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Jiaming Xu

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19 papers

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AAAI Conference 2026 Conference Paper

From Imitation to Discrimination: Toward a Generalized Curriculum Advantage Mechanism Enhancing Cross-Domain Reasoning Tasks

Changpeng Yang
Jinyang Wu
Yuchen Liu
Shuai Zhang
Yang Li
Qiliang Liang
Hongzhen Wang
Shuai Nie

Reinforcement learning has emerged as a paradigm for post-training large language models, boosting their reasoning capabilities. Such approaches compute an advantage value for each sample, reflecting better or worse performance than expected, thereby yielding both positive and negative signals for training. However, existing approaches often mix them indiscriminately, especially in the early stages, leading to ambiguous guidance and limited gains. To address this issue, we propose CAPO (Curriculum Advantage Policy Optimization), an adaptive curriculum mechanism based on advantage signals. The proposed mechanism bootstraps imitation learning with positive-only advantage samples to establish robust foundations, and subsequently introduces negative signals to cultivate discriminative capabilities, thereby improving generalization across complex scenarios. Compatible with diverse optimization methods including GRPO, PPO, RLOO, and Reinforce++, our method consistently achieves stable and significant improvements in mathematical reasoning tasks, and further generalizes effectively to multimodal Graphical User Interface (GUI) reasoning scenarios, establishing itself as a versatile and robust optimization paradigm.

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AAAI Conference 2026 Conference Paper

MoSs: Mixture of Scales for Efficient High-Resolution Autoregressive Image Generation

Yaoxiu Lian
Hao Liang
Zhihong Gou
Yijia Zhang
Jiaming Xu
Guohao Dai
Ningyi Xu

Since next-scale prediction was introduced as a new paradigm for autoregressive image generation, it has attracted extensive research interest. By progressively increasing resolution in a draft-to-refinement process, next-scale prediction demonstrates great potential in both generation quality and efficiency. However, at high resolutions, this paradigm faces a fundamental challenge: token sequences grow quadratically and accumulate across multiple scales, resulting in a key performance bottleneck. Our systematic study uncovers two critical observations: (1) most image regions have stabilized during early drafting stages, making later refinement across the full-scale image token-inefficient; (2) different scales inherently trade off efficiency and fidelity, suggesting that adaptive token dispatch on different scales can focus resources where they yield the greatest quality gains. Motivated by these insights, we propose a training-free Mixture of Scales (MoSs) method for efficient high-resolution autoregressive image generation. MoSs breaks the strict causal dependency across scales in the final refinement steps by parallelizing scales of different resolutions, each responsible for a subset of spatial regions. A lightweight frequency-based token dispatcher analyzes the drafted image and assigns regions to the appropriate scale. The outputs are then composited over the draft to produce the final high-resolution image. The scale-mixture method exhibits remarkable efficiency with little impact on generation quality on various models. For instance, our implementation achieves 2.05-4.96x speedup on the transformer backbone, up to 85.62% KV cache reduction, incurring only 0.1-2.4% loss on GenEval quality, based on the state-of-the-art Infinity model.

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AAAI Conference 2026 Conference Paper

SpecDiff: Accelerating Diffusion Model Inference with Self-Speculation

Jiayi Pan
Jiaming Xu
Yongkang Zhou
Guohao Dai

Feature caching has recently emerged as a promising method for diffusion model acceleration. It effectively alleviates the inefficiency problem caused by high computational requirements by caching similar features in the inference process of the diffusion model. In this paper, we analyze existing feature caching methods from the perspective of information utilization, and point out that relying solely on historical information will lead to constrained accuracy and speed performance. And we propose a novel paradigm that introduces future information via self-speculation based on the information similarity at the same time step across different iteration times. Based on this paradigm, we present SpecDiff, a training-free multi-level feature caching strategy including a cached feature selection algorithm and a multi-level feature classification algorithm. (1) Feature selection algorithm based on self-speculative information. SpecDiff determines a dynamic importance score for each token based on self-speculative information and historical information, and performs cached feature selection through the importance score. (2) Multi-level feature classification algorithm based on feature importance scores.SpecDiff classifies tokens by leveraging the differences in feature importance scores and introduces a multi-level feature calculation strategy. Extensive experiments show that SpecDiff achieves average 2.80×, 2.74×, and 3.17× speedup with negligible quality loss in Stable Diffusion 3, 3.5, and FLUX compared to RFlow on NVIDIA A800-80GB GPU. By merging speculative and historical information, SpecDiff overcomes the speedup-accuracy trade-off bottleneck, pushing the Pareto frontier of speedup and accuracy in the efficient diffusion model inference.

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ICRA Conference 2025 Conference Paper

Learning Coordinated Bimanual Manipulation Policies Using State Diffusion and Inverse Dynamics Models

Haonan Chen
Jiaming Xu
Lily Sheng
Tianchen Ji
Shuijing Liu
Yunzhu Li
Katherine Driggs-Campbell

When performing tasks like laundry, humans naturally coordinate both hands to manipulate objects and anticipate how their actions will change the state of the clothes. However, achieving such coordination in robotics remains challenging due to the need to model object movement, predict future states, and generate precise bimanual actions. In this work, we address these challenges by infusing the predictive nature of human manipulation strategies into robot imitation learning. Specifically, we disentangle task-related state transitions from agent-specific inverse dynamics modeling to enable effective bimanual coordination. Using a demonstration dataset, we train a diffusion model to predict future states given historical observations, envisioning how the scene evolves. Then, we use an inverse dynamics model to compute robot actions that achieve the predicted states. Our key insight is that modeling object movement can help learning policies for bimanual coordination manipulation tasks. Evaluating our framework across diverse simulation and real-world manipulation setups, including multimodal goal configurations, bimanual manipulation, deformable objects, and multi-object setups, we find that it consistently outperforms state-of-the-art state-to-action mapping policies. Our method demonstrates a remarkable capacity to navigate multimodal goal configurations and action distributions, maintain stability across different control modes, and synthesize a broader range of behaviors than those present in the demonstration dataset.

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JMLR Journal 2024 Journal Article

Overparametrized Multi-layer Neural Networks: Uniform Concentration of Neural Tangent Kernel and Convergence of Stochastic Gradient Descent

Jiaming Xu
Hanjing Zhu

There have been exciting progresses in understanding the convergence of gradient descent (GD) and stochastic gradient descent (SGD) in overparameterized neural networks through the lens of neural tangent kernel (NTK). However, there remain two significant gaps between theory and practice. First, the existing convergence theory only takes into account the contribution of the NTK from the last hidden layer, while in practice the intermediate layers also play an instrumental role. Second, most existing works assume that the training data are provided a priori in a batch, while less attention has been paid to the important setting where the training data arrive in a stream. In this paper, we close these two gaps. We first show that with random initialization, the NTK function converges to some deterministic function uniformly for all layers as the number of neurons tends to infinity. Then we apply the uniform convergence result to further prove that the prediction error of multi-layer neural networks under SGD converges in expectation in the streaming data setting. A key ingredient in our proof is to show the number of activation patterns of an $L$-layer neural network with width $m$ is only polynomial in $m$ although there are $mL$ neurons in total. [abs] [ pdf ][ bib ] &copy JMLR 2024. ( edit, beta )

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JMLR Journal 2023 Journal Article

A Non-parametric View of FedAvg and FedProx:Beyond Stationary Points

Lili Su
Jiaming Xu
Pengkun Yang

Federated Learning (FL) is a promising decentralized learning framework and has great potentials in privacy preservation and in lowering the computation load at the cloud. Recent work showed that FedAvg and FedProx -- the two widely-adopted FL algorithms -- fail to reach the stationary points of the global optimization objective even for homogeneous linear regression problems. Further, it is concerned that the common model learned might not generalize well locally at all in the presence of heterogeneity. In this paper, we analyze the convergence and statistical efficiency of FedAvg and FedProx, addressing the above two concerns. Our analysis is based on the standard non-parametric regression in a reproducing kernel Hilbert space (RKHS), and allows for heterogeneous local data distributions and unbalanced local datasets. We prove that the estimation errors, measured in either the empirical norm or the RKHS norm, decay with a rate of $1/t$ in general and exponentially for finite-rank kernels. In certain heterogeneous settings, these upper bounds also imply that both FedAvg and FedProx achieve the optimal error rate. To further analytically quantify the impact of the heterogeneity at each client, we propose and characterize a novel notion-federation gain, defined as the reduction of the estimation error for a client to join the FL. We discover that when the data heterogeneity is moderate, a client with limited local data can benefit from a common model with a large federation gain. Two new insights introduced by considering the statistical aspect are: (1) requiring the standard bounded dissimilarity is pessimistic for the convergence analysis of FedAvg and FedProx; (2) despite inconsistency of stationary points, their limiting points are unbiased estimators of the underlying truth. Numerical experiments further corroborate our theoretical findings. [abs] [ pdf ][ bib ] &copy JMLR 2023. ( edit, beta )

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NeurIPS Conference 2022 Conference Paper

Global Convergence of Federated Learning for Mixed Regression

Lili Su
Jiaming Xu
Pengkun Yang

This paper studies the problem of model training under Federated Learning when clients exhibit cluster structure. We contextualize this problem in mixed regression, where each client has limited local data generated from one of $k$ unknown regression models. We design an algorithm that achieves global convergence from any initialization, and works even when local data volume is highly unbalanced -- there could exist clients that contain $O(1)$ data points only. Our algorithm first runs moment descent on a few anchor clients (each with $\tilde{\Omega}(k)$ data points) to obtain coarse model estimates. Then each client alternately estimates its cluster labels and refines the model estimates based on FedAvg or FedProx. A key innovation in our analysis is a uniform estimate on the clustering errors, which we prove by bounding the VC dimension of general polynomial concept classes based on the theory of algebraic geometry.

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JMLR Journal 2021 Journal Article

Graph Matching with Partially-Correct Seeds

Liren Yu
Jiaming Xu
Xiaojun Lin

Graph matching aims to find the latent vertex correspondence between two edge-correlated graphs and has found numerous applications across different fields. In this paper, we study a seeded graph matching problem, which assumes that a set of seeds, i.e., pre-mapped vertex-pairs, is given in advance. While most previous work requires all seeds to be correct, we focus on the setting where the seeds are partially correct. Specifically, consider two correlated graphs whose edges are sampled independently from a parent Erdos-Renyi graph $\mathcal{G}(n,p)$. A mapping between the vertices of the two graphs is provided as seeds, of which an unknown $\beta$ fraction is correct. We first analyze a simple algorithm that matches vertices based on the number of common seeds in the $1$-hop neighborhoods, and then further propose a new algorithm that uses seeds in the $2$-hop neighborhoods. We establish non-asymptotic performance guarantees of perfect matching for both $1$-hop and $2$-hop algorithms, showing that our new $2$-hop algorithm requires substantially fewer correct seeds than the $1$-hop algorithm when graphs are sparse. Moreover, by combining our new performance guarantees for the $1$-hop and $2$-hop algorithms, we attain the best-known results (in terms of the required fraction of correct seeds) across the entire range of graph sparsity and significantly improve the previous results when $p\ge n^{-5/6}$. For instance, when $p$ is a constant or $p=n^{-3/4}$, we show that only $\Omega(\sqrt{n\log n})$ correct seeds suffice for perfect matching, while the previously best-known results demand $\Omega(n)$ and $\Omega(n^{3/4}\log n)$ correct seeds, respectively. Numerical experiments corroborate our theoretical findings, demonstrating the superiority of our $2$-hop algorithm on a variety of synthetic and real graphs. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2021. ( edit, beta )

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AAAI Conference 2020 Conference Paper

DMRM: A Dual-Channel Multi-Hop Reasoning Model for Visual Dialog

Feilong Chen
Fandong Meng
Jiaming Xu
Peng Li
Bo Xu
Jie Zhou

Visual Dialog is a vision-language task that requires an AI agent to engage in a conversation with humans grounded in an image. It remains a challenging task since it requires the agent to fully understand a given question before making an appropriate response not only from the textual dialog history, but also from the visually-grounded information. While previous models typically leverage single-hop reasoning or single-channel reasoning to deal with this complex multimodal reasoning task, which is intuitively insufﬁcient. In this paper, we thus propose a novel and more powerful Dual-channel Multi-hop Reasoning Model for Visual Dialog, named DMRM. DMRM synchronously captures information from the dialog history and the image to enrich the semantic representation of the question by exploiting dual-channel reasoning. Speciﬁcally, DMRM maintains a dual channel to obtain the question- and history-aware image features and the question- and image-aware dialog history features by a mulithop reasoning process in each channel. Additionally, we also design an effective multimodal attention to further enhance the decoder to generate more accurate responses. Experimental results on the VisDial v0. 9 and v1. 0 datasets demonstrate that the proposed model is effective and outperforms compared models by a signiﬁcant margin.

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IJCAI Conference 2020 Conference Paper

LISNN: Improving Spiking Neural Networks with Lateral Interactions for Robust Object Recognition

Xiang Cheng
Yunzhe Hao
Jiaming Xu
Bo Xu

Spiking Neural Network (SNN) is considered more biologically plausible and energy-efficient on emerging neuromorphic hardware. Recently backpropagation algorithm has been utilized for training SNN, which allows SNN to go deeper and achieve higher performance. However, most existing SNN models for object recognition are mainly convolutional structures or fully-connected structures, which only have inter-layer connections, but no intra-layer connections. Inspired by Lateral Interactions in neuroscience, we propose a high-performance and noise-robust Spiking Neural Network (dubbed LISNN). Based on the convolutional SNN, we model the lateral interactions between spatially adjacent neurons and integrate it into the spiking neuron membrane potential formula, then build a multi-layer SNN on a popular deep learning framework, i. \, e. , PyTorch. We utilize the pseudo-derivative method to solve the non-differentiable problem when applying backpropagation to train LISNN and test LISNN on multiple standard datasets. Experimental results demonstrate that the proposed model can achieve competitive or better performance compared to current state-of-the-art spiking neural networks on MNIST, Fashion-MNIST, and N-MNIST datasets. Besides, thanks to lateral interactions, our model processes stronger noise-robustness than other SNN. Our work brings a biologically plausible mechanism into SNN, hoping that it can help us understand the visual information processing in the brain.

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NeurIPS Conference 2020 Conference Paper

Sequence to Multi-Sequence Learning via Conditional Chain Mapping for Mixture Signals

Jing Shi
Xuankai Chang
Pengcheng Guo
Shinji Watanabe
Yusuke Fujita
Jiaming Xu
Bo Xu
Lei Xie

Neural sequence-to-sequence models are well established for applications which can be cast as mapping a single input sequence into a single output sequence. In this work, we focus on one-to-many sequence transduction problems, such as extracting multiple sequential sources from a mixture sequence. We extend the standard sequence-to-sequence model to a conditional multi-sequence model, which explicitly models the relevance between multiple output sequences with the probabilistic chain rule. Based on this extension, our model can conditionally infer output sequences one-by-one by making use of both input and previously-estimated contextual output sequences. This model additionally has a simple and efficient stop criterion for the end of the transduction, making it able to infer the variable number of output sequences. We take speech data as a primary test field to evaluate our methods since the observed speech data is often composed of multiple sources due to the nature of the superposition principle of sound waves. Experiments on several different tasks including speech separation and multi-speaker speech recognition show that our conditional multi-sequence models lead to consistent improvements over the conventional non-conditional models.

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JMLR Journal 2018 Journal Article

Learning from Comparisons and Choices

Sahand Negahban
Sewoong Oh
Kiran K. Thekumparampil
Jiaming Xu

When tracking user-specific online activities, each user's preference is revealed in the form of choices and comparisons. For example, a user's purchase history is a record of her choices, i.e. which item was chosen among a subset of offerings. A user's preferences can be observed either explicitly as in movie ratings or implicitly as in viewing times of news articles. Given such individualized ordinal data in the form of comparisons and choices, we address the problem of collaboratively learning representations of the users and the items. The learned features can be used to predict a user's preference of an unseen item to be used in recommendation systems. This also allows one to compute similarities among users and items to be used for categorization and search. Motivated by the empirical successes of the MultiNomial Logit (MNL) model in marketing and transportation, and also more recent successes in word embedding and crowdsourced image embedding, we pose this problem as learning the MNL model parameters that best explain the data. We propose a convex relaxation for learning the MNL model, and show that it is minimax optimal up to a logarithmic factor by comparing its performance to a fundamental lower bound. This characterizes the minimax sample complexity of the problem, and proves that the proposed estimator cannot be improved upon other than by a logarithmic factor. Further, the analysis identifies how the accuracy depends on the topology of sampling via the spectrum of the sampling graph. This provides a guideline for designing surveys when one can choose which items are to be compared. This is accompanied by numerical simulations on synthetic and real data sets, confirming our theoretical predictions. [abs] [ pdf ][ bib ] &copy JMLR 2018. ( edit, beta )

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IJCAI Conference 2018 Conference Paper

Listen, Think and Listen Again: Capturing Top-down Auditory Attention for Speaker-independent Speech Separation

Jing Shi
Jiaming Xu
Guangcan Liu
Bo Xu

Recent deep learning methods have made significant progress in multi-talker mixed speech separation. However, most existing models adopt a driftless strategy to separate all the speech channels rather than selectively attend the target one. As a result, those frameworks may be failed to offer a satisfactory solution in complex auditory scene where the number of input sounds is usually uncertain and even dynamic. In this paper, we present a novel neural network based structure motivated by the top-down attention behavior of human when facing complicated acoustical scene. Different from previous works, our method constructs an inference-attention structure to predict interested candidates and extract each speech channel of them. Our work gets rid of the limitation that the number of channels must be given or the high computation complexity for label permutation problem. We evaluated our model on the WSJ0 mixed-speech tasks. In all the experiments, our model gets highly competitive to reach and even outperform the baselines.

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AAAI Conference 2018 Conference Paper

Modeling Attention and Memory for Auditory Selection in a Cocktail Party Environment

Jiaming Xu
Jing Shi
Guangcan Liu
Xiuyi Chen
Bo Xu

Developing a computational auditory model to solve the cocktail party problem has long bedeviled scientists, especially for a single microphone recording. Although recent deep learning based frameworks have made signiﬁcant progress in multi-talker mixed speech separation, most existing deep learning based methods, focusing on separating all the speech channels rather than selectively attending the target speech and ignoring other sounds, may fail to offer a satisfactory solution in a complex auditory scene where the number of input sounds is usually uncertain and even dynamic. In this work, we employ ideas from auditory selective attention of behavioral and cognitive neurosciences and from recent advances of memory-augmented neural networks. Speciﬁcally, a uniﬁed Auditory Selection framework with Attention and Memory (dubbed ASAM) is proposed. Our ASAM ﬁrst accumulates the prior knowledge (that is the acoustic feature to one speciﬁc speaker) into a life-long memory during the training phase, meanwhile a speech perceptor is trained to extract the temporal acoustic feature and update the memory online when a salient speech is given. Then, the learned memory is utilized to interact with the mixture input to attend and ﬁlter the target frequency out from the mixture stream. Finally, the network is trained to minimize the reconstruction error of the attended speech. We evaluate the proposed approach on WSJ0 and THCHS-30 datasets and the experimental results demonstrate that our approach successfully conducts two auditory selection tasks: the top-down task-speciﬁc attention (e. g. to follow a conversation with friend) and the bottom-up stimulus-driven attention (e. g. be attracted by a salient speech). Compared with deep clustering based methods, our method conducts competitive advantages especially in a real noise environment (e. g. street junction). Our code is available at https: //github. com/jacoxu/ASAM.

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JMLR Journal 2018 Journal Article

Submatrix localization via message passing

Bruce Hajek
Yihong Wu
Jiaming Xu

The principal submatrix localization problem deals with recovering a $K\times K$ principal submatrix of elevated mean $\mu$ in a large $n\times n$ symmetric matrix subject to additive standard Gaussian noise, or more generally, mean zero, variance one, subgaussian noise. This problem serves as a prototypical example for community detection, in which the community corresponds to the support of the submatrix. The main result of this paper is that in the regime $\Omega(\sqrt{n}) \leq K \leq o(n)$, the support of the submatrix can be weakly recovered (with $o(K)$ misclassification errors on average) by an optimized message passing algorithm if $\lambda = \mu^2K^2/n$, the signal-to-noise ratio, exceeds $1/e$. This extends a result by Deshpande and Montanari previously obtained for $K=\Theta(\sqrt{n})$ and $\mu=\Theta(1).$ In addition, the algorithm can be combined with a voting procedure to achieve the information-theoretic limit of exact recovery with sharp constants for all $K \geq \frac{n}{\log n} (\frac{1}{8e} + o(1))$. The total running time of the algorithm is $O(n^2\log n)$. Another version of the submatrix localization problem, known as noisy biclustering, aims to recover a $K_1\times K_2$ submatrix of elevated mean $\mu$ in a large $n_1\times n_2$ Gaussian matrix. The optimized message passing algorithm and its analysis are adapted to the bicluster problem assuming $\Omega(\sqrt{n_i}) \leq K_i \leq o(n_i)$ and $K_1\asymp K_2.$ A sharp information-theoretic condition for the weak recovery of both clusters is also identified. [abs] [ pdf ][ bib ] &copy JMLR 2018. ( edit, beta )

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JMLR Journal 2016 Journal Article

Statistical-Computational Tradeoffs in Planted Problems and Submatrix Localization with a Growing Number of Clusters and Submatrices

Yudong Chen
Jiaming Xu

We consider two closely related problems: planted clustering and submatrix localization. In the planted clustering problem, a random graph is generated based on an underlying cluster structure of the nodes; the task is to recover these clusters given the graph. The submatrix localization problem concerns locating hidden submatrices with elevated means inside a large real-valued random matrix. Of particular interest is the setting where the number of clusters/submatrices is allowed to grow unbounded with the problem size. These formulations cover several classical models such as planted clique, planted densest subgraph, planted partition, planted coloring, and the stochastic block model, which are widely used for studying community detection, graph clustering and bi-clustering. For both problems, we show that the space of the model parameters (cluster/submatrix size, edge probabilities and the mean of the submatrices) can be partitioned into four disjoint regions corresponding to decreasing statistical and computational complexities: (1) the impossible regime, where all algorithms fail; (2) the hard regime, where the computationally expensive Maximum Likelihood Estimator (MLE) succeeds; (3) the easy regime, where the polynomial-time convexified MLE succeeds; (4) the simple regime, where a local counting/thresholding procedure succeeds. Moreover, we show that each of these algorithms provably fails in the harder regimes. Our results establish the minimax recovery limits, which are tight up to universal constants and hold even with a growing number of clusters/submatrices, and provide order-wise stronger performance guarantees for polynomial-time algorithms than previously known. Our study demonstrates the tradeoffs between statistical and computational considerations, and suggests that the minimax limits may not be achievable by polynomial-time algorithms. [abs] [ pdf ][ bib ] &copy JMLR 2016. ( edit, beta )

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NeurIPS Conference 2015 Conference Paper

Collaboratively Learning Preferences from Ordinal Data

Sewoong Oh
Kiran Thekumparampil
Jiaming Xu

In personalized recommendation systems, it is important to predict preferences of a user on items that have not been seen by that user yet. Similarly, in revenue management, it is important to predict outcomes of comparisons among those items that have never been compared so far. The MultiNomial Logit model, a popular discrete choice model, captures the structure of the hidden preferences with a low-rank matrix. In order to predict the preferences, we want to learn the underlying model from noisy observations of the low-rank matrix, collected as revealed preferences in various forms of ordinal data. A natural approach to learn such a model is to solve a convex relaxation of nuclear norm minimization. We present the convex relaxation approach in two contexts of interest: collaborative ranking and bundled choice modeling. In both cases, we show that the convex relaxation is minimax optimal. We prove an upper bound on the resulting error with finite samples, and provide a matching information-theoretic lower bound.

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IJCAI Conference 2015 Conference Paper

Convolutional Neural Networks for Text Hashing

Jiaming Xu
Peng Wang
Guanhua Tian
Bo Xu
Jun Zhao
Fangyuan Wang
Hongwei Hao

Hashing, as a popular approximate nearest neighbor search, has been widely used for large-scale similarity search. Recently, a spectrum of machine learning methods are utilized to learn similarity-preserving binary codes. However, most of them directly encode the explicit features, keywords, which fail to preserve the accurate semantic similarities in binary code beyond keyword matching, especially on short texts. Here we propose a novel text hashing framework with convolutional neural networks. In particular, we first embed the keyword features into compact binary code with a locality preserving constraint. Meanwhile word features and position features are together fed into a convolutional network to learn the implicit features which are further incorporated with the explicit features to fit the pre-trained binary code. Such base method can be successfully accomplished without any external tags/labels, and other three model variations are designed to integrate tags/labels. Experimental results show the superiority of our proposed approach over several state-of-the-art hashing methods when tested on one short text dataset as well as one normal text dataset.

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NeurIPS Conference 2014 Conference Paper

Minimax-optimal Inference from Partial Rankings

Bruce Hajek
Sewoong Oh
Jiaming Xu

This paper studies the problem of rank aggregation under the Plackett-Luce model. The goal is to infer a global ranking and related scores of the items, based on partial rankings provided by multiple users over multiple subsets of items. A question of particular interest is how to optimally assign items to users for ranking and how many item assignments are needed to achieve a target estimation error. Without any assumptions on how the items are assigned to users, we derive an oracle lower bound and the Cram\'er-Rao lower bound of the estimation error. We prove an upper bound on the estimation error achieved by the maximum likelihood estimator, and show that both the upper bound and the Cram\'er-Rao lower bound inversely depend on the spectral gap of the Laplacian of an appropriately defined comparison graph. Since random comparison graphs are known to have large spectral gaps, this suggests the use of random assignments when we have the control. Precisely, the matching oracle lower bound and the upper bound on the estimation error imply that the maximum likelihood estimator together with a random assignment is minimax-optimal up to a logarithmic factor. We further analyze a popular rank-breaking scheme that decompose partial rankings into pairwise comparisons. We show that even if one applies the mismatched maximum likelihood estimator that assumes independence (on pairwise comparisons that are now dependent due to rank-breaking), minimax optimal performance is still achieved up to a logarithmic factor.

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