Evaluating novel contextual bandit policies using logged data is crucial in applications where exploration is costly, such as medicine. But it usually relies on the assumption of no unobserved confounders, which is bound to fail in practice. We study the question of policy evaluation when we instead have proxies for the latent confounders and develop an importance weighting method that avoids fitting a latent outcome regression model. We show that unlike the unconfounded case no single set of weights can give unbiased evaluation for all outcome models, yet we propose a new algorithm that can still provably guarantee consistency by instead minimizing an adversarial balance objective. We further develop tractable algorithms for optimizing this objective and demonstrate empirically the power of our method when confounders are latent.
Off-policy evaluation (OPE) in reinforcement learning is an important problem in settings where experimentation is limited, such as education and healthcare. But, in these very same settings, observed actions are often confounded by unobserved variables making OPE even more difficult. We study an OPE problem in an infinite-horizon, ergodic Markov decision process with unobserved confounders, where states and actions can act as proxies for the unobserved confounders. We show how, given only a latent variable model for states and actions, policy value can be identified from off-policy data. Our …
We consider the problem of using expert data with unobserved confounders for imitation and reinforcement learning. We begin by defining the problem of learning from confounded expert data in a contextual MDP setup. We analyze the limitations of learning from such data with and without external reward, and propose an adjustment of standard imitation learning algorithms to fit this setup. We then discuss the problem of distribution shift between the expert data and the online environment when the data is only partially observable. We prove possibility and impossibility results for imitation lear…
Causal discovery from data affected by latent confounders is an important and difficult challenge. Causal functional model-based approaches have not been used to present variables whose relationships are affected by latent confounders, while some constraint-based methods can present them. This paper proposes a causal functional model-based method called repetitive causal discovery (RCD) to discover the causal structure of observed variables affected by latent confounders. RCD repeats inferring the causal directions between a small number of observed variables and determines whether the relatio…
London School of Economics and Political Science（伦敦政治经济学院）；Cornell University（康奈尔大学）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
We consider off-policy evaluation (OPE) in Partially Observable Markov Decision Processes (POMDPs), where the evaluation policy depends only on observable variables and the behavior policy depends on unobservable latent variables. Existing works either assume no unmeasured confounders, or focus on settings where both the observation and the state spaces are tabular. In this work, we first propose novel identification methods for OPE in POMDPs with latent confounders, by introducing bridge functions that link the target policy's value and the observed data distribution. We next propose minimax …
University of California, Los Angeles（加州大学洛杉矶分校）；University of Oxford（牛津大学）；University at Buffalo（布法罗大学）
Estimating the individual treatment effect (ITE) from observational data is essential in medicine. A central challenge in estimating the ITE is handling confounders, which are factors that affect both an intervention and its outcome. Most previous work relies on the unconfoundedness assumption, which posits that all the confounders are measured in the observational data. However, if there are unmeasurable (latent) confounders, then confounding bias is introduced. Fortunately, noisy proxies for the latent confounders are often available and can be used to make an unbiased estimate of the ITE. I…
Granger causality analysis, as one of the most popular time series causality methods, has been widely used in the economics, neuroscience. However, unobserved confounders is a fundamental problem in the observational studies, which is still not solved for the non-linear Granger causality. The application works often deal with this problem in virtue of the proxy variables, who can be treated as a measure of the confounder with noise. But the proxy variables has been proved to be unreliable, because of the bias it may induce. In this paper, we try to "recover" the unobserved confounders for the …
The Hong Kong University of Science and Technology（香港科技大学）
The contextual bandit problem is a theoretically justified framework with wide applications in various fields. While the previous study on this problem usually requires independence between noise and contexts, our work considers a more sensible setting where the noise becomes a latent confounder that affects both contexts and rewards. Such a confounded setting is more realistic and could expand to a broader range of applications. However, the unresolved confounder will cause a bias in reward function estimation and thus lead to a large regret. To deal with the challenges brought by the confoun…
University of Massachusetts, Amherst（马萨诸塞大学阿默斯特分校）；Massachusetts Institute of Technology（麻省理工学院）
Latent confounders---unobserved variables that influence both treatment and outcome---can bias estimates of causal effects. In some cases, these confounders are shared across observations, e.g. all students taking a course are influenced by the course's difficulty in addition to any educational interventions they receive individually. This paper shows how to semiparametrically model latent confounders that have this structure and thereby improve estimates of causal effects. The key innovations are a hierarchical Bayesian model, Gaussian processes with structured latent confounders (GP-SLC), an…
New York University（纽约大学）；Columbia University（哥伦比亚大学）
Causal inference from observational data requires assumptions. These assumptions range from measuring confounders to identifying instruments. Traditionally, causal inference assumptions have focused on estimation of effects for a single treatment. In this work, we construct techniques for estimation with multiple treatments in the presence of unobserved confounding. We develop two assumptions based on shared confounding between treatments and independence of treatments given the confounder. Together, these assumptions lead to a confounder estimator regularized by mutual information. For this e…
University of Amsterdam（阿姆斯特丹大学）；TNO Intelligent Imaging（荷兰应用科学研究组织智能成像）；New York University（纽约大学）；CIMS（库朗数学科学研究所）；Massachusetts Institute of Technology（麻省理工学院）；CSAIL & IMES（计算机科学与人工智能实验室与医学工程与科学研究所）；University of Toronto（多伦多大学）；CIFAR（加拿大高等研究院）
Learning individual-level causal effects from observational data, such as inferring the most effective medication for a specific patient, is a problem of growing importance for policy makers. The most important aspect of inferring causal effects from observational data is the handling of confounders, factors that affect both an intervention and its outcome. A carefully designed observational study attempts to measure all important confounders. However, even if one does not have direct access to all confounders, there may exist noisy and uncertain measurement of proxies for confounders. We buil…
We consider learning a causal ordering of variables in a linear non-Gaussian acyclic model called LiNGAM. Several existing methods have been shown to consistently estimate a causal ordering assuming that all the model assumptions are correct. But, the estimation results could be distorted if some assumptions actually are violated. In this paper, we propose a new algorithm for learning causal orders that is robust against one typical violation of the model assumptions: latent confounders. The key idea is to detect latent confounders by testing independence between estimated external influences …
Identification of Causal Direction under an Arbitrary Number of Latent Confounders
School of Computer Science, Guangdong University of Technology（广东技术大学计算机科学学院）；Department of Philosophy, Carnegie Mellon University（卡内基梅隆大学哲学系）；College of Engineering, Shantou University（汕头大学工程学院）；Peng Cheng Laboratory, Shenzhen, China（深圳鹏城实验室）；Mohamed bin Zayed University of Artificial Intelligence（莫扎德大学人工智能大学）
National University of Singapore（新加坡国立大学）；London School of Economics and Political Science（伦敦政治经济学院）
This work extends causal inference with stochastic confounders. We propose a new approach to variational estimation for causal inference based on a representer theorem with a random input space. We estimate causal effects involving latent confounders that may be interdependent and time-varying from sequential, repeated measurements in an observational study. Our approach extends current work that assumes independent, non-temporal latent confounders, with potentially biased estimators. We introduce a simple yet elegant algorithm without parametric specification on model components. Our method a…
We consider learning the possible causal direction of two observed variables in the presence of latent confounding variables. Several existing methods have been shown to consistently estimate causal direction assuming linear or some type of nonlinear relationship and no latent confounders. However, the estimation results could be distorted if either assumption is actually violated. In this paper, we first propose a new linear non-Gaussian acyclic structural equation model with individual-specific effects that allows latent confounders to be considered. We then propose an empirical Bayesian app…
School of Computer Science, Guangdong University of Technology（广东工业大学计算机学院）；Department of Philosophy, Carnegie Mellon University（卡内基梅隆大学哲学系）；Pazhou Lab（琶洲实验室）；School of Mathematics and Big Data, Foshan University（佛山大学数学与大数据学院）
We consider the problem of estimating a particular type of linear non-Gaussian model. Without resorting to the overcomplete Independent Component Analysis (ICA), we show that under some mild assumptions, the model is uniquely identified by a hybrid method. Our method leverages the advantages of constraint-based methods and independent noise-based methods to handle both confounded and unconfounded situations. The first step of our method uses the FCI procedure, which allows confounders and is able to produce asymptotically correct results. The results, unfortunately, usually determine very few …
Reconstructing the causal relationships behind the phenomena we observe is a fundamental challenge in all areas of science. Discovering causal relationships through experiments is often infeasible, unethical, or expensive in complex systems. However, increases in computational power allow us to process the ever-growing amount of data that modern science generates, leading to an emerging interest in the causal discovery problem from observational data. This work evaluates the LPCMCI algorithm, which aims to find generators compatible with a multi-dimensional, highly autocorrelated time series w…
We consider to learn a causal ordering of variables in a linear non-Gaussian acyclic model called LiNGAM. Several existing methods have been shown to consistently estimate a causal ordering assuming that all the model assumptions are correct. But, the estimation results could be distorted if some assumptions actually are violated. In this paper, we propose a new algorithm for learning causal orders that is robust against one typical violation of the model assumptions: latent confounders. We demonstrate the effectiveness of our method using artificial data.
Informatics Institute（信息学研究所）；University of Amsterdam（阿姆斯特丹大学）
We address the problem of causal discovery from data, making use of the recently proposed causal modeling framework of modular structural causal models (mSCM) to handle cycles, latent confounders and non-linearities. We introduce σ-connection graphs (σ-CG), a new class of mixed graphs (containing undirected, bidirected and directed edges) with additional structure, and extend the concept of σ-separation, the appropriate generalization of the well-known notion of d-separation in this setting, to apply to σ-CGs. We prove the closedness of σ-separation under marginalisation and conditioning and e…
Informatics Institute（信息学研究所）；University of Amsterdam（阿姆斯特丹大学）
We prove the main rules of causal calculus (also called do-calculus) for i/o structural causal models (ioSCMs), a generalization of a recently proposed general class of non-/linear structural causal models that allow for cycles, latent confounders and arbitrary probability distributions. We also generalize adjustment criteria and formulas from the acyclic setting to the general one (i.e. ioSCMs). Such criteria then allow to estimate (conditional) causal effects from observational data that was (partially) gathered under selection bias and cycles. This generalizes the backdoor criterion, the se…
Causal Effect Identification in LiNGAM Models with Latent Confounders
Technical University of Munich（慕尼黑工业大学）；Ecole Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）；Leiden University（莱顿大学）；Munich Center for Machine Learning（慕尼黑机器学习中心）
German Aerospace Center（德国航空航天中心）；Institute of Data Science（数据科学研究所）
We present a new method for linear and nonlinear, lagged and contemporaneous constraint-based causal discovery from observational time series in the presence of latent confounders. We show that existing causal discovery methods such as FCI and variants suffer from low recall in the autocorrelated time series case and identify low effect size of conditional independence tests as the main reason. Information-theoretical arguments show that effect size can often be increased if causal parents are included in the conditioning sets. To identify parents early on, we suggest an iterative procedure th…
We present a sound and complete algorithm, called iterative causal discovery (ICD), for recovering causal graphs in the presence of latent confounders and selection bias. ICD relies on the causal Markov and faithfulness assumptions and recovers the equivalence class of the underlying causal graph. It starts with a complete graph, and consists of a single iterative stage that gradually refines this graph by identifying conditional independence (CI) between connected nodes. Independence and causal relations entailed after any iteration are correct, rendering ICD anytime. Essentially, we tie the …
Guangdong University of Technology（广东工业大学）；Peking University（北京大学）；Pazhou Lab（琶洲实验室）；Carnegie Mellon University（卡内基梅隆大学）；Foshan University（佛山大学）
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…
We consider the task of learning a causal graph in the presence of latent confounders given i.i.d.~samples from the model. While current algorithms for causal structure discovery in the presence of latent confounders are constraint-based, we here propose a score-based approach. We prove that under assumptions weaker than faithfulness, any sparsest independence map (IMAP) of the distribution belongs to the Markov equivalence class of the true model. This motivates the \emph{Sparsest Poset} formulation - that posets can be mapped to minimal IMAPs of the true model such that the sparsest of these…
Random effect models are popular statistical models for detecting and correcting spurious sample correlations due to hidden confounders in genome-wide gene expression data. In applications where some confounding factors are known, estimating simultaneously the contribution of known and latent variance components in random effect models is a challenge that has so far relied on numerical gradient-based optimizers to maximize the likelihood function. This is unsatisfactory because the resulting solution is poorly characterized and the efficiency of the method may be suboptimal. Here we prove anal…
Arizona State University（亚利桑那州立大学）；City University of Hong Kong（香港城市大学）
An important problem in causal inference is to break down the total effect of a treatment on an outcome into different causal pathways and to quantify the causal effect in each pathway. For instance, in causal fairness, the total effect of being a male employee (i.e., treatment) constitutes its direct effect on annual income (i.e., outcome) and the indirect effect via the employee's occupation (i.e., mediator). Causal mediation analysis (CMA) is a formal statistical framework commonly used to reveal such underlying causal mechanisms. One major challenge of CMA in observational studies is handl…
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；New York University（纽约大学）
We describe a method for removing the effect of confounders in order to reconstruct a latent quantity of interest. The method, referred to as half-sibling regression, is inspired by recent work in causal inference using additive noise models. We provide a theoretical justification and illustrate the potential of the method in a challenging astronomy application.
University of Toronto（多伦多大学）；Vector Institute（向量研究所）
How do we learn from biased data? Historical datasets often reflect historical prejudices; sensitive or protected attributes may affect the observed treatments and outcomes. Classification algorithms tasked with predicting outcomes accurately from these datasets tend to replicate these biases. We advocate a causal modeling approach to learning from biased data, exploring the relationship between fair classification and intervention. We propose a causal model in which the sensitive attribute confounds both the treatment and the outcome. Building on prior work in deep learning and generative mod…
Marginal structural models (MSMs) estimate the causal effect of a time-varying treatment in the presence of time-dependent confounding via weighted regression. The standard approach of using inverse probability of treatment weighting (IPTW) can lead to high-variance estimates due to extreme weights and be sensitive to model misspecification. Various methods have been proposed to partially address this, including truncation and stabilized-IPTW to temper extreme weights and covariate balancing propensity score (CBPS) to address treatment model misspecification. In this paper, we present Kernel O…
Detecting and Mitigating Treatment Leakage in Text-Based Causal Inference: Distillation and Sensitivity Analysis
Institute for Analytical Sociology, Linköping University, Sweden（分析社会学研究所，利乌波尔大学）；Department of Computer Science and Engineering, Chalmers University of Technology, Sweden（计算机科学与工程系，查尔姆斯理工大学）；Department of Government, University of Texas at Austin, USA（政府系，德克萨斯大学奥斯汀分校）
