Zhi Geng

ICML Conference 2025 Conference Paper

Causal Attribution Analysis for Continuous Outcomes

• Shanshan Luo
• Yixuan Yu 0006
• Chunchen Liu
• Feng Xie 0002
• Zhi Geng

Previous studies have extensively addressed the attribution problem for binary outcome variables. However, in many practical scenarios, the outcome variable is continuous, and simply binarizing it may result in information loss or biased conclusions. To address this issue, we propose a series of posterior causal estimands for retrospectively evaluating multiple correlated causes from a continuous outcome. These estimands include posterior intervention effects, posterior total causal effects, and posterior natural direct effects. Under assumptions of sequential ignorability, monotonicity, and perfect positive rank, we show that the posterior causal estimands of interest are identifiable and present the corresponding identification equations. We also provide a simple but effective estimation procedure and establish asymptotic properties of the proposed estimators. An artificial hypertension example and a real developmental toxicity dataset are employed to illustrate our method.

ICML Conference 2025 Conference Paper

Data-Driven Selection of Instrumental Variables for Additive Nonlinear, Constant Effects Models

• Xichen Guo
• Feng Xie 0002
• Yan Zeng 0002
• Hao Zhang 0079
• Zhi Geng

We consider the problem of selecting instrumental variables from observational data, a fundamental challenge in causal inference. Existing methods mostly focus on additive linear, constant effects models, limiting their applicability in complex real-world scenarios. In this paper, we tackle a more general and challenging setting: the additive non-linear, constant effects model. We first propose a novel testable condition, termed the Cross Auxiliary-based independent Test (CAT) condition, for selecting the valid IV set. We show that this condition is both necessary and sufficient for identifying valid instrumental variable sets within such a model under milder assumptions. Building on this condition, we develop a practical algorithm for selecting the set of valid instrumental variables. Extensive experiments on both synthetic and two real-world datasets demonstrate the effectiveness and robustness of our proposed approach, highlighting its potential for broader applications in causal analysis.

ICML Conference 2025 Conference Paper

Fairness on Principal Stratum: A New Perspective on Counterfactual Fairness

• Haoxuan Li 0001
• Zeyu Tang 0002
• Zhichao Jiang
• Zhuangyan Fang
• Yue Liu
• Zhi Geng
• Kun Zhang 0001

Fairness in human and algorithmic decision-making is crucial in areas such as criminal justice, education, and social welfare. Recently, counterfactual fairness has drawn increasing research interest, suggesting that decision-making for individuals should remain the same when intervening with different values on protected attributes. Nevertheless, the question of "which attributes and individuals should be protected" is rarely discussed in the existing counterfactual fairness literature. For example, when considering leg disability as a protected attribute, the algorithms should not treat individuals with leg disabilities differently in college admissions, but one may naturally consider this factor when selecting runner athletes. In other words, when and how to enforce fairness is expected to depend on the causal relation between the protected attribute and the outcome of interest. Formally, this paper proposes principal counterfactual fairness using the concept of principal stratification from the causal inference literature, focusing on whether an algorithm is counterfactually fair for individuals whose protected attribute has no individual causal effect on the outcome of interest. To examine whether an algorithm satisfies principal counterfactual fairness, we derive the statistical bounds and propose a post-processing approach to achieving principal counterfactual fairness with minimal individual decision changes. Experiments are conducted using synthetic and real-world datasets to verify the effectiveness of our methods.

ICML Conference 2025 Conference Paper

Local Identifying Causal Relations in the Presence of Latent Variables

• Zheng Li
• Zeyu Liu
• Feng Xie 0002
• Hao Zhang 0079
• Chunchen Liu
• Zhi Geng

We tackle the problem of identifying whether a variable is the cause of a specified target using observational data. State-of-the-art causal learning algorithms that handle latent variables typically rely on identifying the global causal structure, often represented as a partial ancestral graph (PAG), to infer causal relationships. Although effective, these approaches are often redundant and computationally expensive when the focus is limited to a specific causal relationship. In this work, we introduce novel local characterizations that are necessary and sufficient for various types of causal relationships between two variables, enabling us to bypass the need for global structure learning. Leveraging these local insights, we develop efficient and fully localized algorithms that accurately identify causal relationships from observational data. We theoretically demonstrate the soundness and completeness of our approach. Extensive experiments on benchmark networks and real-world datasets further validate the effectiveness and efficiency of our method.

NeurIPS Conference 2025 Conference Paper

Local Learning for Covariate Selection in Nonparametric Causal Effect Estimation with Latent Variables

• Zheng Li
• Xichen Guo
• Feng Xie
• Yan Zeng
• Hao Zhang
• Zhi Geng

Estimating causal effects from nonexperimental data is a fundamental problem in many fields of science. A key component of this task is selecting an appropriate set of covariates for confounding adjustment to avoid bias. Most existing methods for covariate selection often assume the absence of latent variables and rely on learning the global causal structure among variables. However, identifying the global structure can be unnecessary and inefficient, especially when our primary interest lies in estimating the effect of a treatment variable on an outcome variable. To address this limitation, we propose a novel local learning approach for covariate selection in nonparametric causal effect estimation, which accounts for the presence of latent variables. Our approach leverages testable independence and dependence relationships among observed variables to identify a valid adjustment set for a target causal relationship, ensuring both soundness and completeness under standard assumptions. We validate the effectiveness of our algorithm through extensive experiments on both synthetic and real-world data.

NeurIPS Conference 2024 Conference Paper

A Local Method for Satisfying Interventional Fairness with Partially Known Causal Graphs

• Haoxuan Li
• Yue Liu
• Zhi Geng
• Kun Zhang

Developing fair automated machine learning algorithms is critical in making safe and trustworthy decisions. Many causality-based fairness notions have been proposed to address the above issues by quantifying the causal connections between sensitive attributes and decisions, and when the true causal graph is fully known, certain algorithms that achieve interventional fairness have been proposed. However, when the true causal graph is unknown, it is still challenging to effectively and efficiently exploit partially directed acyclic graphs (PDAGs) to achieve interventional fairness. To exploit the PDAGs for achieving interventional fairness, previous methods have been built on variable selection or causal effect identification, but limited to reduced prediction accuracy or strong assumptions. In this paper, we propose a general min-max optimization framework that can achieve interventional fairness with promising prediction accuracy and can be extended to maximally oriented PDAGs (MPDAGs) with added background knowledge. Specifically, we first estimate all possible treatment effects of sensitive attributes on a given prediction model from all possible adjustment sets of sensitive attributes via an efficient local approach. Next, we propose to alternatively update the prediction model and possible estimated causal effects, where the prediction model is trained via a min-max loss to control the worst-case fairness violations. Extensive experiments on synthetic and real-world datasets verify the superiority of our methods. To benefit the research community, we have released our project at https: //github. com/haoxuanli-pku/NeurIPS24-Interventional-Fairness-with-PDAGs.

ICML Conference 2024 Conference Paper

Automating the Selection of Proxy Variables of Unmeasured Confounders

• Feng Xie 0002
• Zhengming Chen 0002
• Shanshan Luo
• Wang Miao
• Ruichu Cai
• Zhi Geng

Recently, interest has grown in the use of proxy variables of unobserved confounding for inferring the causal effect in the presence of unmeasured confounders from observational data. One difficulty inhibiting the practical use is finding valid proxy variables of unobserved confounding to a target causal effect of interest. These proxy variables are typically justified by background knowledge. In this paper, we investigate the estimation of causal effects among multiple treatments and a single outcome, all of which are affected by unmeasured confounders, within a linear causal model, without prior knowledge of the validity of proxy variables. To be more specific, we first extend the existing proxy variable estimator, originally addressing a single unmeasured confounder, to accommodate scenarios where multiple unmeasured confounders exist between the treatments and the outcome. Subsequently, we present two different sets of precise identifiability conditions for selecting valid proxy variables of unmeasured confounders, based on the second-order statistics and higher-order statistics of the data, respectively. Moreover, we propose two data-driven methods for the selection of proxy variables and for the unbiased estimation of causal effects. Theoretical analysis demonstrates the correctness of our proposed algorithms. Experimental results on both synthetic and real-world data show the effectiveness of the proposed approach.

ICLR Conference 2024 Conference Paper

Be Aware of the Neighborhood Effect: Modeling Selection Bias under Interference

• Haoxuan Li 0001
• Chunyuan Zheng 0001
• Sihao Ding 0003
• Peng Wu 0012
• Zhi Geng
• Fuli Feng
• Xiangnan He 0001

Selection bias in recommender system arises from the recommendation process of system filtering and the interactive process of user selection. Many previous studies have focused on addressing selection bias to achieve unbiased learning of the prediction model, but ignore the fact that potential outcomes for a given user-item pair may vary with the treatments assigned to other user-item pairs, named neighborhood effect. To fill the gap, this paper formally formulates the neighborhood effect as an interference problem from the perspective of causal inference, and introduces a treatment representation to capture the neighborhood effect. On this basis, we propose a novel ideal loss that can be used to deal with selection bias in the presence of neighborhood effect. We further develop two new estimators for estimating the proposed ideal loss. We theoretically establish the connection between the proposed and previous debiasing methods ignoring the neighborhood effect, showing that the proposed methods can achieve unbiased learning when both selection bias and neighborhood effects are present, while the existing methods are biased. Extensive semi-synthetic and real-world experiments are conducted to demonstrate the effectiveness of the proposed methods.

ICLR Conference 2024 Conference Paper

Debiased Collaborative Filtering with Kernel-Based Causal Balancing

• Haoxuan Li 0001
• Chunyuan Zheng 0001
• Yanghao Xiao
• Peng Wu 0012
• Zhi Geng
• Xu Chen 0017
• Peng Cui 0001

Collaborative filtering builds personalized models from the collected user feedback. However, the collected data is observational rather than experimental, leading to various biases in the data, which can significantly affect the learned model. To address this issue, many studies have focused on propensity-based methods to combat the selection bias by reweighting the sample loss, and demonstrate that balancing is important for debiasing both theoretically and empirically. However, there are two questions that still need to be addressed: which function class should be balanced and how to effectively balance that function class? In this paper, we first perform theoretical analysis to show the effect of balancing finite-dimensional function classes on the bias of IPS and DR methods, and based on this, we propose a universal kernel-based balancing method to balance functions on the reproducing kernel Hilbert space. In addition, we propose a novel adaptive causal balancing method during the alternating update between unbiased evaluation and training of the prediction model. Specifically, the prediction loss of the model is projected in the kernel-based covariate function space, and the projection coefficients are used to determine which functions should be prioritized for balancing to reduce the estimation bias. We conduct extensive experiments on three real-world datasets to demonstrate the effectiveness of the proposed approach.

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

Identification and Estimation of the Bi-Directional MR with Some Invalid Instruments

• Feng Xie
• Zhen Yao
• Lin Xie
• Yan Zeng
• Zhi Geng

We consider the challenging problem of estimating causal effects from purely observational data in the bi-directional Mendelian randomization (MR), where some invalid instruments, as well as unmeasured confounding, usually exist. To address this problem, most existing methods attempt to find proper valid instrumental variables (IVs) for the target causal effect by expert knowledge or by assuming that the causal model is a one-directional MR model. As such, in this paper, we first theoretically investigate the identification of the bi-directional MR from observational data. In particular, we provide necessary and sufficient conditions under which valid IV sets are correctly identified such that the bi-directional MR model is identifiable, including the causal directions of a pair of phenotypes (i. e. , the treatment and outcome). Moreover, based on the identification theory, we develop a cluster fusion-like method to discover valid IV sets and estimate the causal effects of interest. We theoretically demonstrate the correctness of the proposed algorithm. Experimental results show the effectiveness of our method for estimating causal effects in both one-directional and bi-directional MR models.

ICML Conference 2024 Conference Paper

Local Causal Structure Learning in the Presence of Latent Variables

• Feng Xie 0002
• Zheng Li
• Peng Wu 0012
• Yan Zeng 0002
• Chunchen Liu
• Zhi Geng

Discovering causal relationships from observational data, particularly in the presence of latent variables, poses a challenging problem. While current local structure learning methods have proven effective and efficient when the focus lies solely on the local relationships of a target variable, they operate under the assumption of causal sufficiency. This assumption implies that all the common causes of the measured variables are observed, leaving no room for latent variables. Such a premise can be easily violated in various real-world applications, resulting in inaccurate structures that may adversely impact downstream tasks. In light of this, our paper delves into the primary investigation of locally identifying potential parents and children of a target from observational data that may include latent variables. Specifically, we harness the causal information from m-separation and V-structures to derive theoretical consistency results, effectively bridging the gap between global and local structure learning. Together with the newly developed stop rules, we present a principled method for determining whether a variable is a direct cause or effect of a target. Further, we theoretically demonstrate the correctness of our approach under the standard causal Markov and faithfulness conditions, with infinite samples. Experimental results on both synthetic and real-world data validate the effectiveness and efficiency of our approach.

ICML Conference 2024 Conference Paper

Relaxing the Accurate Imputation Assumption in Doubly Robust Learning for Debiased Collaborative Filtering

• Haoxuan Li 0001
• Chunyuan Zheng 0001
• Shuyi Wang
• Kunhan Wu
• Hao Wang 0049
• Peng Wu 0012
• Zhi Geng
• Xu Chen 0017

Recommender system aims to recommend items or information that may interest users based on their behaviors and preferences. However, there may be sampling selection bias in the data collection process, i. e. , the collected data is not a representative of the target population. Many debiasing methods are developed based on pseudo-labelings. Nevertheless, the validity of these methods relies heavily on accurate pseudo-labelings (i. e. , the imputed labels), which is difficult to satisfy in practice. In this paper, we theoretically propose several novel doubly robust estimators that are unbiased when either (a) the pseudo-labelings deviate from the true labels with an arbitrary user-specific inductive bias, item-specific inductive bias, or a combination of both, or (b) the learned propensities are accurate. We further propose a propensity reconstruction learning approach that adaptively updates the constraint weights using an attention mechanism and effectively controls the variance. Extensive experiments show that our approach outperforms the state-of-the-art on one semi-synthetic and three real-world datasets.

UAI Conference 2023 Conference Paper

Conditional counterfactual causal effect for individual attribution

• Ruiqi Zhao
• Lei Zhang 0006
• Shengyu Zhu 0001
• Zitong Lu
• Zhenhua Dong
• Chaoliang Zhang
• Jun Xu 0001
• Zhi Geng

Identifying the causes of an event, also termed as causal attribution, is a commonly encountered task in many application problems. Available methods, mostly in Bayesian or causal inference literature, suffer from two main drawbacks: 1) cannot attribute for individuals, and 2) attributing one single cause at a time and cannot deal with the interaction effect among multiple causes. In this paper, based on our proposed new measurement, called conditional counterfactual causal effect (CCCE), we introduce an individual causal attribution method, which is able to utilize the individual observation as the evidence and consider common influence and interaction effect of multiple causes simultaneously. We discuss the identifiability of CCCE and also give the identification formulas under proper assumptions. Finally, we conduct experiments on simulated and real data to illustrate the effectiveness of CCCE and the results show that our proposed method outperforms significantly state-of-the-art methods.

NeurIPS Conference 2023 Conference Paper

Removing Hidden Confounding in Recommendation: A Unified Multi-Task Learning Approach

• Haoxuan Li
• Kunhan Wu
• Chunyuan Zheng
• Yanghao Xiao
• Hao Wang
• Zhi Geng
• Fuli Feng
• Xiangnan He

In recommender systems, the collected data used for training is always subject to selection bias, which poses a great challenge for unbiased learning. Previous studies proposed various debiasing methods based on observed user and item features, but ignored the effect of hidden confounding. To address this problem, recent works suggest the use of sensitivity analysis for worst-case control of the unknown true propensity, but only valid when the true propensity is near to the nominal propensity within a finite bound. In this paper, we first perform theoretical analysis to reveal the possible failure of previous approaches, including propensity-based, multi-task learning, and bi-level optimization methods, in achieving unbiased learning when hidden confounding is present. Then, we propose a unified multi-task learning approach to remove hidden confounding, which uses a few unbiased ratings to calibrate the learned nominal propensities and nominal error imputations from biased data. We conduct extensive experiments on three publicly available benchmark datasets containing a fully exposed large-scale industrial dataset, validating the effectiveness of the proposed methods in removing hidden confounding.

ICML Conference 2023 Conference Paper

Trustworthy Policy Learning under the Counterfactual No-Harm Criterion

• Haoxuan Li 0001
• Chunyuan Zheng 0001
• Yixiao Cao
• Zhi Geng
• Yue Liu
• Peng Wu 0012

Trustworthy policy learning has significant importance in making reliable and harmless treatment decisions for individuals. Previous policy learning approaches aim at the well-being of subgroups by maximizing the utility function (e. g. , conditional average causal effects, post-view click-through&conversion rate in recommendations), however, individual-level counterfactual no-harm criterion has rarely been discussed. In this paper, we first formalize the counterfactual no-harm criterion for policy learning from a principal stratification perspective. Next, we propose a novel upper bound for the fraction negatively affected by the policy and show the consistency and asymptotic normality of the estimator. Based on the estimators for the policy utility and harm upper bounds, we further propose a policy learning approach that satisfies the counterfactual no-harm criterion, and prove its consistency to the optimal policy reward for parametric and non-parametric policy classes, respectively. Extensive experiments are conducted to show the effectiveness of the proposed policy learning approach for satisfying the counterfactual no-harm criterion.

AIJ Journal 2022 Journal Article

A local method for identifying causal relations under Markov equivalence

• Zhuangyan Fang
• Yue Liu
• Zhi Geng
• Shengyu Zhu
• Yangbo He

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.

UAI Conference 2020 Conference Paper

Collapsible IDA: Collapsing Parental Sets for Locally Estimating Possible Causal Effects

• Yue Liu
• Zhuangyan Fang
• Yangbo He
• Zhi Geng

It is clear that some causal effects cannot be identified from observational data when the causal directed acyclic graph is absent. In such cases, IDA is a useful framework which estimates all possible causal effects by adjusting for all possible parental sets. In this paper, we combine the adjustment set selection procedure with the original IDA framework. Our goal is to find a common set that can be subtracted from all possible parental sets without influencing the back-door adjustment. To this end, we first introduce graphical conditions to decide whether a treatment’s neighbor or parent in a completed partially directed acyclic graph (CPDAG) can be subtracted and then provide a procedure to construct a subtractable set from those subtractable vertices. We next combine the procedure with the IDA framework and provide a fully local modification of IDA. Experimental results show that, with our modification, both the number of possible parental sets and the size of each possible parental set enumerated by the modified IDA decrease, making it possible to estimate all possible causal effects more efficiently.

JMLR Journal 2020 Journal Article

Local Causal Network Learning for Finding Pairs of Total and Direct Effects

• Yue Liu
• Zhuangyan Fang
• Yangbo He
• Zhi Geng
• Chunchen Liu

In observational studies, it is important to evaluate not only the total effect but also the direct and indirect effects of a treatment variable on a response variable. In terms of local structural learning of causal networks, we try to find all possible pairs of total and direct causal effects, which can further be used to calculate indirect causal effects. An intuitive global learning approach is first to find an essential graph over all variables representing all Markov equivalent causal networks, and then enumerate all equivalent networks and estimate a pair of the total and direct effects for each of them. However, it could be inefficient to learn an essential graph and enumerate equivalent networks when the true causal graph is large. In this paper, we propose a local learning approach instead. In the local learning approach, we first learn locally a chain component containing the treatment. Then, if necessary, we learn locally a chain component containing the response. Next, we locally enumerate all possible pairs of the treatment's parents and the response's parents. Finally based on these pairs, we find all possible pairs of total and direct effects of the treatment on the response. [abs] [ pdf ][ bib ] &copy JMLR 2020. ( edit, beta )

TIST Journal 2019 Journal Article

Local Learning Approaches for Finding Effects of a Specified Cause and Their Causal Paths

• Yue Liu
• Zheng Cai
• Chunchen Liu
• Zhi Geng

Causal networks are used to describe and to discover causal relationships among variables and data generating mechanisms. There have been many approaches for learning a global causal network of all observed variables. In many applications, we may be interested in finding what are the effects of a specified cause variable and what are the causal paths from the cause variable to its effects. Instead of learning a global causal network, we propose several local learning approaches for finding all effects (or descendants) of the specified cause variable and the causal paths from the cause variable to some effect variable of interest. We discuss the identifiability of the effects and the causal paths from observed data and prior knowledge. For the case that the causal paths are not identifiable, our approaches try to find a path set that contains the causal paths of interest.

TIST Journal 2015 Journal Article

Bounds on Direct and Indirect Effects of Treatment on a Continuous Endpoint

• Peng Luo
• Zhi Geng

Direct effect of a treatment variable on an endpoint variable and indirect effect through a mediate variable are important concepts for understanding a causal mechanism. However, the randomized assignment of treatment is not sufficient for identifying the direct and indirect effects, and extra assumptions and conditions are required, such as the sequential ignorability assumption without unobserved confounders or the sequential potential ignorability assumption. But these assumptions may not be credible in many applications. In this article, we consider the bounds on controlled direct effect, natural direct effect, and natural indirect effect without these extra assumptions. Cai et al. [2008] presented the bounds for the case of a binary endpoint, and we extend their results to the general case for an arbitrary endpoint.

TIST Journal 2015 Journal Article

Semiparametric Inference of the Complier Average Causal Effect with Nonignorable Missing Outcomes

• Hua Chen
• Peng Ding
• Zhi Geng
• Xiao-Hua Zhou

Noncompliance and missing data often occur in randomized trials, which complicate the inference of causal effects. When both noncompliance and missing data are present, previous papers proposed moment and maximum likelihood estimators for binary and normally distributed continuous outcomes under the latent ignorable missing data mechanism. However, the latent ignorable missing data mechanism may be violated in practice, because the missing data mechanism may depend directly on the missing outcome itself. Under noncompliance and an outcome-dependent nonignorable missing data mechanism, previous studies showed the identifiability of complier average causal effect for discrete outcomes. In this article, we study the semiparametric identifiability and estimation of complier average causal effect in randomized clinical trials with both all-or-none noncompliance and outcome-dependent nonignorable missing continuous outcomes, and propose a two-step maximum likelihood estimator in order to eliminate the infinite dimensional nuisance parameter. Our method does not need to specify a parametric form for the missing data mechanism. We also evaluate the finite sample property of our method via extensive simulation studies and sensitivity analysis, with an application to a double-blinded psychiatric clinical trial.

JMLR Journal 2008 Journal Article

A Recursive Method for Structural Learning of Directed Acyclic Graphs

• Xianchao Xie
• Zhi Geng

In this paper, we propose a recursive method for structural learning of directed acyclic graphs (DAGs), in which a problem of structural learning for a large DAG is first decomposed into two problems of structural learning for two small vertex subsets, each of which is then decomposed recursively into two problems of smaller subsets until none subset can be decomposed further. In our approach, search for separators of a pair of variables in a large DAG is localized to small subsets, and thus the approach can improve the efficiency of searches and the power of statistical tests for structural learning. We show how the recent advances in the learning of undirected graphical models can be employed to facilitate the decomposition. Simulations are given to demonstrate the performance of the proposed method. [abs] [ pdf ][ bib ] &copy JMLR 2008. ( edit, beta )

JMLR Journal 2008 Journal Article

Active Learning of Causal Networks with Intervention Experiments and Optimal Designs

• Yang-Bo He
• Zhi Geng

The causal discovery from data is important for various scientific investigations. Because we cannot distinguish the different directed acyclic graphs (DAGs) in a Markov equivalence class learned from observational data, we have to collect further information on causal structures from experiments with external interventions. In this paper, we propose an active learning approach for discovering causal structures in which we first find a Markov equivalence class from observational data, and then we orient undirected edges in every chain component via intervention experiments separately. In the experiments, some variables are manipulated through external interventions. We discuss two kinds of intervention experiments, randomized experiment and quasi-experiment. Furthermore, we give two optimal designs of experiments, a batch-intervention design and a sequential-intervention design, to minimize the number of manipulated variables and the set of candidate structures based on the minimax and the maximum entropy criteria. We show theoretically that structural learning can be done locally in subgraphs of chain components without need of checking illegal v-structures and cycles in the whole network and that a Markov equivalence subclass obtained after each intervention can still be depicted as a chain graph. [abs] [ pdf ][ bib ] &copy JMLR 2008. ( edit, beta )

JMLR Journal 2008 Journal Article

Structural Learning of Chain Graphs via Decomposition

• Zongming Ma
• Xianchao Xie
• Zhi Geng

Chain graphs present a broad class of graphical models for description of conditional independence structures, including both Markov networks and Bayesian networks as special cases. In this paper, we propose a computationally feasible method for the structural learning of chain graphs based on the idea of decomposing the learning problem into a set of smaller scale problems on its decomposed subgraphs. The decomposition requires conditional independencies but does not require the separators to be complete subgraphs. Algorithms for both skeleton recovery and complex arrow orientation are presented. Simulations under a variety of settings demonstrate the competitive performance of our method, especially when the underlying graph is sparse. [abs] [ pdf ][ bib ] &copy JMLR 2008. ( edit, beta )

AIJ Journal 2006 Journal Article

Decomposition of structural learning about directed acyclic graphs

• Xianchao Xie
• Zhi Geng
• Qiang Zhao