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Biwei Huang

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52 papers

2 author rows

JMLR Journal 2026 Journal Article

Identifying Weight-Variant Latent Causal Models

Yuhang Liu
Zhen Zhang
Dong Gong
Mingming Gong
Biwei Huang
Anton van den Hengel
Kun Zhang
Javen Qinfeng Shi

The task of causal representation learning aims to uncover latent higher-level causal variables that affect lower-level observations. Identifying the true latent causal variables from observed data, while allowing instantaneous causal relations among latent variables, remains a challenge, however. To this end, we start with the analysis of three intrinsic indeterminacies in identifying latent variables from observations: transitivity, permutation indeterminacy, and scaling indeterminacy. We find that transitivity acts as a key role in impeding the identifiability of latent causal variables. To address the unidentifiable issue due to transitivity, we introduce a novel identifiability condition where the underlying latent causal model satisfies a linear-Gaussian model, in which the causal coefficients and the distribution of Gaussian noise are modulated by an additional observed variable. Under certain assumptions, including the existence of a reference condition under which latent causal influences vanish, we can show that the latent causal variables can be identified up to trivial permutation and scaling, and that partial identifiability results can still be obtained when this reference condition is violated for a subset of latent variables. Furthermore, based on these theoretical results, we propose a novel method, termed Structural caUsAl Variational autoEncoder (SuaVE), which directly learns causal representations and causal relationships among them, together with the mapping from the latent causal variables to the observed ones. Experimental results on synthetic and real data demonstrate the identifiability and consistency results and the efficacy of SuaVE in learning causal representations. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2026. ( edit, beta )

AAAI Conference 2026 Conference Paper

Revisiting Differentiable Structure Learning: Inconsistency of L1 Penalty and Beyond

Kaifeng Jin
Ignavier Ng
Kun Zhang
Biwei Huang

Recent advances in differentiable structure learning have framed the combinatorial problem of learning directed acyclic graphs as a continuous optimization problem. Various aspects, including data standardization, have been studied to identify factors that influence the empirical performance of these methods. In this work, we investigate critical limitations in differentiable structure learning methods, focusing on settings where the true structure can be identified up to Markov equivalence classes, particularly in the linear Gaussian case. While recent work highlighted potential non-convexity issues in this setting, we demonstrate and explain why the use of L1-penalized likelihood in such cases is fundamentally inconsistent, even if the global optimum of the optimization problem can be found. To resolve this limitation, we develop a hybrid differentiable structure learning method based on L0-penalized likelihood with hard acyclicity constraint, where the L0 penalty can be approximated by different techniques including Gumbel-Softmax. Specifically, we first estimate the underlying moral graph, and use it to restrict the search space of the optimization problem, which helps alleviate the non-convexity issue. Experimental results show that the proposed method enhances empirical performance both before and after data standardization, providing a more reliable path for future advancements in differentiable structure learning, especially for learning Markov equivalence classes.

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ICLR Conference 2025 Conference Paper

A Skewness-Based Criterion for Addressing Heteroscedastic Noise in Causal Discovery

Yingyu Lin
Yuxing Huang
Wenqin Liu
Haoran Deng
Ignavier Ng
Kun Zhang 0001
Mingming Gong
Yian Ma

Real-world data often violates the equal-variance assumption (homoscedasticity), making it essential to account for heteroscedastic noise in causal discovery. In this work, we explore heteroscedastic symmetric noise models (HSNMs), where the effect $Y$ is modeled as $Y = f(X) + \sigma(X)N$, with $X$ as the cause and $N$ as independent noise following a symmetric distribution. We introduce a novel criterion for identifying HSNMs based on the skewness of the score (i.e., the gradient of the log density) of the data distribution. This criterion establishes a computationally tractable measurement that is zero in the causal direction but nonzero in the anticausal direction, enabling the causal direction discovery. We extend this skewness-based criterion to the multivariate setting and propose \texttt{SkewScore}, an algorithm that handles heteroscedastic noise without requiring the extraction of exogenous noise. We also conduct a case study on the robustness of \texttt{SkewScore} in a bivariate model with a latent confounder, providing theoretical insights into its performance. Empirical studies further validate the effectiveness of the proposed method.

NeurIPS Conference 2025 Conference Paper

Activation Control for Efficiently Eliciting Long Chain-of-thought Ability of Language Models

Zekai Zhao
Qi Liu
Kun Zhou
Zihan Liu
Yifei Shao
Zhiting Hu
Biwei Huang

Despite the remarkable reasoning performance, eliciting the long chain-of-thought(CoT) ability in large language models(LLMs) typically requires costly reinforcement learning or supervised fine-tuning on high-quality distilled data. We investigate the internal mechanisms behind this capability and show that a small set of high-impact activations in the last few layers, greatly govern the long-form reasoning attributes, e. g. output length and self-reflection. Through simply amplifying these activations and adding ``wait'' tokens, the long CoT ability can be invoked without training, leading to significantly increased self-reflection rate and accuracy. In addition, we also find that the activation changes follow predictable trajectories, i. e. a sharp rise after special tokens and a subsequent exponential decay. Based on these insights, we introduce a general training-free activation control technique. It utilizes a few contrastive examples to identify the relevant activations, and then incorporates simple analytic functions to adjust their values at inference time to elicit long CoTs. Extensive experiments have verified the effectiveness of our methods in efficiently eliciting the long CoT ability of LLMs and improving the performance. Besides, we further propose a parameter-efficient fine-tuning method that trains only the last-layer activation amplification module and a few LoRA layers, outperforming LoRA on reasoning benchmarks with much fewer parameters. Our code and data will be fully public released.

ICLR Conference 2025 Conference Paper

Analytic DAG Constraints for Differentiable DAG Learning

Zhen Zhang 0008
Ignavier Ng
Dong Gong
Yuhang Liu 0002
Mingming Gong
Biwei Huang
Kun Zhang 0001
Anton van den Hengel

Recovering the underlying Directed Acyclic Graph (DAG) structures from observational data presents a formidable challenge, partly due to the combinatorial nature of the DAG-constrained optimization problem. Recently, researchers have identified gradient vanishing as one of the primary obstacles in differentiable DAG learning and have proposed several DAG constraints to mitigate this issue. By developing the necessary theory to establish a connection between analytic functions and DAG constraints, we demonstrate that analytic functions from the set $\\{f(x) = c_0 + \\sum_{i=1}^{\infty}c_ix^i | \\forall i > 0, c_i > 0; r = \\lim_{i\\rightarrow \\infty}c_{i}/c_{i+1} > 0\\}$ can be employed to formulate effective DAG constraints. Furthermore, we establish that this set of functions is closed under several functional operators, including differentiation, summation, and multiplication. Consequently, these operators can be leveraged to create novel DAG constraints based on existing ones. Using these properties, we design a series of DAG constraints and develop an efficient algorithm to evaluate them. Experiments in various settings demonstrate that our DAG constraints outperform previous state-of-the-art comparators. Our implementation is available at https://github.com/zzhang1987/AnalyticDAGLearning.

NeurIPS Conference 2025 Conference Paper

Causality Meets Locality: Provably Generalizable and Scalable Policy Learning for Networked Systems

Hao Liang
shuqing shi
Yudi Zhang
Biwei Huang
Yali Du

Large‑scale networked systems, such as traffic, power, and wireless grids, challenge reinforcement‑learning agents with both scale and environment shifts. To address these challenges, we propose \texttt{GSAC} (\textbf{G}eneralizable and \textbf{S}calable \textbf{A}ctor‑\textbf{C}ritic), a framework that couples causal representation learning with meta actor‑critic learning to achieve both scalability and domain generalization. Each agent first learns a sparse local causal mask that provably identifies the minimal neighborhood variables influencing its dynamics, yielding exponentially tight approximately compact representations (ACRs) of state and domain factors. These ACRs bound the error of truncating value functions to $\kappa$-hop neighborhoods, enabling efficient learning on graphs. A meta actor‑critic then trains a shared policy across multiple source domains while conditioning on the compact domain factors; at test time, a few trajectories suffice to estimate the new domain factor and deploy the adapted policy. We establish finite‑sample guarantees on causal recovery, actor-critic convergence, and adaptation gap, and show that \texttt{GSAC} adapts rapidly and significantly outperforms learning-from-scratch and conventional adaptation baselines.

ICLR Conference 2025 Conference Paper

Differentiable Causal Discovery for Latent Hierarchical Causal Models

Parjanya Prajakta Prashant
Ignavier Ng
Kun Zhang 0001
Biwei Huang

Discovering causal structures with latent variables from observational data is a fundamental challenge in causal discovery. Existing methods often rely on constraint-based, iterative discrete searches, limiting their scalability for large numbers of variables. Moreover, these methods frequently assume linearity or invertibility, restricting their applicability to real-world scenarios. We present new theoretical results on the identifiability of non-linear latent hierarchical causal models, relaxing previous assumptions in the literature about the deterministic nature of latent variables and exogenous noise. Building on these insights, we develop a novel differentiable causal discovery algorithm that efficiently estimates the structure of such models. To the best of our knowledge, this is the first work to propose a differentiable causal discovery method for non-linear latent hierarchical models. Our approach outperforms existing methods in both accuracy and scalability. Furthermore, we demonstrate its practical utility by learning interpretable hierarchical latent structures from high-dimensional image data and demonstrate its effectiveness on downstream tasks such as transfer learning.

TMLR Journal 2025 Journal Article

Latent Covariate Shift: Unlocking Partial Identifiability for Multi-Source Domain Adaptation

Yuhang Liu
Zhen Zhang
Dong Gong
Mingming Gong
Biwei Huang
Anton van den Hengel
Kun Zhang
Javen Qinfeng Shi

Multi-source domain adaptation (MSDA) addresses the challenge of learning a label prediction function for an unlabeled target domain by leveraging both the labeled data from multiple source domains and the unlabeled data from the target domain. Conventional MSDA approaches often rely on covariate shift or conditional shift paradigms, which assume a consistent label distribution across domains. However, this assumption proves limiting in practical scenarios where label distributions do vary across domains, diminishing its applicability in real-world settings. For example, animals from different regions exhibit diverse characteristics due to varying diets and genetics. Motivated by this, we propose a novel paradigm called latent covariate shift (LCS), which introduces significantly greater variability and adaptability across domains. Notably, it provides a theoretical assurance for recovering the latent cause of the label variable, which we refer to as the latent content variable. Within this new paradigm, we present an intricate causal generative model by introducing latent noises across domains, along with a latent content variable and a latent style variable to achieve more nuanced rendering of observational data. We demonstrate that the latent content variable can be identified up to block identifiability due to its versatile yet distinct causal structure. We anchor our theoretical insights into a novel MSDA method, which learns the label distribution conditioned on the identifiable latent content variable, thereby accommodating more substantial distribution shifts. The proposed approach showcases exceptional performance and efficacy on both simulated and real-world datasets.

TMLR Journal 2025 Journal Article

MACCA: Offline Multi-agent Reinforcement Learning with Causal Credit Assignment

Ziyan Wang
Yali Du
Yudi Zhang
Meng Fang
Biwei Huang

Offline Multi-agent Reinforcement Learning (MARL) is valuable in scenarios where online interaction is impractical or risky. While independent learning in MARL offers flexibility and scalability, accurately assigning credit to individual agents in offline settings poses challenges because interactions with an environment are prohibited. In this paper, we propose a new framework, namely \textbf{M}ulti-\textbf{A}gent \textbf{C}ausal \textbf{C}redit \textbf{A}ssignment (\textbf{MACCA}), to address credit assignment in the offline MARL setting. Our approach, MACCA, characterizing the generative process as a Dynamic Bayesian Network, captures relationships between environmental variables, states, actions, and rewards. Estimating this model on offline data, MACCA can learn each agent's contribution by analyzing the causal relationship of their individual rewards, ensuring accurate and interpretable credit assignment. Additionally, the modularity of our approach allows it to integrate with various offline MARL methods seamlessly. Theoretically, we proved that under the setting of the offline dataset, the underlying causal structure and the function for generating the individual rewards of agents are identifiable, which laid the foundation for the correctness of our modeling. In our experiments, we demonstrate that MACCA not only outperforms state-of-the-art methods but also enhances performance when integrated with other backbones.

ICML Conference 2025 Conference Paper

MissScore: High-Order Score Estimation in the Presence of Missing Data

Wenqin Liu
Haoze Hou
Erdun Gao
Biwei Huang
Qiuhong Ke
Howard D. Bondell
Mingming Gong

Score-based generative models are essential in various machine learning applications, with strong capabilities in generation quality. In particular, high-order derivatives (scores) of data density offer deep insights into data distributions, building on the proven effectiveness of first-order scores for modeling and generating synthetic data, unlocking new possibilities for applications. However, learning them typically requires complete data, which is often unavailable in domains such as healthcare and finance due to data corruption, acquisition constraints, or incomplete records. To tackle this challenge, we introduce MissScore, a novel framework for estimating high-order scores in the presence of missing data. We derive objective functions for estimating high-order scores under different missing data mechanisms and propose a new algorithm specifically designed to handle missing data effectively. Our empirical results demonstrate that MissScore accurately and efficiently learns the high-order scores from incomplete data and generates high-quality samples, resulting in strong performance across a range of downstream tasks.

ICLR Conference 2025 Conference Paper

Modeling Unseen Environments with Language-guided Composable Causal Components in Reinforcement Learning

Xinyue Wang
Biwei Huang

Generalization in reinforcement learning (RL) remains a significant challenge, especially when agents encounter novel environments with unseen dynamics. Drawing inspiration from human compositional reasoning—where known components are reconfigured to handle new situations—we introduce World Modeling with Compositional Causal Components (WM3C). This novel framework enhances RL generalization by learning and leveraging compositional causal components. Unlike previous approaches focusing on invariant representation learning or meta-learning, WM3C identifies and utilizes causal dynamics among composable elements, facilitating robust adaptation to new tasks. Our approach integrates language as a compositional modality to decompose the latent space into meaningful components and provides theoretical guarantees for their unique identification under mild assumptions. Our practical implementation uses a masked autoencoder with mutual information constraints and adaptive sparsity regularization to capture high-level semantic information and effectively disentangle transition dynamics. Experiments on numerical simulations and real-world robotic manipulation tasks demonstrate that WM3C significantly outperforms existing methods in identifying latent processes, improving policy learning, and generalizing to unseen tasks.

NeurIPS Conference 2025 Conference Paper

Practical Kernel Selection for Kernel-based Conditional Independence Test

Wenjie Wang
Mingming Gong
Biwei Huang
James Bailey
Bo Han
Kun Zhang
Feng Liu

Conditional independence (CI) testing is a fundamental yet challenging task in modern statistics and machine learning. One pivotal class of methods for assessing conditional independence encompasses kernel-based approaches, known for assessing CI by detecting general conditional dependence without imposing strict assumptions on relationships or data distributions. As with any method utilizing kernels, selecting appropriate kernels is crucial for precise identification. However, it remains underexplored in kernel-based CI methods, where the kernels are often determined manually or heuristically. In this paper, we analyze and propose a kernel parameter selection approach for the kernel-based conditional independence test (KCI). The kernel parameters are selected based on the ratio of the statistic to the asymptotic variance, which approximates the test power for the given parameters at large sample sizes. The search procedure is grid-based, allowing for parallelization with manageable additional computation time. We theoretically demonstrate the consistency of the proposed criterion and conduct extensive experiments on both synthetic and real data to show the effectiveness of our method.

TMLR Journal 2025 Journal Article

Reinforcement Learning for Causal Discovery without Acyclicity Constraints

Bao Duong
Hung Le
Biwei Huang
Thin Nguyen

Recently, reinforcement learning (RL) has proved a promising alternative for conventional local heuristics in score-based approaches to learning directed acyclic causal graphs (DAGs) from observational data. However, the intricate acyclicity constraint still challenges the efficient exploration of the vast space of DAGs in existing methods. In this study, we introduce ALIAS (reinforced dAg Learning wIthout Acyclicity conStraints), a novel approach to causal discovery powered by the RL machinery. Our method features an efficient policy for generating DAGs in just a single step with an optimal quadratic complexity, fueled by a novel parametrization of DAGs that directly translates a continuous space to the space of all DAGs, bypassing the need for explicitly enforcing acyclicity constraints. This approach enables us to navigate the search space more effectively by utilizing policy gradient methods and established scoring functions. In addition, we provide compelling empirical evidence for the strong performance of ALIAS in comparison with state-of-the-arts in causal discovery over increasingly difficult experiment conditions on both synthetic and real datasets. Our implementation is provided at https://github.com/baosws/ALIAS.

NeurIPS Conference 2025 Conference Paper

Towards General Continuous Memory for Vision-Language Models

Wenyi WU
Zixuan Song
Kun Zhou
Yifei Shao
Zhiting Hu
Biwei Huang

Language models (LMs) and their extension, vision-language models (VLMs), have achieved remarkable performance across various tasks. However, they still struggle with complex reasoning tasks that require multimodal or multilingual real world knowledge. To support such capabilities, an external memory system that can efficiently provide relevant multimodal information is essential. Existing approaches generally concatenate image and text tokens into a long sequence as memory, which, however, may drastically increase context length and even degrade performance. In contrast, we propose using continuous memory-a compact set of dense embeddings-to more effectively and efficiently represent multimodal and multilingual knowledge. Our key insight is that a VLM can serve as its own continuous memory encoder. We empirically show that this design improves performance on complex multimodal reasoning tasks. Building on this, we introduce a data-efficient and parameter-efficient method to fine-tune the VLM into a memory encoder, requiring only 1. 2\% of the model’s parameters and a small corpus of 15. 6K self-synthesized samples. Our approach CoMEM utilizes VLM's original capabilities to encode arbitrary multimodal and multilingual knowledge into just 8 continuous embeddings. Since the inference-time VLM remains frozen, our memory module is plug-and-play and can be flexibly integrated as needed. Extensive experiments across eight multimodal reasoning benchmarks demonstrate the effectiveness of our approach. Code and data is publicly released here https: //github. com/WenyiWU0111/CoMEM.

ICLR Conference 2025 Conference Paper

Towards Generalizable Reinforcement Learning via Causality-Guided Self-Adaptive Representations

Yupei Yang
Biwei Huang
Fan Feng
Xinyue Wang
Shikui Tu
Lei Xu 0001

General intelligence requires quick adaptation across tasks. While existing reinforcement learning (RL) methods have made progress in generalization, they typically assume only distribution changes between source and target domains. In this paper, we explore a wider range of scenarios where not only the distribution but also the environment spaces may change. For example, in the CoinRun environment, we train agents from easy levels and generalize them to difficulty levels where there could be new enemies that have never occurred before. To address this challenging setting, we introduce a causality-guided self-adaptive representation-based approach, called CSR, that equips the agent to generalize effectively across tasks with evolving dynamics. Specifically, we employ causal representation learning to characterize the latent causal variables within the RL system. Such compact causal representations uncover the structural relationships among variables, enabling the agent to autonomously determine whether changes in the environment stem from distribution shifts or variations in space, and to precisely locate these changes. We then devise a three-step strategy to fine-tune the causal model under different scenarios accordingly. Empirical experiments show that CSR efficiently adapts to the target domains with only a few samples and outperforms state-of-the-art baselines on a wide range of scenarios, including our simulated environments, CartPole, CoinRun and Atari games.

ICLR Conference 2024 Conference Paper

A Versatile Causal Discovery Framework to Allow Causally-Related Hidden Variables

Xinshuai Dong
Biwei Huang
Ignavier Ng
Xiangchen Song
Yujia Zheng 0001
Songyao Jin
Roberto Legaspi
Peter Spirtes

Most existing causal discovery methods rely on the assumption of no latent confounders, limiting their applicability in solving real-life problems. In this paper, we introduce a novel, versatile framework for causal discovery that accommodates the presence of causally-related hidden variables almost everywhere in the causal network (for instance, they can be effects of measured variables), based on rank information of covariance matrix over measured variables. We start by investigating the efficacy of rank in comparison to conditional independence and, theoretically, establish necessary and sufficient conditions for the identifiability of certain latent structural patterns. Furthermore, we develop a Rank-based Latent Causal Discovery algorithm, RLCD, that can efficiently locate hidden variables, determine their cardinalities, and discover the entire causal structure over both measured and hidden ones. We also show that, under certain graphical conditions, RLCD correctly identifies the Markov Equivalence Class of the whole latent causal graph asymptotically. Experimental results on both synthetic and real-world personality data sets demonstrate the efficacy of the proposed approach in finite-sample cases. Our code will be publicly available.

AAAI Conference 2024 Conference Paper

ACAMDA: Improving Data Efficiency in Reinforcement Learning through Guided Counterfactual Data Augmentation

Yuewen Sun
Erli Wang
Biwei Huang
Chaochao Lu
Lu Feng
Changyin Sun
Kun Zhang

Data augmentation plays a crucial role in improving the data efficiency of reinforcement learning (RL). However, the generation of high-quality augmented data remains a significant challenge. To overcome this, we introduce ACAMDA (Adversarial Causal Modeling for Data Augmentation), a novel framework that integrates two causality-based tasks: causal structure recovery and counterfactual estimation. The unique aspect of ACAMDA lies in its ability to recover temporal causal relationships from limited non-expert datasets. The identification of the sequential cause-and-effect allows the creation of realistic yet unobserved scenarios. We utilize this characteristic to generate guided counterfactual datasets, which, in turn, substantially reduces the need for extensive data collection. By simulating various state-action pairs under hypothetical actions, ACAMDA enriches the training dataset for diverse and heterogeneous conditions. Our experimental evaluation shows that ACAMDA outperforms existing methods, particularly when applied to novel and unseen domains.

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ICML Conference 2024 Conference Paper

An Empirical Examination of Balancing Strategy for Counterfactual Estimation on Time Series

Qiang Huang
Chuizheng Meng
Defu Cao
Biwei Huang
Yi Chang 0001
Yan Liu 0002

Counterfactual estimation from observations represents a critical endeavor in numerous application fields, such as healthcare and finance, with the primary challenge being the mitigation of treatment bias. The balancing strategy aimed at reducing covariate disparities between different treatment groups serves as a universal solution. However, when it comes to the time series data, the effectiveness of balancing strategies remains an open question, with a thorough analysis of the robustness and applicability of balancing strategies still lacking. This paper revisits counterfactual estimation in the temporal setting and provides a brief overview of recent advancements in balancing strategies. More importantly, we conduct a critical empirical examination for the effectiveness of the balancing strategies within the realm of temporal counterfactual estimation in various settings on multiple datasets. Our findings could be of significant interest to researchers and practitioners and call for a reexamination of the balancing strategy in time series settings.

IJCAI Conference 2024 Conference Paper

Boosting Efficiency in Task-Agnostic Exploration through Causal Knowledge

Yupei Yang
Biwei Huang
Shikui Tu
Lei Xu

The effectiveness of model training heavily relies on the quality of available training resources. However, budget constraints often impose limitations on data collection efforts. To tackle this challenge, we introduce causal exploration in this paper, a strategy that leverages the underlying causal knowledge for both data collection and model training. We, in particular, focus on enhancing the sample efficiency and reliability of the world model learning within the domain of task-agnostic reinforcement learning. During the exploration phase, the agent actively selects actions expected to yield causal insights most beneficial for world model training. Concurrently, the causal knowledge is acquired and incrementally refined with the ongoing collection of data. We demonstrate that causal exploration aids in learning accurate world models using fewer data and provide theoretical guarantees for its convergence. Empirical experiments, on both synthetic data and real-world applications, further validate the benefits of causal exploration. The source code is available at https: //github. com/CMACH508/CausalExploration.

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JMLR Journal 2024 Journal Article

Causal-learn: Causal Discovery in Python

Yujia Zheng
Biwei Huang
Wei Chen
Joseph Ramsey
Mingming Gong
Ruichu Cai
Shohei Shimizu
Peter Spirtes

Causal discovery aims at revealing causal relations from observational data, which is a fundamental task in science and engineering. We describe causal-learn, an open-source Python library for causal discovery. This library focuses on bringing a comprehensive collection of causal discovery methods to both practitioners and researchers. It provides easy-to-use APIs for non-specialists, modular building blocks for developers, detailed documentation for learners, and comprehensive methods for all. Different from previous packages in R or Java, causal-learn is fully developed in Python, which could be more in tune with the recent preference shift in programming languages within related communities. The library is available at https://github.com/py-why/causal-learn. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2024. ( edit, beta )

ICLR Conference 2024 Conference Paper

Federated Causal Discovery from Heterogeneous Data

Loka Li
Ignavier Ng
Gongxu Luo
Biwei Huang
Guangyi Chen 0002
Tongliang Liu
Bin Gu 0001
Kun Zhang 0001

Conventional causal discovery methods rely on centralized data, which is inconsistent with the decentralized nature of data in many real-world situations. This discrepancy has motivated the development of federated causal discovery (FCD) approaches. However, existing FCD methods may be limited by their potentially restrictive assumptions of identifiable functional causal models or homogeneous data distributions, narrowing their applicability in diverse scenarios. In this paper, we propose a novel FCD method attempting to accommodate arbitrary causal models and heterogeneous data. We first utilize a surrogate variable corresponding to the client index to account for the data heterogeneity across different clients. We then develop a federated conditional independence test (FCIT) for causal skeleton discovery and establish a federated independent change principle (FICP) to determine causal directions. These approaches involve constructing summary statistics as a proxy of the raw data to protect data privacy. Owing to the nonparametric properties, FCIT and FICP make no assumption about particular functional forms, thereby facilitating the handling of arbitrary causal models. We conduct extensive experiments on synthetic and real datasets to show the efficacy of our method. The code is available at https://github.com/lokali/FedCDH.git.

JMLR Journal 2024 Journal Article

Generalized Independent Noise Condition for Estimating Causal Structure with Latent Variables

Feng Xie
Biwei Huang
Zhengming Chen
Ruichu Cai
Clark Glymour
Zhi Geng
Kun Zhang

We investigate the challenging task of learning causal structure in the presence of latent variables, including locating latent variables, determining their quantity, and identifying causal relationships among both latent and observed variables. To address this, we propose a Generalized Independent Noise (GIN) condition for linear non-Gaussian acyclic causal models that incorporate latent variables, which establishes the independence between a linear combination of certain measured variables and some other measured variables. Specifically, for two observed random vectors $\bf{Y}$ and $\bf{Z}$, GIN holds if and only if $\omega^{\intercal}\mathbf{Y}$ and $\mathbf{Z}$ are statistically independent, where $\omega$ is a non-zero parameter vector determined by the cross-covariance between $\mathbf{Y}$ and $\mathbf{Z}$. We then give necessary and sufficient graphical criteria of the GIN condition in linear non-Gaussian acyclic causal models. From a graphical perspective, roughly speaking, GIN implies the existence of a set $\mathcal{S}$ such that $\mathcal{S}$ is causally earlier (w.r.t. the causal ordering) than $\mathbf{Y}$, and that every active (collider-free) path between $\mathbf{Y}$ and $\mathbf{Z}$ must contain a node from $\mathcal{S}$. Interestingly, we find that the independent noise condition (i.e., if there is no confounder, causes are independent of the residual derived from regressing the effect on the causes) can be seen as a special case of GIN. With such a connection between GIN and latent causal structures, we further leverage the proposed GIN condition, together with a well-designed search procedure, to efficiently estimate Linear, Non-Gaussian Latent Hierarchical Models (LiNGLaHs), where latent confounders may also be causally related and may even follow a hierarchical structure. We show that the underlying causal structure of a LiNGLaH is identifiable in light of GIN conditions under mild assumptions. Experimental results on both synthetic and three real-world data sets show the effectiveness of the proposed approach. [abs] [ pdf ][ bib ] &copy JMLR 2024. ( edit, beta )

NeurIPS Conference 2024 Conference Paper

Identifiability Analysis of Linear ODE Systems with Hidden Confounders

Yuanyuan Wang
Biwei Huang
Wei Huang
Xi Geng
Mingming Gong

The identifiability analysis of linear Ordinary Differential Equation (ODE) systems is a necessary prerequisite for making reliable causal inferences about these systems. While identifiability has been well studied in scenarios where the system is fully observable, the conditions for identifiability remain unexplored when latent variables interact with the system. This paper aims to address this gap by presenting a systematic analysis of identifiability in linear ODE systems incorporating hidden confounders. Specifically, we investigate two cases of such systems. In the first case, latent confounders exhibit no causal relationships, yet their evolution adheres to specific functional forms, such as polynomial functions of time $t$. Subsequently, we extend this analysis to encompass scenarios where hidden confounders exhibit causal dependencies, with the causal structure of latent variables described by a Directed Acyclic Graph (DAG). The second case represents a more intricate variation of the first case, prompting a more comprehensive identifiability analysis. Accordingly, we conduct detailed identifiability analyses of the second system under various observation conditions, including both continuous and discrete observations from single or multiple trajectories. To validate our theoretical results, we perform a series of simulations, which support and substantiate our findings.

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ICLR Conference 2024 Conference Paper

Identifiable Latent Polynomial Causal Models through the Lens of Change

Yuhang Liu 0002
Zhen Zhang 0008
Dong Gong
Mingming Gong
Biwei Huang
Anton van den Hengel
Kun Zhang 0001
Qinfeng Shi

Causal representation learning aims to unveil latent high-level causal representations from observed low-level data. One of its primary tasks is to provide reliable assurance of identifying these latent causal models, known as \textit{identifiability}. A recent breakthrough explores identifiability by leveraging the change of causal influences among latent causal variables across multiple environments \citep{liu2022identifying}. However, this progress rests on the assumption that the causal relationships among latent causal variables adhere strictly to linear Gaussian models. In this paper, we extend the scope of latent causal models to involve nonlinear causal relationships, represented by polynomial models, and general noise distributions conforming to the exponential family. Additionally, we investigate the necessity of imposing changes on all causal parameters and present partial identifiability results when part of them remains unchanged. Further, we propose a novel empirical estimation method, grounded in our theoretical finding, that enables learning consistent latent causal representations. Our experimental results, obtained from both synthetic and real-world data, validate our theoretical contributions concerning identifiability and consistency.

NeurIPS Conference 2024 Conference Paper

Identifying Latent State-Transition Processes for Individualized Reinforcement Learning

Yuewen Sun
Biwei Huang
Yu Yao
Donghuo Zeng
Xinshuai Dong
Songyao Jin
Boyang Sun
Roberto Legaspi

The application of reinforcement learning (RL) involving interactions with individuals has grown significantly in recent years. These interactions, influenced by factors such as personal preferences and physiological differences, causally influence state transitions, ranging from health conditions in healthcare to learning progress in education. As a result, different individuals may exhibit different state-transition processes. Understanding individualized state-transition processes is essential for optimizing individualized policies. In practice, however, identifying these state-transition processes is challenging, as individual-specific factors often remain latent. In this paper, we establish the identifiability of these latent factors and introduce a practical method that effectively learns these processes from observed state-action trajectories. Experiments on various datasets show that the proposed method can effectively identify latent state-transition processes and facilitate the learning of individualized RL policies.

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NeurIPS Conference 2024 Conference Paper

Learning Discrete Concepts in Latent Hierarchical Models

Lingjing Kong
Guangyi Chen
Biwei Huang
Eric Xing
Yuejie Chi
Kun Zhang

Learning concepts from natural high-dimensional data (e. g. , images) holds potential in building human-aligned and interpretable machine learning models. Despite its encouraging prospect, formalization and theoretical insights into this crucial task are still lacking. In this work, we formalize concepts as discrete latent causal variables that are related via a hierarchical causal model that encodes different abstraction levels of concepts embedded in high-dimensional data (e. g. , a dog breed and its eye shapes in natural images). We formulate conditions to facilitate the identification of the proposed causal model, which reveals when learning such concepts from unsupervised data is possible. Our conditions permit complex causal hierarchical structures beyond latent trees and multi-level directed acyclic graphs in prior work and can handle high-dimensional, continuous observed variables, which is well-suited for unstructured data modalities such as images. We substantiate our theoretical claims with synthetic data experiments. Further, we discuss our theory's implications for understanding the underlying mechanisms of latent diffusion models and provide corresponding empirical evidence for our theoretical insights.

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NeurIPS Conference 2024 Conference Paper

Natural Counterfactuals With Necessary Backtracking

Guang-Yuan Hao
Jiji Zhang
Biwei Huang
Hao Wang
Kun Zhang

Counterfactual reasoning is pivotal in human cognition and especially important for providing explanations and making decisions. While Judea Pearl's influential approach is theoretically elegant, its generation of a counterfactual scenario often requires too much deviation from the observed scenarios to be feasible, as we show using simple examples. To mitigate this difficulty, we propose a framework of natural counterfactuals and a method for generating counterfactuals that are more feasible with respect to the actual data distribution. Our methodology incorporates a certain amount of backtracking when needed, allowing changes in causally preceding variables to minimize deviations from realistic scenarios. Specifically, we introduce a novel optimization framework that permits but also controls the extent of backtracking with a "naturalness'' criterion. Empirical experiments demonstrate the effectiveness of our method. The code is available at https: //github. com/GuangyuanHao/natural_counterfactuals.

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NeurIPS Conference 2024 Conference Paper

On Causal Discovery in the Presence of Deterministic Relations

Loka Li
Haoyue Dai
Hanin Al Ghothani
Biwei Huang
Jiji Zhang
Shahar Harel
Isaac Bentwich
Guangyi Chen

Many causal discovery methods typically rely on the assumption of independent noise, yet real-life situations often involve deterministic relationships. In these cases, observed variables are represented as deterministic functions of their parental variables without noise. When determinism is present, constraint-based methods encounter challenges due to the violation of the faithfulness assumption. In this paper, we find, supported by both theoretical analysis and empirical evidence, that score-based methods with exact search can naturally address the issues of deterministic relations under rather mild assumptions. Nonetheless, exact score-based methods can be computationally expensive. To enhance the efficiency and scalability, we develop a novel framework for causal discovery that can detect and handle deterministic relations, called Determinism-aware Greedy Equivalent Search (DGES). DGES comprises three phases: (1) identify minimal deterministic clusters (i. e. , a minimal set of variables with deterministic relationships), (2) run modified Greedy Equivalent Search (GES) to obtain an initial graph, and (3) perform exact search exclusively on the deterministic cluster and its neighbors. The proposed DGES accommodates both linear and nonlinear causal relationships, as well as both continuous and discrete data types. Furthermore, we investigate the identifiability conditions of DGES. We conducted extensive experiments on both simulated and real-world datasets to show the efficacy of our proposed method.

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NeurIPS Conference 2024 Conference Paper

On the Parameter Identifiability of Partially Observed Linear Causal Models

Xinshuai Dong
Ignavier Ng
Biwei Huang
Yuewen Sun
Songyao Jin
Roberto Legaspi
Peter Spirtes
Kun Zhang

Linear causal models are important tools for modeling causal dependencies and yet in practice, only a subset of the variables can be observed. In this paper, we examine the parameter identifiability of these models by investigating whether the edge coefficients can be recovered given the causal structure and partially observed data. Our setting is more general than that of prior research—we allow all variables, including both observed and latent ones, to be flexibly related, and we consider the coefficients of all edges, whereas most existing works focus only on the edges between observed variables. Theoretically, we identify three types of indeterminacy for the parameters in partially observed linear causal models. We then provide graphical conditions that are sufficient for all parameters to be identifiable and show that some of them are provably necessary. Methodologically, we propose a novel likelihood-based parameter estimation method that addresses the variance indeterminacy of latent variables in a specific way and can asymptotically recover the underlying parameters up to trivial indeterminacy. Empirical studies on both synthetic and real-world datasets validate our identifiability theory and the effectiveness of the proposed method in the finite-sample regime.

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ICML Conference 2024 Conference Paper

Optimal Kernel Choice for Score Function-based Causal Discovery

Wenjie Wang
Biwei Huang
Feng Liu 0003
Xinge You
Tongliang Liu
Kun Zhang 0001
Mingming Gong

Score-based methods have demonstrated their effectiveness in discovering causal relationships by scoring different causal structures based on their goodness of fit to the data. Recently, Huang et al. proposed a generalized score function that can handle general data distributions and causal relationships by modeling the relations in reproducing kernel Hilbert space (RKHS). The selection of an appropriate kernel within this score function is crucial for accurately characterizing causal relationships and ensuring precise causal discovery. However, the current method involves manual heuristic selection of kernel parameters, making the process tedious and less likely to ensure optimality. In this paper, we propose a kernel selection method within the generalized score function that automatically selects the optimal kernel that best fits the data. Specifically, we model the generative process of the variables involved in each step of the causal graph search procedure as a mixture of independent noise variables. Based on this model, we derive an automatic kernel selection method by maximizing the marginal likelihood of the variables involved in each search step. We conduct experiments on both synthetic data and real-world benchmarks, and the results demonstrate that our proposed method outperforms heuristic kernel selection methods.

ICML Conference 2024 Conference Paper

Score-Based Causal Discovery of Latent Variable Causal Models

Ignavier Ng
Xinshuai Dong
Haoyue Dai
Biwei Huang
Peter Spirtes
Kun Zhang 0001

Identifying latent variables and the causal structure involving them is essential across various scientific fields. While many existing works fall under the category of constraint-based methods (with e. g. conditional independence or rank deficiency tests), they may face empirical challenges such as testing-order dependency, error propagation, and choosing an appropriate significance level. These issues can potentially be mitigated by properly designed score-based methods, such as Greedy Equivalence Search (GES) (Chickering, 2002) in the specific setting without latent variables. Yet, formulating score-based methods with latent variables is highly challenging. In this work, we develop score-based methods that are capable of identifying causal structures containing causally-related latent variables with identifiability guarantees. Specifically, we show that a properly formulated scoring function can achieve score equivalence and consistency for structure learning of latent variable causal models. We further provide a characterization of the degrees of freedom for the marginal over the observed variables under multiple structural assumptions considered in the literature, and accordingly develop both exact and continuous score-based methods. This offers a unified view of several existing constraint-based methods with different structural assumptions. Experimental results validate the effectiveness of the proposed methods.

ICLR Conference 2024 Conference Paper

Structural Estimation of Partially Observed Linear Non-Gaussian Acyclic Model: A Practical Approach with Identifiability

Songyao Jin
Feng Xie 0002
Guangyi Chen 0002
Biwei Huang
Zhengming Chen 0002
Xinshuai Dong
Kun Zhang 0001

Conventional causal discovery approaches, which seek to uncover causal relationships among measured variables, are typically fragile to the presence of latent variables. While various methods have been developed to address this confounding issue, they often rely on strong assumptions about the underlying causal structure. In this paper, we consider a general scenario where measured and latent variables collectively form a partially observed causally sufficient linear system and latent variables may be anywhere in the causal structure. We theoretically show that with the aid of high-order statistics, the causal graph is (almost) fully identifiable if, roughly speaking, each latent set has a sufficient number of pure children, which can be either latent or measured. Naturally, LiNGAM, a model without latent variables, is encompassed as a special case. Based on the identification theorem, we develop a principled algorithm to identify the causal graph by testing for statistical independence involving only measured variables in specific manners. Experimental results show that our method effectively recovers the causal structure, even when latent variables are influenced by measured variables.

NeurIPS Conference 2023 Conference Paper

Generator Identification for Linear SDEs with Additive and Multiplicative Noise

Yuanyuan Wang
Xi Geng
Wei Huang
Biwei Huang
Mingming Gong

In this paper, we present conditions for identifying the generator of a linear stochastic differential equation (SDE) from the distribution of its solution process with a given fixed initial state. These identifiability conditions are crucial in causal inference using linear SDEs as they enable the identification of the post-intervention distributions from its observational distribution. Specifically, we derive a sufficient and necessary condition for identifying the generator of linear SDEs with additive noise, as well as a sufficient condition for identifying the generator of linear SDEs with multiplicative noise. We show that the conditions derived for both types of SDEs are generic. Moreover, we offer geometric interpretations of the derived identifiability conditions to enhance their understanding. To validate our theoretical results, we perform a series of simulations, which support and substantiate the established findings.

NeurIPS Conference 2023 Conference Paper

Identification of Nonlinear Latent Hierarchical Models

Lingjing Kong
Biwei Huang
Feng Xie
Eric Xing
Yuejie Chi
Kun Zhang

Identifying latent variables and causal structures from observational data is essential to many real-world applications involving biological data, medical data, and unstructured data such as images and languages. However, this task can be highly challenging, especially when observed variables are generated by causally related latent variables and the relationships are nonlinear. In this work, we investigate the identification problem for nonlinear latent hierarchical causal models in which observed variables are generated by a set of causally related latent variables, and some latent variables may not have observed children. We show that the identifiability of causal structures and latent variables (up to invertible transformations) can be achieved under mild assumptions: on causal structures, we allow for multiple paths between any pair of variables in the graph, which relaxes latent tree assumptions in prior work; on structural functions, we permit general nonlinearity and multi-dimensional continuous variables, alleviating existing work's parametric assumptions. Specifically, we first develop an identification criterion in the form of novel identifiability guarantees for an elementary latent variable model. Leveraging this criterion, we show that both causal structures and latent variables of the hierarchical model can be identified asymptotically by explicitly constructing an estimation procedure. To the best of our knowledge, our work is the first to establish identifiability guarantees for both causal structures and latent variables in nonlinear latent hierarchical models.

NeurIPS Conference 2023 Conference Paper

Interpretable Reward Redistribution in Reinforcement Learning: A Causal Approach

Yudi Zhang
Yali Du
Biwei Huang
Ziyan Wang
Jun Wang
Meng Fang
Mykola Pechenizkiy

A major challenge in reinforcement learning is to determine which state-action pairs are responsible for future rewards that are delayed. Reward redistribution serves as a solution to re-assign credits for each time step from observed sequences. While the majority of current approaches construct the reward redistribution in an uninterpretable manner, we propose to explicitly model the contributions of state and action from a causal perspective, resulting in an interpretable reward redistribution and preserving policy invariance. In this paper, we start by studying the role of causal generative models in reward redistribution by characterizing the generation of Markovian rewards and trajectory-wise long-term return and further propose a framework, called Generative Return Decomposition (GRD), for policy optimization in delayed reward scenarios. Specifically, GRD first identifies the unobservable Markovian rewards and causal relations in the generative process. Then, GRD makes use of the identified causal generative model to form a compact representation to train policy over the most favorable subspace of the state space of the agent. Theoretically, we show that the unobservable Markovian reward function is identifiable, as well as the underlying causal structure and causal models. Experimental results show that our method outperforms state-of-the-art methods and the provided visualization further demonstrates the interpretability of our method. The project page is located at https: //reedzyd. github. io/GenerativeReturnDecomposition/.

NeurIPS Conference 2023 Conference Paper

Learning World Models with Identifiable Factorization

Yuren Liu
Biwei Huang
Zhengmao Zhu
Honglong Tian
Mingming Gong
Yang Yu
Kun Zhang

Extracting a stable and compact representation of the environment is crucial for efficient reinforcement learning in high-dimensional, noisy, and non-stationary environments. Different categories of information coexist in such environments -- how to effectively extract and disentangle the information remains a challenging problem. In this paper, we propose IFactor, a general framework to model four distinct categories of latent state variables that capture various aspects of information within the RL system, based on their interactions with actions and rewards. Our analysis establishes block-wise identifiability of these latent variables, which not only provides a stable and compact representation but also discloses that all reward-relevant factors are significant for policy learning. We further present a practical approach to learning the world model with identifiable blocks, ensuring the removal of redundancies but retaining minimal and sufficient information for policy optimization. Experiments in synthetic worlds demonstrate that our method accurately identifies the ground-truth latent variables, substantiating our theoretical findings. Moreover, experiments in variants of the DeepMind Control Suite and RoboDesk showcase the superior performance of our approach over baselines.

ICML Conference 2022 Conference Paper

Action-Sufficient State Representation Learning for Control with Structural Constraints

Biwei Huang
Chaochao Lu
Liu Leqi
José Miguel Hernández-Lobato
Clark Glymour
Bernhard Schölkopf
Kun Zhang 0001

Perceived signals in real-world scenarios are usually high-dimensional and noisy, and finding and using their representation that contains essential and sufficient information required by downstream decision-making tasks will help improve computational efficiency and generalization ability in the tasks. In this paper, we focus on partially observable environments and propose to learn a minimal set of state representations that capture sufficient information for decision-making, termed Action-Sufficient state Representations (ASRs). We build a generative environment model for the structural relationships among variables in the system and present a principled way to characterize ASRs based on structural constraints and the goal of maximizing cumulative reward in policy learning. We then develop a structured sequential Variational Auto-Encoder to estimate the environment model and extract ASRs. Our empirical results on CarRacing and VizDoom demonstrate a clear advantage of learning and using ASRs for policy learning. Moreover, the estimated environment model and ASRs allow learning behaviors from imagined outcomes in the compact latent space to improve sample efficiency.

ICLR Conference 2022 Conference Paper

AdaRL: What, Where, and How to Adapt in Transfer Reinforcement Learning

Biwei Huang
Fan Feng
Chaochao Lu
Sara Magliacane
Kun Zhang 0001

One practical challenge in reinforcement learning (RL) is how to make quick adaptations when faced with new environments. In this paper, we propose a principled framework for adaptive RL, called AdaRL, that adapts reliably and efficiently to changes across domains with a few samples from the target domain, even in partially observable environments. Specifically, we leverage a parsimonious graphical representation that characterizes structural relationships over variables in the RL system. Such graphical representations provide a compact way to encode what and where the changes across domains are, and furthermore inform us with a minimal set of changes that one has to consider for the purpose of policy adaptation. We show that by explicitly leveraging this compact representation to encode changes, we can efficiently adapt the policy to the target domain, in which only a few samples are needed and further policy optimization is avoided. We illustrate the efficacy of AdaRL through a series of experiments that vary factors in the observation, transition and reward functions for Cartpole and Atari games.

NeurIPS Conference 2022 Conference Paper

Factored Adaptation for Non-Stationary Reinforcement Learning

Fan Feng
Biwei Huang
Kun Zhang
Sara Magliacane

Dealing with non-stationarity in environments (e. g. , in the transition dynamics) and objectives (e. g. , in the reward functions) is a challenging problem that is crucial in real-world applications of reinforcement learning (RL). While most current approaches model the changes as a single shared embedding vector, we leverage insights from the recent causality literature to model non-stationarity in terms of individual latent change factors, and causal graphs across different environments. In particular, we propose Factored Adaptation for Non-Stationary RL (FANS-RL), a factored adaption approach that learns jointly both the causal structure in terms of a factored MDP, and a factored representation of the individual time-varying change factors. We prove that under standard assumptions, we can completely recover the causal graph representing the factored transition and reward function, as well as a partial structure between the individual change factors and the state components. Through our general framework, we can consider general non-stationary scenarios with different function types and changing frequency, including changes across episodes and within episodes. Experimental results demonstrate that FANS-RL outperforms existing approaches in terms of return, compactness of the latent state representation, and robustness to varying degrees of non-stationarity.

ICML Conference 2022 Conference Paper

Identification of Linear Non-Gaussian Latent Hierarchical Structure

Feng Xie 0002
Biwei Huang
Zhengming Chen 0002
Yangbo He
Zhi Geng
Kun Zhang 0001

Traditional causal discovery methods mainly focus on estimating causal relations among measured variables, but in many real-world problems, such as questionnaire-based psychometric studies, measured variables are generated by latent variables that are causally related. Accordingly, this paper investigates the problem of discovering the hidden causal variables and estimating the causal structure, including both the causal relations among latent variables and those between latent and measured variables. We relax the frequently-used measurement assumption and allow the children of latent variables to be latent as well, and hence deal with a specific type of latent hierarchical causal structure. In particular, we define a minimal latent hierarchical structure and show that for linear non-Gaussian models with the minimal latent hierarchical structure, the whole structure is identifiable from only the measured variables. Moreover, we develop a principled method to identify the structure by testing for Generalized Independent Noise (GIN) conditions in specific ways. Experimental results on both synthetic and real-world data show the effectiveness of the proposed approach.

NeurIPS Conference 2022 Conference Paper

Latent Hierarchical Causal Structure Discovery with Rank Constraints

Biwei Huang
Charles Jia Han Low
Feng Xie
Clark Glymour
Kun Zhang

Most causal discovery procedures assume that there are no latent confounders in the system, which is often violated in real-world problems. In this paper, we consider a challenging scenario for causal structure identification, where some variables are latent and they may form a hierarchical graph structure to generate the measured variables; the children of latent variables may still be latent and only leaf nodes are measured, and moreover, there can be multiple paths between every pair of variables (i. e. , it is beyond tree structure). We propose an estimation procedure that can efficiently locate latent variables, determine their cardinalities, and identify the latent hierarchical structure, by leveraging rank deficiency constraints over the measured variables. We show that the proposed algorithm can find the correct Markov equivalence class of the whole graph asymptotically under proper restrictions on the graph structure and with linear causal relations.

AAAI Conference 2021 Conference Paper

DeepTrader: A Deep Reinforcement Learning Approach for Risk-Return Balanced Portfolio Management with Market Conditions Embedding

Zhicheng Wang
Biwei Huang
Shikui Tu
Kun Zhang
Lei Xu

Most existing reinforcement learning (RL)-based portfolio management models do not take into account the market conditions, which limits their performance in risk-return balancing. In this paper, we propose Deep- Trader, a deep RL method to optimize the investment policy. In particular, to tackle the risk-return balancing problem, our model embeds macro market conditions as an indicator to dynamically adjust the proportion between long and short funds, to lower the risk of market fluctuations, with the negative maximum drawdown as the reward function. Additionally, the model involves a unit to evaluate individual assets, which learns dynamic patterns from historical data with the price rising rate as the reward function. Both temporal and spatial dependencies between assets are captured hierarchically by a specific type of graph structure. Particularly, we find that the estimated causal structure best captures the interrelationships between assets, compared to industry classification and correlation. The two units are complementary and integrated to generate a suitable portfolio which fits the market trend well and strikes a balance between return and risk effectively. Experiments on three well-known stock indexes demonstrate the superiority of DeepTrader in terms of risk-gain criteria.

JMLR Journal 2020 Journal Article

Causal Discovery from Heterogeneous/Nonstationary Data

Biwei Huang
Kun Zhang
Jiji Zhang
Joseph Ramsey
Ruben Sanchez-Romero
Clark Glymour
Bernhard Schölkopf

It is commonplace to encounter heterogeneous or nonstationary data, of which the underlying generating process changes across domains or over time. Such a distribution shift feature presents both challenges and opportunities for causal discovery. In this paper, we develop a framework for causal discovery from such data, called Constraint-based causal Discovery from heterogeneous/NOnstationary Data (CD-NOD), to find causal skeleton and directions and estimate the properties of mechanism changes. First, we propose an enhanced constraint-based procedure to detect variables whose local mechanisms change and recover the skeleton of the causal structure over observed variables. Second, we present a method to determine causal orientations by making use of independent changes in the data distribution implied by the underlying causal model, benefiting from information carried by changing distributions. After learning the causal structure, next, we investigate how to efficiently estimate the “driving force” of the nonstationarity of a causal mechanism. That is, we aim to extract from data a low-dimensional representation of changes. The proposed methods are nonparametric, with no hard restrictions on data distributions and causal mechanisms, and do not rely on window segmentation. Furthermore, we find that data heterogeneity benefits causal structure identification even with particular types of confounders. Finally, we show the connection between heterogeneity/nonstationarity and soft intervention in causal discovery. Experimental results on various synthetic and real-world data sets (task-fMRI and stock market data) are presented to demonstrate the efficacy of the proposed methods. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2020. ( edit, beta )

AAAI Conference 2020 Conference Paper

Causal Discovery from Multiple Data Sets with Non-Identical Variable Sets

Biwei Huang
Kun Zhang
Mingming Gong
Clark Glymour

A number of approaches to causal discovery assume that there are no hidden confounders and are designed to learn a ﬁxed causal model from a single data set. Over the last decade, with closer cooperation across laboratories, we are able to accumulate more variables and data for analysis, while each lab may only measure a subset of them, due to technical constraints or to save time and cost. This raises a question of how to handle causal discovery from multiple data sets with non-identical variable sets, and at the same time, it would be interesting to see how more recorded variables can help to mitigate the confounding problem. In this paper, we propose a principled method to uniquely identify causal relationships over the integrated set of variables from multiple data sets, in linear, non-Gaussian cases. The proposed method also allows distribution shifts across data sets. Theoretically, we show that the causal structure over the integrated set of variables is identiﬁable under testable conditions. Furthermore, we present two types of approaches to parameter estimation: one is based on maximum likelihood, and the other is likelihood free and leverages generative adversarial nets to improve scalability of the estimation procedure. Experimental results on various synthetic and real-world data sets are presented to demonstrate the eﬃcacy of our methods.

NeurIPS Conference 2020 Conference Paper

Domain Adaptation as a Problem of Inference on Graphical Models

Kun Zhang
Mingming Gong
Petar Stojanov
Biwei Huang
Qingsong Liu
Clark Glymour

This paper is concerned with data-driven unsupervised domain adaptation, where it is unknown in advance how the joint distribution changes across domains, i. e. , what factors or modules of the data distribution remain invariant or change across domains. To develop an automated way of domain adaptation with multiple source domains, we propose to use a graphical model as a compact way to encode the change property of the joint distribution, which can be learned from data, and then view domain adaptation as a problem of Bayesian inference on the graphical models. Such a graphical model distinguishes between constant and varied modules of the distribution and specifies the properties of the changes across domains, which serves as prior knowledge of the changing modules for the purpose of deriving the posterior of the target variable $Y$ in the target domain. This provides an end-to-end framework of domain adaptation, in which additional knowledge about how the joint distribution changes, if available, can be directly incorporated to improve the graphical representation. We discuss how causality-based domain adaptation can be put under this umbrella. Experimental results on both synthetic and real data demonstrate the efficacy of the proposed framework for domain adaptation.

NeurIPS Conference 2020 Conference Paper

Generalized Independent Noise Condition for Estimating Latent Variable Causal Graphs

Feng Xie
Ruichu Cai
Biwei Huang
Clark Glymour
Zhifeng Hao
Kun Zhang

Causal discovery aims to recover causal structures or models underlying the observed data. Despite its success in certain domains, most existing methods focus on causal relations between observed variables, while in many scenarios the observed ones may not be the underlying causal variables (e. g. , image pixels), but are generated by latent causal variables or confounders that are causally related. To this end, in this paper, we consider Linear, Non-Gaussian Latent variable Models (LiNGLaMs), in which latent confounders are also causally related, and propose a Generalized Independent Noise (GIN) condition to estimate such latent variable graphs. Specifically, for two observed random vectors $\mathbf{Y}$ and $\mathbf{Z}$, GIN holds if and only if $\omega^{\intercal}\mathbf{Y}$ and $\mathbf{Z}$ are statistically independent, where $\omega$ is a parameter vector characterized from the cross-covariance between $\mathbf{Y}$ and $\mathbf{Z}$. From the graphical view, roughly speaking, GIN implies that causally earlier latent common causes of variables in $\mathbf{Y}$ d-separate $\mathbf{Y}$ from $\mathbf{Z}$. Interestingly, we find that the independent noise condition, i. e. , if there is no confounder, causes are independent from the error of regressing the effect on the causes, can be seen as a special case of GIN. Moreover, we show that GIN helps locate latent variables and identify their causal structure, including causal directions. We further develop a recursive learning algorithm to achieve these goals. Experimental results on synthetic and real-world data demonstrate the effectiveness of our method.

ICML Conference 2019 Conference Paper

Causal Discovery and Forecasting in Nonstationary Environments with State-Space Models

Biwei Huang
Kun Zhang 0001
Mingming Gong
Clark Glymour

In many scientific fields, such as economics and neuroscience, we are often faced with nonstationary time series, and concerned with both finding causal relations and forecasting the values of variables of interest, both of which are particularly challenging in such nonstationary environments. In this paper, we study causal discovery and forecasting for nonstationary time series. By exploiting a particular type of state-space model to represent the processes, we show that nonstationarity helps to identify the causal structure, and that forecasting naturally benefits from learned causal knowledge. Specifically, we allow changes in both causal strengths and noise variances in the nonlinear state-space models, which, interestingly, renders both the causal structure and model parameters identifiable. Given the causal model, we treat forecasting as a problem in Bayesian inference in the causal model, which exploits the time-varying property of the data and adapts to new observations in a principled manner. Experimental results on synthetic and real-world data sets demonstrate the efficacy of the proposed methods.

NeurIPS Conference 2019 Conference Paper

Specific and Shared Causal Relation Modeling and Mechanism-Based Clustering

Biwei Huang
Kun Zhang
Pengtao Xie
Mingming Gong
Eric Xing
Clark Glymour

State-of-the-art approaches to causal discovery usually assume a fixed underlying causal model. However, it is often the case that causal models vary across domains or subjects, due to possibly omitted factors that affect the quantitative causal effects. As a typical example, causal connectivity in the brain network has been reported to vary across individuals, with significant differences across groups of people, such as autistics and typical controls. In this paper, we develop a unified framework for causal discovery and mechanism-based group identification. In particular, we propose a specific and shared causal model (SSCM), which takes into account the variabilities of causal relations across individuals/groups and leverages their commonalities to achieve statistically reliable estimation. The learned SSCM gives the specific causal knowledge for each individual as well as the general trend over the population. In addition, the estimated model directly provides the group information of each individual. Experimental results on synthetic and real-world data demonstrate the efficacy of the proposed method.

NeurIPS Conference 2018 Conference Paper

Multi-domain Causal Structure Learning in Linear Systems

AmirEmad Ghassami
Negar Kiyavash
Biwei Huang
Kun Zhang

We study the problem of causal structure learning in linear systems from observational data given in multiple domains, across which the causal coefficients and/or the distribution of the exogenous noises may vary. The main tool used in our approach is the principle that in a causally sufficient system, the causal modules, as well as their included parameters, change independently across domains. We first introduce our approach for finding causal direction in a system comprising two variables and propose efficient methods for identifying causal direction. Then we generalize our methods to causal structure learning in networks of variables. Most of previous work in structure learning from multi-domain data assume that certain types of invariance are held in causal modules across domains. Our approach unifies the idea in those works and generalizes to the case that there is no such invariance across the domains. Our proposed methods are generally capable of identifying causal direction from fewer than ten domains. When the invariance property holds, two domains are generally sufficient.

IJCAI Conference 2017 Conference Paper

Causal Discovery from Nonstationary/Heterogeneous Data: Skeleton Estimation and Orientation Determination

Kun Zhang
Biwei Huang
Jiji Zhang
Clark Glymour
Bernhard Schölkopf

It is commonplace to encounter nonstationary or heterogeneous data, of which the underlying generating process changes over time or across data sets (the data sets may have different experimental conditions or data collection conditions). Such a distribution shift feature presents both challenges and opportunities for causal discovery. In this paper we develop a principled framework for causal discovery from such data, called Constraint-based causal Discovery from Nonstationary/heterogeneous Data (CD-NOD), which addresses two important questions. First, we propose an enhanced constraint-based procedure to detect variables whose local mechanisms change and recover the skeleton of the causal structure over observed variables. Second, we present a way to determine causal orientations by making use of independence changes in the data distribution implied by the underlying causal model, benefiting from information carried by changing distributions. Experimental results on various synthetic and real-world data sets are presented to demonstrate the efficacy of our methods.

UAI Conference 2016 Conference Paper

On the Identifiability and Estimation of Functional Causal Models in the Presence of Outcome-Dependent Selection

Kun Zhang 0001
Jiji Zhang
Biwei Huang
Bernhard Schölkopf
Clark Glymour

We study the identifiability and estimation of functional causal models under selection bias, with a focus on the situation where the selection depends solely on the e↵ect variable, which is known as outcome-dependent selection. We address two questions of identifiability: the identifiability of the causal direction between two variables in the presence of selection bias, and, given the causal direction, the identifiability of the model with outcomedependent selection. Regarding the first, we show that in the framework of post-nonlinear causal models, once outcome-dependent selection is properly modeled, the causal direction between two variables is generically identifiable; regarding the second, we identify some mild conditions under which an additive noise causal model with outcome-dependent selection is to a large extent identifiable. We also propose two methods for estimating an additive noise model from data that are generated with outcome-dependent selection.

IJCAI Conference 2015 Conference Paper

Identification of Time-Dependent Causal Model: A Gaussian Process Treatment

Biwei Huang
Kun Zhang
Bernhard Sch
ouml; lkopf

Most approaches to causal discovery assume a fixed (or time-invariant) causal model; however, in practical situations, especially in neuroscience and economics, causal relations might be timedependent for various reasons. This paper aims to identify the time-dependent causal relations from observational data. We consider general formulations for time-varying causal modeling on stochastic processes, which can also capture the causal influence from a certain type of unobserved confounders. We focus on two issues: one is whether such a causal model, including the causal direction, is identifiable from observational data; the other is how to estimate such a model in a principled way. We show that under appropriate assumptions, the causal structure is identifiable according to our formulated model. We then propose a principled way for its estimation by extending Gaussian Process regression, which enables an automatic way to learn how the causal model changes over time. Experimental results on both artificial and real data demonstrate the practical usefulness of time-dependent causal modeling and the effectiveness of the proposed approach for estimation.