This paper investigates the problem of learning robust, generalizable prediction models from a combination of multiple datasets and qualitative assumptions about the underlying data-generating model. Part of the challenge of learning robust models lies in the influence of unobserved confounders that void many of the invariances and principles of minimum error presently used for this problem. Our approach is to define a different invariance property of causal solutions in the presence of unobserved confounders which, through a relaxation of this invariance, can be connected with an explicit distributionally robust optimization problem over a set of affine combination of data distributions. Concretely, our objective takes the form of a standard loss, plus a regularization term that encourages partial equality of error derivatives with respect to model parameters. We demonstrate the empirical performance of our approach on healthcare data from different modalities, including image, speech and tabular data.
When observed decisions depend only on observed features, off-policy policy evaluation (OPE) methods for sequential decision making problems can estimate the performance of evaluation policies before deploying them. This assumption is frequently violated due to unobserved confounders, unrecorded variables that impact both the decisions and their outcomes. We assess robustness of OPE methods under unobserved confounding by developing worst-case bounds on the performance of an evaluation policy. When unobserved confounders can affect every decision in an episode, we demonstrate that even small a…
University of Cambridge（剑桥大学）；The Alan Turing Institute（艾伦·图灵研究所）；University of California Los Angeles（加州大学洛杉矶分校）
Unobserved confounding is one of the greatest challenges for causal discovery. The case in which unobserved variables have a widespread effect on many of the observed ones is particularly difficult because most pairs of variables are conditionally dependent given any other subset, rendering the causal effect unidentifiable. In this paper we show that beyond conditional independencies, under the principle of independent mechanisms, unobserved confounding in this setting leaves a statistical footprint in the observed data distribution that allows for disentangling spurious and causal effects. Us…
Unobserved confounding is a central barrier to drawing causal inferences from observational data. Several authors have recently proposed that this barrier can be overcome in the case where one attempts to infer the effects of several variables simultaneously. In this paper, we present two simple, analytical counterexamples that challenge the general claims that are central to these approaches. In addition, we show that nonparametric identification is impossible in this setting. We discuss practical implications, and suggest alternatives to the methods that have been proposed so far in this lin…
We consider causal inference in the presence of unobserved confounding. We study the case where a proxy is available for the unobserved confounding in the form of a network connecting the units. For example, the link structure of a social network carries information about its members. We show how to effectively use the proxy to do causal inference. The main idea is to reduce the causal estimation problem to a semi-supervised prediction of both the treatments and outcomes. Networks admit high-quality embedding models that can be used for this semi-supervised prediction. We show that the method …
We study the problem of learning conditional average treatment effects (CATE) from observational data with unobserved confounders. The CATE function maps baseline covariates to individual causal effect predictions and is key for personalized assessments. Recent work has focused on how to learn CATE under unconfoundedness, i.e., when there are no unobserved confounders. Since CATE may not be identified when unconfoundedness is violated, we develop a functional interval estimator that predicts bounds on the individual causal effects under realistic violations of unconfoundedness. Our estimator t…
We study the problem of learning personalized decision policies from observational data while accounting for possible unobserved confounding. Previous approaches, which assume unconfoundedness, i.e., that no unobserved confounders affect both the treatment assignment as well as outcome, can lead to policies that introduce harm rather than benefit when some unobserved confounding is present, as is generally the case with observational data. Instead, since policy value and regret may not be point-identifiable, we study a method that minimizes the worst-case estimated regret of a candidate policy…
The Graduate University for Advanced Studies（综合研究大学院大学）；The Institute of Statistical Mathematics（统计数学研究所）
NOTE: This preprint has a flawed theoretical formulation. Please avoid it and refer to the ICLR22 publication https://openreview.net/forum?id=q7n2RngwOM. Also, arXiv:2109.15062 contains some new ideas on unobserved Confounding. As an important problem of causal inference, we discuss the identification and estimation of treatment effects under unobserved confounding. Representing the confounder as a latent variable, we propose Intact-VAE, a new variant of variational autoencoder (VAE), motivated by the prognostic score that is sufficient for identifying treatment effects. We theoretically show …
University of Oxford（牛津大学）；Technion – Israel Institute of Technology（以色列理工学院）
We study the problem of learning conditional average treatment effects (CATE) from high-dimensional, observational data with unobserved confounders. Unobserved confounders introduce ignorance -- a level of unidentifiability -- about an individual's response to treatment by inducing bias in CATE estimates. We present a new parametric interval estimator suited for high-dimensional data, that estimates a range of possible CATE values when given a predefined bound on the level of hidden confounding. Further, previous interval estimators do not account for ignorance about the CATE associated with s…
Negative control is a strategy for learning the causal relationship between treatment and outcome in the presence of unmeasured confounding. The treatment effect can nonetheless be identified if two auxiliary variables are available: a negative control treatment (which has no effect on the actual outcome), and a negative control outcome (which is not affected by the actual treatment). These auxiliary variables can also be viewed as proxies for a traditional set of control variables, and they bear resemblance to instrumental variables. I propose a family of algorithms based on kernel ridge regr…
Google Research（谷歌研究院）；Weill Cornell Medicine（威尔康奈尔医学院）
It is a truth universally acknowledged that an observed association without known mechanism must be in want of a causal estimate. However, causal estimation from observational data often relies on the (untestable) assumption of `no unobserved confounding'. Violations of this assumption can induce bias in effect estimates. In principle, such bias could invalidate or reverse the conclusions of a study. However, in some cases, we might hope that the influence of unobserved confounders is weak relative to a `large' estimated effect, so the qualitative conclusions are robust to bias from unobserved…
The estimation of the treatment effect is often biased in the presence of unobserved confounding variables which are commonly referred to as hidden variables. Although a few methods have been recently proposed to handle the effect of hidden variables, these methods often overlook the possibility of any interaction between the observed treatment variable and the unobserved covariates. In this work, we address this shortcoming by studying a multivariate response regression problem with both unobserved and heterogeneous confounding variables of the form $Y=A^T X+ B^T Z+ \sum_{j=1}^{p} C^T_j X_j Z…
University of Torontoland（多伦多兰大学）；University of Edenborrow（伊登伯勒大学）
Off-policy evaluation of sequential decision policies from observational data is necessary in applications of batch reinforcement learning such as education and healthcare. In such settings, however, unobserved variables confound observed actions, rendering exact evaluation of new policies impossible, i.e., unidentifiable. We develop a robust approach that estimates sharp bounds on the (unidentifiable) value of a given policy in an infinite-horizon problem given data from another policy with unobserved confounding, subject to a sensitivity model. We consider stationary or baseline unobserved c…
Understanding and quantifying cause and effect is an important problem in many domains. The generally-agreed solution to this problem is to perform a randomised controlled trial. However, even when randomised controlled trials can be performed, they usually have relatively short duration's due to cost considerations. This makes learning long-term causal effects a very challenging task in practice, since the long-term outcome is only observed after a long delay. In this paper, we study the identification and estimation of long-term treatment effects when both experimental and observational data…
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…
Causal Discovery of Linear Non-Gaussian Causal Models with Unobserved Confounding
TUM School of Computation, Information and Technology（慕尼黑工业大学计算、信息与技术学院）；Technical University of Munich（慕尼黑工业大学）；University of British Columbia（不列颠哥伦比亚大学）；Munich Center for Machine Learning（慕尼黑机器学习中心）
Munich Center for Machine Learning（慕尼黑机器学习中心）；LMU Munich（慕尼黑大学）
Estimating conditional average treatment effects (CATEs) from observational data is relevant in many fields such as personalized medicine. However, in practice, the treatment assignment is usually confounded by unobserved variables and thus introduces bias. A remedy to remove the bias is the use of instrumental variables (IVs). Such settings are widespread in medicine (e.g., trials where the treatment assignment is used as binary IV). In this paper, we propose a novel, multiply robust machine learning framework, called MRIV, for estimating CATEs using binary IVs and thus yield an unbiased CATE…
Rochester Institute of Technology（罗切斯特理工学院）；Dalhousie University（达尔豪斯大学）
While deep representation learning has become increasingly capable of separating task-relevant representations from other confounding factors in the data, two significant challenges remain. First, there is often an unknown and potentially infinite number of confounding factors coinciding in the data. Second, not all of these factors are readily observable. In this paper, we present a deep conditional generative model that learns to disentangle a task-relevant representation from an unknown number of confounding factors that may grow infinitely. This is achieved by marrying the representational…
Unobserved confounding is a major hurdle for causal inference from observational data. Confounders---the variables that affect both the causes and the outcome---induce spurious non-causal correlations between the two. Wang & Blei (2018) lower this hurdle with "the blessings of multiple causes," where the correlation structure of multiple causes provides indirect evidence for unobserved confounding. They leverage these blessings with an algorithm, called the deconfounder, that uses probabilistic factor models to correct for the confounders. In this paper, we take a causal graphical view of the …
University of Toronto（多伦多大学）；Massachusetts Institute of Technology（麻省理工学院）；Harvard University（哈佛大学）
Domain shift, encountered when using a trained model for a new patient population, creates significant challenges for sequential decision making in healthcare since the target domain may be both data-scarce and confounded. In this paper, we propose a method for off-policy transfer by modeling the underlying generative process with a causal mechanism. We use informative priors from the source domain to augment counterfactual trajectories in the target in a principled manner. We demonstrate how this addresses data-scarcity in the presence of unobserved confounding. The causal parametrization of …
We study the offline contextual bandit problem, where we aim to acquire an optimal policy using observational data. However, this data usually contains two deficiencies: (i) some variables that confound actions are not observed, and (ii) missing observations exist in the collected data. Unobserved confounders lead to a confounding bias and missing observations cause bias and inefficiency problems. To overcome these challenges and learn the optimal policy from the observed dataset, we present a new algorithm called Causal-Adjusted Pessimistic (CAP) policy learning, which forms the reward functi…
Instrumental and Proximal Causal Inference with Gaussian Processes
Department of Statistics and Actuarial Science, University of Hong Kong（香港大学统计与精算科学系）；Rational Intelligence Lab, CISPA Helmholtz Center for Information Security（CISPA霍普夫信息安全中心理性智能实验室）；Australian Institute for Machine Learning, Adelaide University（阿德莱德大学澳大利亚机器学习研究所）；College of Computing & Data Science, Nanyang Technological University（南洋理工大学计算与数据科学学院）
A Convex Framework for Confounding Robust Inference
Department of Mathematics ETH Zurich（苏黎世联邦理工学院数学系）；Department of Computer Science ETH Zurich（苏黎世联邦理工学院计算机科学系）；School of Computing Institute of Science Tokyo（东京科学大学计算学部）；RIKEN AIP（日本理化学研究所AIP）
I argue that regularizing terms in standard regression methods not only help against overfitting finite data, but sometimes also yield better causal models in the infinite sample regime. I first consider a multi-dimensional variable linearly influencing a target variable with some multi-dimensional unobserved common cause, where the confounding effect can be decreased by keeping the penalizing term in Ridge and Lasso regression even in the population limit. Choosing the size of the penalizing term, is however challenging, because cross validation is pointless. Here it is done by first estimati…
NYU Center for Data Science（纽约大学数据科学中心）；NYU Grossman School of Medicine（纽约大学格罗斯曼医学院）；Genentech（基因泰克）
We propose generative multitask learning (GMTL), a simple and scalable approach to causal representation learning for multitask learning. Our approach makes a minor change to the conventional multitask inference objective, and improves robustness to target shift. Since GMTL only modifies the inference objective, it can be used with existing multitask learning methods without requiring additional training. The improvement in robustness comes from mitigating unobserved confounders that cause the targets, but not the input. We refer to them as \emph{target-causing confounders}. These confounders …
ProximalFM: Amortized Proximal Causal Inference under Hidden Confounding
University of Oxford（牛津大学）；Harvard University（哈佛大学）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Perelman School of Medicine, University of Pennsylvania（宾夕法尼亚大学佩雷尔曼医学院）；Vector Institute（向量研究所）；University College London（伦敦大学学院）
The treatment effects of medications play a key role in guiding medical prescriptions. They are usually assessed with randomized controlled trials (RCTs), which are expensive. Recently, large-scale electronic health records (EHRs) have become available, opening up new opportunities for more cost-effective assessments. However, assessing a treatment effect from EHRs is challenging: it is biased by unobserved confounders, unmeasured variables that affect both patients' medical prescription and their outcome, e.g. the patients' social economic status. To adjust for unobserved confounders, we deve…
Stanford University（斯坦福大学）；Hoover Institution（胡佛研究所）；Wharton School, University of Pennsylvania（宾夕法尼亚大学沃顿商学院）；Princeton University（普林斯顿大学）
The empirical practice of using factor models to adjust for shared, unobserved confounders, $\mathbf{Z}$, in observational settings with multiple treatments, $\mathbf{A}$, is widespread in fields including genetics, networks, medicine, and politics. Wang and Blei (2019, WB) formalizes these procedures and develops the "deconfounder," a causal inference method using factor models of $\mathbf{A}$ to estimate "substitute confounders," $\hat{\mathbf{Z}}$, then estimating treatment effects by regressing the outcome, $\mathbf{Y}$, on part of $\mathbf{A}$ while adjusting for $\hat{\mathbf{Z}}$. WB cl…
Columbia University（哥伦比亚大学）；Netflix Inc.（奈飞公司）；Mila；HEC Montréal（蒙特利尔高等商学院）
The goal of recommendation is to show users items that they will like. Though usually framed as a prediction, the spirit of recommendation is to answer an interventional question---for each user and movie, what would the rating be if we "forced" the user to watch the movie? To this end, we develop a causal approach to recommendation, one where watching a movie is a "treatment" and a user's rating is an "outcome." The problem is there may be unobserved confounders, variables that affect both which movies the users watch and how they rate them; unobserved confounders impede causal predictions wi…
