Ruoxuan Xiong

Anpeng Wu, Kun Kuang, Ruoxuan Xiong et al.

Causal inference is the process of using assumptions, study designs, and estimation strategies to draw conclusions about the causal relationships between variables based on data. This allows researchers to better understand the underlying mechanisms at work in complex systems and make more informed decisions. In many settings, we may not fully observe all the confounders that affect both the treatment and outcome variables, complicating the estimation of causal effects. To address this problem, a growing literature in both causal inference and machine learning proposes to use Instrumental Variables (IV). This paper serves as the first effort to systematically and comprehensively introduce and discuss the IV methods and their applications in both causal inference and machine learning. First, we provide the formal definition of IVs and discuss the identification problem of IV regression methods under different assumptions. Second, we categorize the existing work on IV methods into three streams according to the focus on the proposed methods, including two-stage least squares with IVs, control function with IVs, and evaluation of IVs. For each stream, we present both the classical causal inference methods, and recent developments in the machine learning literature. Then, we introduce a variety of applications of IV methods in real-world scenarios and provide a summary of the available datasets and algorithms. Finally, we summarize the literature, discuss the open problems and suggest promising future research directions for IV methods and their applications. We also develop a toolkit of IVs methods reviewed in this survey at https://github.com/causal-machine-learning-lab/mliv.

Yingrong Wang, Haoxuan Li, Minqin Zhu et al.

Causal inference plays an important role in explanatory analysis and decision making across various fields like statistics, marketing, health care, and education. Its main task is to estimate treatment effects and make intervention policies. Traditionally, most of the previous works typically focus on the binary treatment setting that there is only one treatment for a unit to adopt or not. However, in practice, the treatment can be much more complex, encompassing multi-valued, continuous, or bundle options. In this paper, we refer to these as complex treatments and systematically and comprehensively review the causal inference methods for addressing them. First, we formally revisit the problem definition, the basic assumptions, and their possible variations under specific conditions. Second, we sequentially review the related methods for multi-valued, continuous, and bundled treatment settings. In each situation, we tentatively divide the methods into two categories: those conforming to the unconfoundedness assumption and those violating it. Subsequently, we discuss the available datasets and open-source codes. Finally, we provide a brief summary of these works and suggest potential directions for future research.

Ziyu Zhao, Yuqi Bai, Kun Kuang et al.

Estimates of individual treatment effects from networked observational data are attracting increasing attention these days. One major challenge in network scenarios is the violation of the stable unit treatment value assumption (SUTVA), which assumes that the treatment assignment of a unit does not influence others' outcomes. In network data, due to interference, the outcome of a unit is influenced not only by its treatment (i.e., direct effects) but also by others' treatments (i.e., spillover effects). Furthermore, the influences from other units are always heterogeneous (e.g., friends with similar interests affect a person differently than friends with different interests). In this paper, we focus on the problem of estimating individual treatment effects (both direct and spillover effects) under heterogeneous interference. To address this issue, we propose a novel Dual Weighting Regression (DWR) algorithm by simultaneously learning attention weights that capture the heterogeneous interference and sample weights to eliminate the complex confounding bias in networks. We formulate the entire learning process as a bi-level optimization problem. In theory, we present generalization error bounds for individual treatment effect estimation. Extensive experiments on four benchmark datasets demonstrate that the proposed DWR algorithm outperforms state-of-the-art methods for estimating individual treatment effects under heterogeneous interference.

Anpeng Wu, Kun Kuang, Ruoxuan Xiong et al.

The advent of the big data era brought new opportunities and challenges to draw treatment effect in data fusion, that is, a mixed dataset collected from multiple sources (each source with an independent treatment assignment mechanism). Due to possibly omitted source labels and unmeasured confounders, traditional methods cannot estimate individual treatment assignment probability and infer treatment effect effectively. Therefore, we propose to reconstruct the source label and model it as a Group Instrumental Variable (GIV) to implement IV-based Regression for treatment effect estimation. In this paper, we conceptualize this line of thought and develop a unified framework (Meta-EM) to (1) map the raw data into a representation space to construct Linear Mixed Models for the assigned treatment variable; (2) estimate the distribution differences and model the GIV for the different treatment assignment mechanisms; and (3) adopt an alternating training strategy to iteratively optimize the representations and the joint distribution to model GIV for IV regression. Empirical results demonstrate the advantages of our Meta-EM compared with state-of-the-art methods.

Anpeng Wu, Kun Kuang, Ruoxuan Xiong et al.

This paper studies the confounding effects from the unmeasured confounders and the imbalance of observed confounders in IV regression and aims at unbiased causal effect estimation. Recently, nonlinear IV estimators were proposed to allow for nonlinear model in both stages. However, the observed confounders may be imbalanced in stage 2, which could still lead to biased treatment effect estimation in certain cases. To this end, we propose a Confounder Balanced IV Regression (CB-IV) algorithm to jointly remove the bias from the unmeasured confounders and the imbalance of observed confounders. Theoretically, by redefining and solving an inverse problem for potential outcome function, we show that our CB-IV algorithm can unbiasedly estimate treatment effects and achieve lower variance. The IV methods have a major disadvantage in that little prior or theory is currently available to pre-define a valid IV in real-world scenarios. Thus, we study two more challenging settings without pre-defined valid IVs: (1) indistinguishable IVs implicitly present in observations, i.e., mixed-variable challenge, and (2) latent IVs don't appear in observations, i.e., latent-variable challenge. To address these two challenges, we extend our CB-IV by a latent-variable module, namely CB-IV-L algorithm. Extensive experiments demonstrate that our CB-IV(-L) outperforms the existing approaches.

Anpeng Wu, Kun Kuang, Ruoxuan Xiong et al.

In causal inference, encouragement designs (EDs) are widely used to analyze causal effects, when randomized controlled trials (RCTs) are impractical or compliance to treatment cannot be perfectly enforced. Unlike RCTs, which directly allocate treatments, EDs randomly assign encouragement policies that positively motivate individuals to engage in a specific treatment. These random encouragements act as instrumental variables (IVs), facilitating the identification of causal effects through leveraging exogenous perturbations in discrete treatment scenarios. However, real-world applications of encouragement designs often face challenges such as incomplete randomization, limited experimental data, and significantly fewer encouragements compared to treatments, hindering precise causal effect estimation. To address this, this paper introduces novel theories and algorithms for identifying the Conditional Average Treatment Effect (CATE) using variations in encouragement. Further, by leveraging both observational and encouragement data, we propose a generalized IV estimator, named Encouragement-based Counterfactual Regression (EnCounteR), to effectively estimate the causal effects. Extensive experiments on both synthetic and real-world datasets demonstrate the superiority of EnCounteR over existing methods.

Zihan Liang, Ziwen Pan, Ruoxuan Xiong

Multimodal clinical records contain structured measurements and clinical notes recorded over time, offering rich temporal information about the evolution of patient health. Yet these observations are sparse, and whether they are recorded depends on the patient's latent condition. Observation patterns also differ across modalities, as structured measurements and clinical notes arise under distinct recording processes. While prior work has developed methods that accommodate missingness in clinical time series, how to extract and use the information carried by the observation process itself remains underexplored. We therefore propose a patient representation learning framework for multimodal clinical time series that explicitly leverages informative missingness. The framework combines (1) a multimodal encoder that captures signals from structured and textual data together with their observation patterns, (2) a Bayesian filtering module that updates a latent patient state over time from observed multimodal signals, and (3) downstream modules for offline treatment policy learning and patient outcome prediction based on the learned patient state. We evaluate the framework on ICU sepsis cohorts from MIMIC-III, MIMIC-IV, and eICU. It improves both offline treatment policy learning and adverse outcome prediction, achieving FQE 0.679 versus 0.528 for clinician behavior and AUROC 0.886 for post-72-hour mortality prediction on MIMIC-III.

Hongyu Chen, David Simchi-Levi, Ruoxuan Xiong

Estimating population quantities such as mean outcomes from user feedback is fundamental to platform evaluation and social science, yet feedback is often missing not at random (MNAR): users with stronger opinions are more likely to respond, so standard estimators are biased and the estimand is not identified without additional assumptions. Existing approaches typically rely on strong parametric assumptions or bespoke auxiliary variables that may be unavailable in practice. In this paper, we develop a partial identification framework in which sharp bounds on the estimand are obtained by solving a pair of linear programs whose constraints encode the observed data structure. This formulation naturally incorporates outcome predictions from pretrained models, including large language models (LLMs), as additional linear constraints that tighten the feasible set. We call these predictions weak shadow variables: they satisfy a conditional independence assumption with respect to missingness but need not meet the completeness conditions required by classical shadow-variable methods. When predictions are sufficiently informative, the bounds collapse to a point, recovering standard identification as a special case. In finite samples, to provide valid coverage of the identified set, we propose a set-expansion estimator that achieves slower-than-$\sqrt{n}$ convergence rate in the set-identified regime and the standard $\sqrt{n}$ rate under point identification. In simulations and semi-synthetic experiments on customer-service dialogues, we find that LLM predictions are often ill-conditioned for classical shadow-variable methods yet remain highly effective in our framework. They shrink identification intervals by 75--83\% while maintaining valid coverage under realistic MNAR mechanisms.

Minqin Zhu, Anpeng Wu, Haoxuan Li et al. · pku

Estimating the individuals' potential response to varying treatment doses is crucial for decision-making in areas such as precision medicine and management science. Most recent studies predict counterfactual outcomes by learning a covariate representation that is independent of the treatment variable. However, such independence constraints neglect much of the covariate information that is useful for counterfactual prediction, especially when the treatment variables are continuous. To tackle the above issue, in this paper, we first theoretically demonstrate the importance of the balancing and prognostic representations for unbiased estimation of the heterogeneous dose-response curves, that is, the learned representations are constrained to satisfy the conditional independence between the covariates and both of the treatment variables and the potential responses. Based on this, we propose a novel Contrastive balancing Representation learning Network using a partial distance measure, called CRNet, for estimating the heterogeneous dose-response curves without losing the continuity of treatments. Extensive experiments are conducted on synthetic and real-world datasets demonstrating that our proposal significantly outperforms previous methods.

Mohsen Bayati, Yuwei Luo, William Overman et al.

Accurate estimation of treatment effects is essential for decision-making across various scientific fields. This task, however, becomes challenging in areas like social sciences and online marketplaces, where treating one experimental unit can influence outcomes for others through direct or indirect interactions. Such interference can lead to biased treatment effect estimates, particularly when the structure of these interactions is unknown. We address this challenge by introducing a new class of estimators based on causal message-passing, specifically designed for settings with pervasive, unknown interference. Our estimator draws on information from the sample mean and variance of unit outcomes and treatments over time, enabling efficient use of observed data to estimate the evolution of the system state. Concretely, we construct non-linear features from the moments of unit outcomes and treatments and then learn a function that maps these features to future mean and variance of unit outcomes. This allows for the estimation of the treatment effect over time. Extensive simulations across multiple domains, using synthetic and real network data, demonstrate the efficacy of our approach in estimating total treatment effect dynamics, even in cases where interference exhibits non-monotonic behavior in the probability of treatment.

Sadegh Shirani, Yuwei Luo, William Overman et al.

Randomized experiments have become a cornerstone of evidence-based decision-making in contexts ranging from online platforms to public health. However, in experimental settings with network interference, a unit's treatment can influence outcomes of other units, challenging both causal effect estimation and its validation. Classic validation approaches fail as outcomes are only observable under a single treatment scenario and exhibit complex correlation patterns due to interference. To address these challenges, we introduce a framework that facilitates the use of machine learning tools for both estimation and validation in causal inference. Central to our approach is the new distribution-preserving network bootstrap, a theoretically-grounded technique that generates multiple statistically-valid subpopulations from a single experiment's data. This amplification of experimental samples enables our second contribution: a counterfactual cross-validation procedure. This procedure adapts the principles of model validation to the unique constraints of causal settings, providing a rigorous, data-driven method for selecting and evaluating estimators. We extend recent causal message-passing developments by incorporating heterogeneous unit-level characteristics and varying local interactions, ensuring reliable finite-sample performance through non-asymptotic analysis. Additionally, we develop and publicly release a comprehensive benchmark toolbox featuring diverse experimental environments, from networks of interacting AI agents to ride-sharing applications. These environments provide known ground truth values while maintaining realistic complexities, enabling systematic evaluation of causal inference methods. Extensive testing across these environments demonstrates our method's robustness to diverse forms of network interference.

Zihan Liang, Ziwen Pan, Ruoxuan Xiong

Clinical notes contain rich patient information, such as diagnoses or medications, making them valuable for patient representation learning. Recent advances in large language models have further improved the ability to extract meaningful representations from clinical texts. However, clinical notes are often missing. For example, in our analysis of the MIMIC-IV dataset, 24.5% of patients have no available discharge summaries. In such cases, representations can be learned from other modalities such as structured data, chest X-rays, or radiology reports. Yet the availability of these modalities is influenced by clinical decision-making and varies across patients, resulting in modality missing-not-at-random (MMNAR) patterns. We propose a causal representation learning framework that leverages observed data and informative missingness in multimodal clinical records. It consists of: (1) an MMNAR-aware modality fusion component that integrates structured data, imaging, and text while conditioning on missingness patterns to capture patient health and clinician-driven assignment; (2) a modality reconstruction component with contrastive learning to ensure semantic sufficiency in representation learning; and (3) a multitask outcome prediction model with a rectifier that corrects for residual bias from specific modality observation patterns. Comprehensive evaluations across MIMIC-IV and eICU show consistent gains over the strongest baselines, achieving up to 13.8% AUC improvement for hospital readmission and 13.1% for ICU admission.

Yingrong Wang, Anpeng Wu, Baohong Li et al.

This paper studies the cumulative causal effects of sequential treatments in the presence of unmeasured confounders. It is a critical issue in sequential decision-making scenarios where treatment decisions and outcomes dynamically evolve over time. Advanced causal methods apply transformer as a backbone to model such time sequences, which shows superiority in capturing long time dependence and periodic patterns via attention mechanism. However, even they control the observed confounding, these estimators still suffer from unmeasured confounders, which influence both treatment assignments and outcomes. How to adjust the latent confounding bias in sequential treatment effect estimation remains an open challenge. Therefore, we propose a novel Decomposing Sequential Instrumental Variable framework for CounterFactual Regression (DSIV-CFR), relying on a common negative control assumption. Specifically, an instrumental variable (IV) is a special negative control exposure, while the previous outcome serves as a negative control outcome. This allows us to recover the IVs latent in observation variables and estimate sequential treatment effects via a generalized moment condition. We conducted experiments on 4 datasets and achieved significant performance in one- and multi-step prediction, supported by which we can identify optimal treatments for dynamic systems.

Ruoxuan Xiong, Alex Chin, Sean J. Taylor

We study the design and analysis of switchback experiments conducted on a single aggregate unit. The design problem is to partition the continuous time space into intervals and switch treatments between intervals, in order to minimize the estimation error of the treatment effect. We show that the estimation error depends on four factors: carryover effects, periodicity, serially correlated outcomes, and impacts from simultaneous experiments. We derive a rigorous bias-variance decomposition and show the tradeoffs of the estimation error from these factors. The decomposition provides three new insights in choosing a design: First, balancing the periodicity between treated and control intervals reduces the variance; second, switching less frequently reduces the bias from carryover effects while increasing the variance from correlated outcomes, and vice versa; third, randomizing interval start and end points reduces both bias and variance from simultaneous experiments. Combining these insights, we propose a new empirical Bayes design approach. This approach uses prior data and experiments for designing future experiments. We illustrate this approach using real data from a ride-sharing platform, yielding a design that reduces MSE by 33% compared to the status quo design used on the platform.

Yingrong Wang, Anpeng Wu, Haoxuan Li et al.

This paper focuses on developing Pareto-optimal estimation and policy learning to identify the most effective treatment that maximizes the total reward from both short-term and long-term effects, which might conflict with each other. For example, a higher dosage of medication might increase the speed of a patient's recovery (short-term) but could also result in severe long-term side effects. Although recent works have investigated the problems about short-term or long-term effects or the both, how to trade-off between them to achieve optimal treatment remains an open challenge. Moreover, when multiple objectives are directly estimated using conventional causal representation learning, the optimization directions among various tasks can conflict as well. In this paper, we systematically investigate these issues and introduce a Pareto-Efficient algorithm, comprising Pareto-Optimal Estimation (POE) and Pareto-Optimal Policy Learning (POPL), to tackle them. POE incorporates a continuous Pareto module with representation balancing, enhancing estimation efficiency across multiple tasks. As for POPL, it involves deriving short-term and long-term outcomes linked with various treatment levels, facilitating an exploration of the Pareto frontier emanating from these outcomes. Results on both the synthetic and real-world datasets demonstrate the superiority of our method.

Junkun Yuan, Xu Ma, Ruoxuan Xiong et al.

Domain generalization (DG) aims to learn from multiple source domains a model that can generalize well on unseen target domains. Existing DG methods mainly learn the representations with invariant marginal distribution of the input features, however, the invariance of the conditional distribution of the labels given the input features is more essential for unknown domain prediction. Meanwhile, the existing of unobserved confounders which affect the input features and labels simultaneously cause spurious correlation and hinder the learning of the invariant relationship contained in the conditional distribution. Interestingly, with a causal view on the data generating process, we find that the input features of one domain are valid instrumental variables for other domains. Inspired by this finding, we propose an instrumental variable-driven DG method (IV-DG) by removing the bias of the unobserved confounders with two-stage learning. In the first stage, it learns the conditional distribution of the input features of one domain given input features of another domain. In the second stage, it estimates the relationship by predicting labels with the learned conditional distribution. Theoretical analyses and simulation experiments show that it accurately captures the invariant relationship. Extensive experiments on real-world datasets demonstrate that IV-DG method yields state-of-the-art results.

Ruoxuan Xiong, Allison Koenecke, Michael Powell et al.

We are interested in estimating the effect of a treatment applied to individuals at multiple sites, where data is stored locally for each site. Due to privacy constraints, individual-level data cannot be shared across sites; the sites may also have heterogeneous populations and treatment assignment mechanisms. Motivated by these considerations, we develop federated methods to draw inference on the average treatment effects of combined data across sites. Our methods first compute summary statistics locally using propensity scores and then aggregate these statistics across sites to obtain point and variance estimators of average treatment effects. We show that these estimators are consistent and asymptotically normal. To achieve these asymptotic properties, we find that the aggregation schemes need to account for the heterogeneity in treatment assignments and in outcomes across sites. We demonstrate the validity of our federated methods through a comparative study of two large medical claims databases.

Kun Kuang, Ruoxuan Xiong, Peng Cui et al.

For many machine learning algorithms, two main assumptions are required to guarantee performance. One is that the test data are drawn from the same distribution as the training data, and the other is that the model is correctly specified. In real applications, however, we often have little prior knowledge on the test data and on the underlying true model. Under model misspecification, agnostic distribution shift between training and test data leads to inaccuracy of parameter estimation and instability of prediction across unknown test data. To address these problems, we propose a novel Decorrelated Weighting Regression (DWR) algorithm which jointly optimizes a variable decorrelation regularizer and a weighted regression model. The variable decorrelation regularizer estimates a weight for each sample such that variables are decorrelated on the weighted training data. Then, these weights are used in the weighted regression to improve the accuracy of estimation on the effect of each variable, thus help to improve the stability of prediction across unknown test data. Extensive experiments clearly demonstrate that our DWR algorithm can significantly improve the accuracy of parameter estimation and stability of prediction with model misspecification and agnostic distribution shift.

Ruoxuan Xiong, Susan Athey, Mohsen Bayati et al.

In this paper, we study the design and analysis of experiments conducted on a set of units over multiple time periods where the starting time of the treatment may vary by unit. The design problem involves selecting an initial treatment time for each unit in order to most precisely estimate both the instantaneous and cumulative effects of the treatment. We first consider non-adaptive experiments, where all treatment assignment decisions are made prior to the start of the experiment. For this case, we show that the optimization problem is generally NP-hard, and we propose a near-optimal solution. Under this solution, the fraction entering treatment each period is initially low, then high, and finally low again. Next, we study an adaptive experimental design problem, where both the decision to continue the experiment and treatment assignment decisions are updated after each period's data is collected. For the adaptive case, we propose a new algorithm, the Precision-Guided Adaptive Experiment (PGAE) algorithm, that addresses the challenges at both the design stage and at the stage of estimating treatment effects, ensuring valid post-experiment inference accounting for the adaptive nature of the design. Using realistic settings, we demonstrate that our proposed solutions can reduce the opportunity cost of the experiments by over 50%, compared to static design benchmarks.

Pan Li, Baihong Jin, Ruoxuan Xiong et al.

We present a machine learning approach to the solution of chance constrained optimizations in the context of voltage regulation problems in power system operation. The novelty of our approach resides in approximating the feasible region of uncertainty with an ellipsoid. We formulate this problem using a learning model similar to Support Vector Machines (SVM) and propose a sampling algorithm that efficiently trains the model. We demonstrate our approach on a voltage regulation problem using standard IEEE distribution test feeders.

Kun Kuang, Ruoxuan Xiong, Peng Cui et al.

In many important machine learning applications, the training distribution used to learn a probabilistic classifier differs from the testing distribution on which the classifier will be used to make predictions. Traditional methods correct the distribution shift by reweighting the training data with the ratio of the density between test and training data. In many applications training takes place without prior knowledge of the testing distribution on which the algorithm will be applied in the future. Recently, methods have been proposed to address the shift by learning causal structure, but those methods rely on the diversity of multiple training data to a good performance, and have complexity limitations in high dimensions. In this paper, we propose a novel Deep Global Balancing Regression (DGBR) algorithm to jointly optimize a deep auto-encoder model for feature selection and a global balancing model for stable prediction across unknown environments. The global balancing model constructs balancing weights that facilitate estimating of partial effects of features (holding fixed all other features), a problem that is challenging in high dimensions, and thus helps to identify stable, causal relationships between features and outcomes. The deep auto-encoder model is designed to reduce the dimensionality of the feature space, thus making global balancing easier. We show, both theoretically and with empirical experiments, that our algorithm can make stable predictions across unknown environments. Our experiments on both synthetic and real world datasets demonstrate that our DGBR algorithm outperforms the state-of-the-art methods for stable prediction across unknown environments.