Conditional average treatment effects (CATEs) allow us to understand the effect heterogeneity across a large population of individuals. However, typical CATE learners assume all confounding variables are measured in order for the CATE to be identifiable. This requirement can be satisfied by collecting many variables, at the expense of increased sample complexity for estimating CATEs. To combat this, we propose an energy-based model (EBM) that learns a low-dimensional representation of the variables by employing a noise contrastive loss function. With our EBM we introduce a preprocessing step that alleviates the dimensionality curse for any existing learner developed for estimating CATEs. We prove that our EBM keeps the representations partially identifiable up to some universal constant, as well as having universal approximation capability. These properties enable the representations to converge and keep the CATE estimates consistent. Experiments demonstrate the convergence of the representations, as well as show that estimating CATEs on our representations performs better than on the variables or the representations obtained through other dimensionality reduction methods.
Identifiable Exchangeable Mechanisms for Causal Structure and Representation Learning
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；University of Cambridge（剑桥大学）；ELLIS Institute Tübingen（埃利斯研究所蒂宾根分所）；Tübingen AI Center（蒂宾根人工智能中心）
The Institute of Scientific and Industrial Research, Osaka University（大阪大学产业科学研究所）；Graduate School of Science, Osaka University（大阪大学研究生院）；Graduate School of Informatics, Kyoto University（京都大学情报学研究科）
Discovering causal relations among observed variables in a given data set is a main topic in studies of statistics and artificial intelligence. Recently, some techniques to discover an identifiable causal structure have been explored based on non-Gaussianity of the observed data distribution. However, most of these are limited to continuous data. In this paper, we present a novel causal model for binary data and propose a new approach to derive an identifiable causal structure governing the data based on skew Bernoulli distributions of external noise. Experimental evaluation shows excellent pe…
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）
As an important problem in causal inference, we discuss the estimation of treatment effects (TEs). 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 TEs. Our VAE also naturally gives representations balanced for treatment groups, using its prior. Experiments on (semi-)synthetic datasets show state-of-the-art performance under diverse settings, including unobserved confounding. Based on the identifiability of our model, we prove identification of TEs under …
InfluenceField: A Differentiable Field with Interventionally Identifiable Causal Structure for Multimodal World Modeling
Mathematical Institute, University of Oxford（牛津大学数学研究所）；Department of Computer Science, University of Oxford（牛津大学计算机科学系）；School of Mathematical Sciences, University of Nottingham Ningbo China（宁波诺丁汉大学数学科学学院）
Identifiable Latent Polynomial Causal Models Through the Lens of Change
Australian Institute for Machine Learning, The University of Adelaide（阿德莱德大学澳大利亚机器学习研究所）；School of Computer Science and Engineering, The University of New South Wales（新南威尔士大学计算机科学与工程学院）；School of Mathematics and Statistics, The University of Melbourne（墨尔本大学数学与统计学院）；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）；Halicioğlu Data Science Institute (HDSI), University of California San Diego（加州大学圣地亚哥分校哈利西奥格鲁数据科学研究所）；Carnegie Mellon University（卡内基梅隆大学）
Causal Effect Estimation using identifiable Variational AutoEncoder with Latent Confounders and Post-Treatment Variables
College of Informatics, Huazhong Agricultural University（华中农业大学信息学院）；Data 61, Commonwealth Scientific and Industrial Research Organisation (CSIRO)（联邦科学与工业研究组织数据61分部）；STEM, University of South Australia（南澳大学 STEM 学院）
Massachusetts Institute of Technology（麻省理工学院）；Microsoft Research（微软研究院）
Recent advances in probabilistic generative modeling have motivated learning Structural Causal Models (SCM) from observational datasets using deep conditional generative models, also known as Deep Structural Causal Models (DSCM). If successful, DSCMs can be utilized for causal estimation tasks, e.g., for answering counterfactual queries. In this work, we warn practitioners about non-identifiability of counterfactual inference from observational data, even in the absence of unobserved confounding and assuming known causal structure. We prove counterfactual identifiability of monotonic generatio…
By taking into account the nonlinear effect of the cause, the inner noise effect, and the measurement distortion effect in the observed variables, the post-nonlinear (PNL) causal model has demonstrated its excellent performance in distinguishing the cause from effect. However, its identifiability has not been properly addressed, and how to apply it in the case of more than two variables is also a problem. In this paper, we conduct a systematic investigation on its identifiability in the two-variable case. We show that this model is identifiable in most cases; by enumerating all possible situat…
Gatsby Unit, UCL（伦敦大学学院盖茨比单元）；King’s College London（伦敦国王学院）；University of Helsinki（赫尔辛基大学）
Two apparently unrelated fields -- normalizing flows and causality -- have recently received considerable attention in the machine learning community. In this work, we highlight an intrinsic correspondence between a simple family of autoregressive normalizing flows and identifiable causal models. We exploit the fact that autoregressive flow architectures define an ordering over variables, analogous to a causal ordering, to show that they are well-suited to performing a range of causal inference tasks, ranging from causal discovery to making interventional and counterfactual predictions. First,…
Demystifying amortized causal discovery with transformers
Institute of Science and Technology Austria（奥地利科学与技术研究所）；Chan Zuckerberg Initiative（查纳·泽克伯格倡议）；Mila - Quebec AI Institute and Université de Montréal（蒙特利尔AI研究所和蒙特利尔大学）
The most widely discussed methods for estimating the Average Causal Effect/Average Treatment Effect are those for intervention in discrete binary variables whose value represents intervention/non-intervention groups. On the other hand, methods for intervening in continuous variables independent of data generating models have not been developed. In this study, we give a method for estimating the average causal effect for intervention in continuous variables that can be applied to data of any generating models as long as the causal effect is identifiable. The proposing method is independent of m…
Kalisch and Bühlmann (2007) showed that for linear Gaussian models, under the Causal Markov Assumption, the Strong Causal Faithfulness Assumption, and the assumption of causal sufficiency, the PC algorithm is a uniformly consistent estimator of the Markov Equivalence Class of the true causal DAG for linear Gaussian models; it follows from this that for the identifiable causal effects in the Markov Equivalence Class, there are uniformly consistent estimators of causal effects as well. The $k$-Triangle-Faithfulness Assumption is a strictly weaker assumption that avoids some implausible implicati…
Scalable Contrastive Causal Discovery under Unknown Soft Interventions
Department of Systems Biology, Columbia University Irving Institute for Cancer Dynamics, Columbia University（系统生物学系，哥伦比亚大学伊万尼癌症动力学研究所，哥伦比亚大学）；Irving Institute for Cancer Dynamics, Columbia University（伊万尼癌症动力学研究所，哥伦比亚大学）；Department of Computer Science, Columbia University（计算机科学系，哥伦比亚大学）；Department of Biomedical Engineering, Columbia University（生物医学工程系，哥伦比亚大学）；Data Science Institute, Columbia University（数据科学研究所，哥伦比亚大学）
Paris-Dauphine University - PSL（巴黎多芬大学-PSL大学）；CNRS（法国国家科学研究中心）；Ai Square Connect；AdWay Groupe（AdWay集团）
Estimating the Individual Treatment Effect from observational data, defined as the difference between outcomes with and without treatment or intervention, while observing just one of both, is a challenging problems in causal learning. In this paper, we formulate this problem as an inference from hidden variables and enforce causal constraints based on a model of four exclusive causal populations. We propose a new version of the EM algorithm, coined as Expected-Causality-Maximization (ECM) algorithm and provide hints on its convergence under mild conditions. We compare our algorithm to baseline…
Do-calculus is concerned with estimating the interventional distribution of an action from the observed joint probability distribution of the variables in a given causal structure. All identifiable causal effects can be derived using the rules of do-calculus, but the rules themselves do not give any direct indication whether the effect in question is identifiable or not. Shpitser and Pearl constructed an algorithm for identifying joint interventional distributions in causal models, which contain unobserved variables and induce directed acyclic graphs. This algorithm can be seen as a repeated a…
Qualcomm AI Research（高通人工智能研究院）；University of Amsterdam（阿姆斯特丹大学）
Learning high-level causal representations together with a causal model from unstructured low-level data such as pixels is impossible from observational data alone. We prove under mild assumptions that this representation is however identifiable in a weakly supervised setting. This involves a dataset with paired samples before and after random, unknown interventions, but no further labels. We then introduce implicit latent causal models, variational autoencoders that represent causal variables and causal structure without having to optimize an explicit discrete graph structure. On simple image…
This paper provides a link between causal inference and machine learning techniques - specifically, Classification and Regression Trees (CART) - in observational studies where the receipt of the treatment is not randomized, but the assignment to the treatment can be assumed to be randomized (irregular assignment mechanism). The paper contributes to the growing applied machine learning literature on causal inference, by proposing a modified version of the Causal Tree (CT) algorithm to draw causal inference from an irregular assignment mechanism. The proposed method is developed by merging the C…
The long-standing identification problem for causal effects in graphical models has many partial results but lacks a systematic study. We show how computer algebra can be used to either prove that a causal effect can be identified, generically identified, or show that the effect is not generically identifiable. We report on the results of our computations for linear structural equation models, where we determine precisely which causal effects are generically identifiable for all graphs on three and four vertices.
Causal Discovery with Fewer Conditional Independence Tests
Eric and Wendy Schmidt Center, Broad Institute（埃里克和温迪·施密特中心，布罗德研究所）；Laboratory for Information & Decision Systems, Massachusetts Institute of Technology（麻省理工学院信息与决策系统实验室）
While many areas of machine learning have benefited from the increasing availability of large and varied datasets, the benefit to causal inference has been limited given the strong assumptions needed to ensure identifiability of causal effects; these are often not satisfied in real-world datasets. For example, many large observational datasets (e.g., case-control studies in epidemiology, click-through data in recommender systems) suffer from selection bias on the outcome, which makes the average treatment effect (ATE) unidentifiable. We propose a general algorithm to estimate causal effects fr…
A widely applied approach to causal inference from a non-experimental time series $X$, often referred to as "(linear) Granger causal analysis", is to regress present on past and interpret the regression matrix $\hat{B}$ causally. However, if there is an unmeasured time series $Z$ that influences $X$, then this approach can lead to wrong causal conclusions, i.e., distinct from those one would draw if one had additional information such as $Z$. In this paper we take a different approach: We assume that $X$ together with some hidden $Z$ forms a first order vector autoregressive (VAR) process with…
Forest-based methods have recently gained in popularity for non-parametric treatment effect estimation. Building on this line of work, we introduce causal survival forests, which can be used to estimate heterogeneous treatment effects in a survival and observational setting where outcomes may be right-censored. Our approach relies on orthogonal estimating equations to robustly adjust for both censoring and selection effects under unconfoundedness. In our experiments, we find our approach to perform well relative to a number of baselines.
LMU Munich（慕尼黑大学）；Munich Center for Machine Learning（慕尼黑机器学习中心）；ETH Zurich（苏黎世联邦理工学院）
In medical practice, treatments are selected based on the expected causal effects on patient outcomes. Here, the gold standard for estimating causal effects are randomized controlled trials; however, such trials are costly and sometimes even unethical. Instead, medical practice is increasingly interested in estimating causal effects among patient (sub)groups from electronic health records, that is, observational data. In this paper, we aim at estimating the average causal effect (ACE) from observational data (patient trajectories) that are collected over time. For this, we propose DeepACE: an …
Amazon（亚马逊）；Massachusetts Institute of Technology（麻省理工学院）
We extend the definition of the marginal causal effect to the continuous treatment setting and develop a novel characterization of causal bias in the framework of structural causal models. We prove that our derived bias expression is zero if, and only if, the causal effect is identifiable via covariate adjustment. We show that under some restrictions on the structural equations, the causal bias can be estimated efficiently and allows for causal regularization of predictive probabilistic models. We demonstrate the effectiveness of our method for causal bias quantification in various settings wh…
Unobserved confounding presents a major threat to causal inference from observational studies. Recently, several authors suggest that this problem may be overcome in a shared confounding setting where multiple treatments are independent given a common latent confounder. It has been shown that under a linear Gaussian model for the treatments, the causal effect is not identifiable without parametric assumptions on the outcome model. In this paper, we show that the causal effect is indeed identifiable if we assume a general binary choice model for the outcome with a non-probit link. Our identific…
Causal discovery for quantitative data has been extensively studied but less is known for categorical data. We propose a novel causal model for categorical data based on a new classification model, termed classification with optimal label permutation (COLP). By design, COLP is a parsimonious classifier, which gives rise to a provably identifiable causal model. A simple learning algorithm via comparing likelihood functions of causal and anti-causal models suffices to learn the causal direction. Through experiments with synthetic and real data, we demonstrate the favorable performance of the pro…
In this paper, we deal with the problem of inferring causal directions when the data is on discrete domain. By considering the distribution of the cause $P(X)$ and the conditional distribution mapping cause to effect $P(Y|X)$ as independent random variables, we propose to infer the causal direction via comparing the distance correlation between $P(X)$ and $P(Y|X)$ with the distance correlation between $P(Y)$ and $P(X|Y)$. We infer "$X$ causes $Y$" if the dependence coefficient between $P(X)$ and $P(Y|X)$ is smaller. Experiments are performed to show the performance of the proposed method.
Despite the major advances taken in causal modeling, causality is still an unfamiliar topic for many statisticians. In this paper, it is demonstrated from the beginning to the end how causal effects can be estimated from observational data assuming that the causal structure is known. To make the problem more challenging, the causal effects are highly nonlinear and the data are missing at random. The tools used in the estimation include causal models with design, causal calculus, multiple imputation and generalized additive models. The main message is that a trained statistician can estimate ca…
MIT（麻省理工学院）；MIT-IBM Watson AI Lab（麻省理工学院-IBM沃森人工智能实验室）；IBM Research（IBM研究院）
Entropic causal inference is a framework for inferring the causal direction between two categorical variables from observational data. The central assumption is that the amount of unobserved randomness in the system is not too large. This unobserved randomness is measured by the entropy of the exogenous variable in the underlying structural causal model, which governs the causal relation between the observed variables. Kocaoglu et al. conjectured that the causal direction is identifiable when the entropy of the exogenous variable is not too large. In this paper, we prove a variant of their con…
We develop new algorithms for estimating heterogeneous treatment effects, combining recent developments in transfer learning for neural networks with insights from the causal inference literature. By taking advantage of transfer learning, we are able to efficiently use different data sources that are related to the same underlying causal mechanisms. We compare our algorithms with those in the extant literature using extensive simulation studies based on large-scale voter persuasion experiments and the MNIST database. Our methods can perform an order of magnitude better than existing benchmarks…
Estimation of causal effects is fundamental in situations were the underlying system will be subject to active interventions. Part of building a causal inference engine is defining how variables relate to each other, that is, defining the functional relationship between variables given conditional dependencies. In this paper, we deviate from the common assumption of linear relationships in causal models by making use of neural autoregressive density estimators and use them to estimate causal effects within the Pearl's do-calculus framework. Using synthetic data, we show that the approach can r…
Given only data generated by a standard confounding graph with unobserved confounder, the Average Treatment Effect (ATE) is not identifiable. To estimate the ATE, a practitioner must then either (a) collect deconfounded data;(b) run a clinical trial; or (c) elucidate further properties of the causal graph that might render the ATE identifiable. In this paper, we consider the benefit of incorporating a large confounded observational dataset (confounder unobserved) alongside a small deconfounded observational dataset (confounder revealed) when estimating the ATE. Our theoretical results suggest …
Obtaining a non-parametric expression for an interventional distribution is one of the most fundamental tasks in causal inference. Such an expression can be obtained for an identifiable causal effect by an algorithm or by manual application of do-calculus. Often we are left with a complicated expression which can lead to biased or inefficient estimates when missing data or measurement errors are involved. We present an automatic simplification algorithm that seeks to eliminate symbolically unnecessary variables from these expressions by taking advantage of the structure of the underlying graph…
We propose a method to classify the causal relationship between two discrete variables given only the joint distribution of the variables, acknowledging that the method is subject to an inherent baseline error. We assume that the causal system is acyclicity, but we do allow for hidden common causes. Our algorithm presupposes that the probability distributions $P(C)$ of a cause $C$ is independent from the probability distribution $P(E\mid C)$ of the cause-effect mechanism. While our classifier is trained with a Bayesian assumption of flat hyperpriors, we do not make this assumption about our te…
