However, parameter learning algorithms for latent variable models have predominantly relied on local search heuristics such as expectation maximization (EM). We propose a fast, local-minimum-free spectral algorithm for learning latent variable models with arbitrary tree topologies, and show that the joint distribution of the observed variables can be reconstructed from the marginals of triples of observed variables irrespective of the maximum degree of the tree. We demonstrate the performance of our spectral algorithm on synthetic and real datasets; for large training sizes, our algorithm performs comparable to or better than EM while being orders of magnitude faster.

NeurIPS Conference 2011 Conference Paper

Kernel Bayes' Rule

• Kenji Fukumizu
• Le Song
• Arthur Gretton

A nonparametric kernel-based method for realizing Bayes' rule is proposed, based on kernel representations of probabilities in reproducing kernel Hilbert spaces. The prior and conditional probabilities are expressed as empirical kernel mean and covariance operators, respectively, and the kernel mean of the posterior distribution is computed in the form of a weighted sample. The kernel Bayes' rule can be applied to a wide variety of Bayesian inference problems: we demonstrate Bayesian computation without likelihood, and filtering with a nonparametric state-space model. A consistency rate for the posterior estimate is established.

NeurIPS Conference 2011 Conference Paper

Kernel Embeddings of Latent Tree Graphical Models

• Le Song
• Eric Xing
• Ankur Parikh

Latent tree graphical models are natural tools for expressing long range and hierarchical dependencies among many variables which are common in computer vision, bioinformatics and natural language processing problems. However, existing models are largely restricted to discrete and Gaussian variables due to computational constraints; furthermore, algorithms for estimating the latent tree structure and learning the model parameters are largely restricted to heuristic local search. We present a method based on kernel embeddings of distributions for latent tree graphical models with continuous and non-Gaussian variables. Our method can recover the latent tree structures with provable guarantees and perform local-minimum free parameter learning and efficient inference. Experiments on simulated and real data show the advantage of our proposed approach.

NeurIPS Conference 2011 Conference Paper

Spectral Methods for Learning Multivariate Latent Tree Structure

• Animashree Anandkumar
• Kamalika Chaudhuri
• Daniel Hsu
• Sham Kakade
• Le Song
• Tong Zhang

This work considers the problem of learning the structure of multivariate linear tree models, which include a variety of directed tree graphical models with continuous, discrete, and mixed latent variables such as linear-Gaussian models, hidden Markov models, Gaussian mixture models, and Markov evolutionary trees. The setting is one where we only have samples from certain observed variables in the tree, and our goal is to estimate the tree structure (i. e. , the graph of how the underlying hidden variables are connected to each other and to the observed variables). We propose the Spectral Recursive Grouping algorithm, an efficient and simple bottom-up procedure for recovering the tree structure from independent samples of the observed variables. Our finite sample size bounds for exact recovery of the tree structure reveal certain natural dependencies on underlying statistical and structural properties of the underlying joint distribution. Furthermore, our sample complexity guarantees have no explicit dependence on the dimensionality of the observed variables, making the algorithm applicable to many high-dimensional settings. At the heart of our algorithm is a spectral quartet test for determining the relative topology of a quartet of variables from second-order statistics.

ICML Conference 2010 Conference Paper

Hilbert Space Embeddings of Hidden Markov Models

• Le Song
• Byron Boots
• Sajid M. Siddiqi
• Geoffrey J. Gordon
• Alexander J. Smola

ICML Conference 2009 Conference Paper

Dynamic mixed membership blockmodel for evolving networks

• Wenjie Fu 0002
• Le Song
• Eric P. Xing

In a dynamic social or biological environment, interactions between the underlying actors can undergo large and systematic changes. Each actor can assume multiple roles and their degrees of affiliation to these roles can also exhibit rich temporal phenomena. We propose a state space mixed membership stochastic blockmodel which can track across time the evolving roles of the actors. We also derive an efficient variational inference procedure for our model, and apply it to the Enron email networks, and rewiring gene regulatory networks of yeast. In both cases, our model reveals interesting dynamical roles of the actors.

ICML Conference 2009 Conference Paper

Hilbert space embeddings of conditional distributions with applications to dynamical systems

• Le Song
• Jonathan Huang
• Alexander J. Smola
• Kenji Fukumizu

In this paper, we extend the Hilbert space embedding approach to handle conditional distributions. We derive a kernel estimate for the conditional embedding, and show its connection to ordinary embeddings. Conditional embeddings largely extend our ability to manipulate distributions in Hilbert spaces, and as an example, we derive a nonparametric method for modeling dynamical systems where the belief state of the system is maintained as a conditional embedding. Our method is very general in terms of both the domains and the types of distributions that it can handle, and we demonstrate the effectiveness of our method in various dynamical systems. We expect that conditional embeddings will have wider applications beyond modeling dynamical systems.

NeurIPS Conference 2009 Conference Paper

Sparsistent Learning of Varying-coefficient Models with Structural Changes

• Mladen Kolar
• Le Song
• Eric Xing

To estimate the changing structure of a varying-coefficient varying-structure (VCVS) model remains an important and open problem in dynamic system modelling, which includes learning trajectories of stock prices, or uncovering the topology of an evolving gene network. In this paper, we investigate sparsistent learning of a sub-family of this model --- piecewise constant VCVS models. We analyze two main issues in this problem: inferring time points where structural changes occur and estimating model structure (i. e. , model selection) on each of the constant segments. We propose a two-stage adaptive procedure, which first identifies jump points of structural changes and then identifies relevant covariates to a response on each of the segments. We provide an asymptotic analysis of the procedure, showing that with the increasing sample size, number of structural changes, and number of variables, the true model can be consistently selected. We demonstrate the performance of the method on synthetic data and apply it to the brain computer interface dataset. We also consider how this applies to structure estimation of time-varying probabilistic graphical models.

NeurIPS Conference 2009 Conference Paper

Time-Varying Dynamic Bayesian Networks

• Le Song
• Mladen Kolar
• Eric Xing

Directed graphical models such as Bayesian networks are a favored formalism to model the dependency structures in complex multivariate systems such as those encountered in biology and neural sciences. When the system is undergoing dynamic transformation, often a temporally rewiring network is needed for capturing the dynamic causal influences between covariates. In this paper, we propose a time-varying dynamic Bayesian network (TV-DBN) for modeling the structurally varying directed dependency structures underlying non-stationary biological/neural time series. This is a challenging problem due the non-stationarity and sample scarcity of the time series. We present a kernel reweighted $\ell_1$ regularized auto-regressive procedure for learning the TV-DBN model. Our method enjoys nice properties such as computational efficiency and provable asymptotic consistency. Applying TV-DBN to time series measurements during yeast cell cycle and brain response to visual stimuli reveals interesting dynamics underlying the respective biological systems.

NeurIPS Conference 2008 Conference Paper

Kernel Measures of Independence for non-iid Data

• Xinhua Zhang
• Le Song
• Arthur Gretton
• Alex Smola

Many machine learning algorithms can be formulated in the framework of statistical independence such as the Hilbert Schmidt Independence Criterion. In this paper, we extend this criterion to deal with with structured and interdependent observations. This is achieved by modeling the structures using undirected graphical models and comparing the Hilbert space embeddings of distributions. We apply this new criterion to independent component analysis and sequence clustering.

NeurIPS Conference 2008 Conference Paper

Kernelized Sorting

• Novi Quadrianto
• Le Song
• Alex Smola

Object matching is a fundamental operation in data analysis. It typically requires the definition of a similarity measure between the classes of objects to be matched. Instead, we develop an approach which is able to perform matching by requiring a similarity measure only within each of the classes. This is achieved by maximizing the dependency between matched pairs of observations by means of the Hilbert Schmidt Independence Criterion. This problem can be cast as one of maximizing a quadratic assignment problem with special structure and we present a simple algorithm for finding a locally optimal solution.

ICML Conference 2008 Conference Paper

Tailoring density estimation via reproducing kernel moment matching

• Le Song
• Xinhua Zhang
• Alexander J. Smola
• Arthur Gretton
• Bernhard Schölkopf

ICML Conference 2007 Conference Paper

A dependence maximization view of clustering

• Le Song
• Alexander J. Smola
• Arthur Gretton
• Karsten M. Borgwardt

NeurIPS Conference 2007 Conference Paper

A Kernel Statistical Test of Independence

• Arthur Gretton
• Kenji Fukumizu
• Choon Teo
• Le Song
• Bernhard Schölkopf
• Alex Smola

Although kernel measures of independence have been widely applied in machine learning (notably in kernel ICA), there is as yet no method to determine whether they have detected statistically significant dependence. We provide a novel test of the independence hypothesis for one particular kernel independence measure, the Hilbert-Schmidt independence criterion (HSIC). The resulting test costs O(m2), where m is the sample size. We demonstrate that this test outperforms established contingency table and functional correlation-based tests, and that this advantage is greater for multivariate data. Finally, we show the HSIC test also applies to text (and to structured data more generally), for which no other independence test presently exists.

NeurIPS Conference 2007 Conference Paper

Colored Maximum Variance Unfolding

• Le Song
• Arthur Gretton
• Karsten Borgwardt
• Alex Smola

Maximum variance unfolding (MVU) is an effective heuristic for dimensionality reduction. It produces a low-dimensional representation of the data by maximiz- ing the variance of their embeddings while preserving the local distances of the original data. We show that MVU also optimizes a statistical dependence measure which aims to retain the identity of individual observations under the distance- preserving constraints. This general view allows us to design “colored” variants of MVU, which produce low-dimensional representations for a given task, e. g. subject to class labels or other side information.

ICML Conference 2007 Conference Paper

Supervised feature selection via dependence estimation

• Le Song
• Alexander J. Smola
• Arthur Gretton
• Karsten M. Borgwardt
• Justin Bedo

ICML Conference 2006 Conference Paper

Classifying EEG for brain-computer interfaces: learning optimal filters for dynamical system features

• Le Song
• Julien Epps

YNIMG Journal 2006 Journal Article

The ‘when’ and ‘where’ of perceiving signals of threat versus non-threat

• Leanne M. Williams
• Donna Palmer
• Belinda J. Liddell
• Le Song
• Evian Gordon

NeurIPS Conference 2005 Conference Paper

Phase Synchrony Rate for the Recognition of Motor Imagery in Brain-Computer Interface

• Le Song
• Evian Gordon
• Elly Gysels

Motor imagery attenuates EEG and rhythms over sensorimotor cortices. These amplitude changes are most successfully captured by the method of Common Spatial Patterns (CSP) and widely used in braincomputer interfaces (BCI). BCI methods based on amplitude information, however, have not incoporated the rich phase dynamics in the EEG rhythm. This study reports on a BCI method based on phase synchrony rate (SR). SR, computed from binarized phase locking value, describes the number of discrete synchronization events within a window. Statistical nonparametric tests show that SRs contain significant differences between 2 types of motor imageries. Classifiers trained on SRs consistently demonstrate satisfactory results for all 5 subjects. It is further observed that, for 3 subjects, phase is more discriminative than amplitude in the first 1. 5-2. 0 s, which suggests that phase has the potential to boost the information transfer rate in BCIs.