In observational studies, weighting methods that directly optimize the balance between treatment and covariates have received much attention lately; however these have mainly focused on binary treatments. Inspired by domain adaptation, we show that such methods can be actually reformulated as specific implementations of a discrepancy minimization problem aimed at tackling a shift of distribution from observational to interventional data. More precisely, we introduce a new framework, Covariate Balance via Discrepancy Minimization (CBDM), that provably encompasses most of the existing balancing weight methods and formally extends them to treatments of arbitrary types (e.g., continuous or multivariate). We establish theoretical guarantees for our framework that both offer generalizations of properties known when the treatment is binary, and give a better grasp on what hyperparameters to choose in non-binary settings. Based on such insights, we propose a particular implementation of CBDM for estimating dose-response curves and demonstrate through experiments its competitive performance relative to other existing approaches for continuous treatments.
In many scientific fields such as biology, psychology and sociology, there is an increasing interest in estimating the causal effect of a matrix exposure on an outcome. Covariate balancing is crucial in causal inference and both exact balancing and approximate balancing methods have been proposed in the past decades. However, due to the large number of constraints, it is difficult to achieve exact balance or to select the threshold parameters for approximate balancing methods when the treatment is a matrix. To meet these challenges, we propose the weighted Euclidean balancing method, which app…
Amazon.com, Inc.（亚马逊公司）；Wharton School of the University of Pennsylvania（宾夕法尼亚大学沃顿商学院）
We study the problem of observational causal inference with continuous treatments in the framework of inverse propensity-score weighting. To obtain stable weights, we design a new algorithm based on entropy balancing that learns weights to directly maximize causal inference accuracy using end-to-end optimization. In the process of optimization, these weights are automatically tuned to the specific dataset and causal inference algorithm being used. We provide a theoretical analysis demonstrating consistency of our approach. Using synthetic and real-world data, we show that our algorithm estimat…
Causal inference has received great attention across different fields from economics, statistics, education, medicine, to machine learning. Within this area, inferring causal effects at individual level in observational studies has become an important task, especially in high dimensional settings. In this paper, we propose a framework for estimating Individualized Treatment Effects in high-dimensional non-experimental data. We provide both theoretical and empirical justifications, the latter by comparing our framework with current best-performing methods. Our proposed framework rivals the stat…
Recursive linear structural equation models are widely used to postulate causal mechanisms underlying observational data. In these models, each variable equals a linear combination of a subset of the remaining variables plus an error term. When there is no unobserved confounding or selection bias, the error terms are assumed to be independent. We consider estimating a total causal effect in this setting. The causal structure is assumed to be known only up to a maximally oriented partially directed acyclic graph (MPDAG), a general class of graphs that can represent a Markov equivalence class of…
Propensity scores are often used for stratification of treatment and control groups of subjects in observational data to remove confounding bias when estimating of causal effect of the treatment on an outcome in so-called potential outcome causal modeling framework. In this article, we try to get some insights into basic behavior of the propensity scores in a probabilistic sense. We do a simple analysis of their usage confining to the case of discrete confounding covariates and outcomes. While making clear about behavior of the propensity score our analysis shows how the so-called prognostic s…
LaMME（拉梅实验室）；Paris Saclay University / UEVE（巴黎萨克雷大学/埃夫里大学）；LaMME - CNRS（拉梅实验室-法国国家科学研究中心）；IBISC（IBISC实验室）
Individual Treatment Effects (ITE) estimation methods have risen in popularity in the last years. Most of the time, individual effects are better presented as Conditional Average Treatment Effects (CATE). Recently, representation balancing techniques have gained considerable momentum in causal inference from observational data, still limited to continuous (and binary) outcomes. However, in numerous pathologies, the outcome of interest is a (possibly censored) survival time. Our paper proposes theoretical guarantees for a representation balancing framework applied to counterfactual inference in…
The idea of covariate balance is at the core of causal inference. Inverse propensity weights play a central role because they are the unique set of weights that balance the covariate distributions of different treatment groups. We discuss two broad approaches to estimating these weights: the more traditional one, which fits a propensity score model and then uses the reciprocal of the estimated propensity score to construct weights, and the balancing approach, which estimates the inverse propensity weights essentially by the method of moments, finding weights that achieve balance in the sample.…
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…
Weighting methods are used in observational studies to adjust for covariate imbalances between treatment and control groups. Entropy balancing (EB) is an alternative to inverse probability weighting with an estimated propensity score. The EB weights are constructed to satisfy balance constraints and optimized towards stability. We describe large sample properties of EB estimators of the average causal treatment effect, based on the Kullback-Leibler and quadratic Rényi relative entropies. Additionally, we propose estimators of their asymptotic variances. Even though the objective of EB is to re…
We expand upon the simulation study of Setodji et al. (2017) which compared three promising balancing methods when assessing the average treatment effect on the treated for binary treatments: generalized boosted models (GBM), covariate-balancing propensity scores (CBPS), and entropy balance (EB). The study showed that GBM can outperform CBPS and EB when there are likely to be non-linear associations in both the treatment assignment and outcome models and CBPS and EB are fine-tuned to obtain balance only on first order moments. We explore the potential benefit of using higher-order moments in t…
We study optimal covariate balance for causal inferences from observational data when rich covariates and complex relationships necessitate flexible modeling with neural networks. Standard approaches such as propensity weighting and matching/balancing fail in such settings due to miscalibrated propensity nets and inappropriate covariate representations, respectively. We propose a new method based on adversarial training of a weighting and a discriminator network that effectively addresses this methodological gap. This is demonstrated through new theoretical characterizations of the method as w…
This paper presents a randomization-based framework for estimating causal effects under interference between units, motivated by challenges that arise in analyzing experiments on social networks. The framework integrates three components: (i) an experimental design that defines the probability distribution of treatment assignments, (ii) a mapping that relates experimental treatment assignments to exposures received by units in the experiment, and (iii) estimands that make use of the experiment to answer questions of substantive interest. We develop the case of estimating average unit-level cau…
Forest Kernel Balancing Weights: Outcome-Guided Features for Causal Inference
University of California, Berkeley（加州大学伯克利分校）；Carnegie Mellon University（卡内基梅隆大学）；University of Pennsylvania（宾夕法尼亚大学）；University of Texas, Austin（德克萨斯大学奥斯汀分校）
Many scientific questions require estimating the effects of continuous treatments. Outcome modeling and weighted regression based on the generalized propensity score are the most commonly used methods to evaluate continuous effects. However, these techniques may be sensitive to model misspecification, extreme weights or both. In this paper, we propose Kernel Optimal Orthogonality Weighting (KOOW), a convex optimization-based method, for estimating the effects of continuous treatments. KOOW finds weights that minimize the worst-case penalized functional covariance between the continuous treatme…
A common concern in observational studies focuses on properly evaluating the causal effect, which usually refers to the average treatment effect or the average treatment effect on the treated. In this paper, we propose a data preprocessing method, the Kernel-distance-based covariate balancing, for observational studies with binary treatments. This proposed method yields a set of unit weights for the treatment and control groups, respectively, such that the reweighted covariate distributions can satisfy a set of pre-specified balance conditions. This preprocessing methodology can effectively re…
Randomized controlled trials are the gold standard for measuring causal effects. However, they are often not always feasible, and causal treatment effects must be estimated from observational data. Observational studies do not allow robust conclusions about causal relationships unless statistical techniques account for the imbalance of pretreatment confounders across groups while key assumptions hold. Propensity score and balance weighting (PSBW) are useful techniques that aim to reduce the imbalances between treatment groups by weighting the groups to look alike on the observed confounders. T…
In the absence of unobserved confounders, matching and weighting methods are widely used to estimate causal quantities including the Average Treatment Effect on the Treated (ATT). Unfortunately, these methods do not necessarily achieve their goal of making the multivariate distribution of covariates for the control group identical to that of the treated, leaving some (potentially multivariate) functions of the covariates with different means between the two groups. When these "imbalanced" functions influence the non-treatment potential outcome, the conditioning on observed covariates fails, an…
We apply causal forests to a dataset derived from the National Study of Learning Mindsets, and consider resulting practical and conceptual challenges. In particular, we discuss how causal forests use estimated propensity scores to be more robust to confounding, and how they handle data with clustered errors.
Functional data analysis, which handles data arising from curves, surfaces, volumes, manifolds and beyond in a variety of scientific fields, is a rapidly developing area in modern statistics and data science in the recent decades. The effect of a functional variable on an outcome is an essential theme in functional data analysis, but a majority of related studies are restricted to correlational effects rather than causal effects. This paper makes the first attempt to study the causal effect of a functional variable as a treatment in observational studies. Despite the lack of a probability dens…
IBM Research（IBM研究院）；McGill University（麦吉尔大学）；IBM Research-Haifa（IBM海法研究院）
Biases in observational data of treatments pose a major challenge to estimating expected treatment outcomes in different populations. An important technique that accounts for these biases is reweighting samples to minimize the discrepancy between treatment groups. We present a novel reweighting approach that uses bi-level optimization to alternately train a discriminator to minimize classification error, and a balancing weights generator that uses exponentiated gradient descent to maximize this error. This approach borrows principles from generative adversarial networks (GANs) to exploit the p…
Inverse probability weights are commonly used in epidemiology to estimate causal effects in observational studies. Researchers can typically focus on either the average treatment effect or the average treatment effect on the treated with inverse probability weighting estimators. However, when overlap between the treated and control groups is poor, this can produce extreme weights that can result in biased estimates and large variances. One alternative to inverse probability weights are overlap weights, which target the population with the most overlap on observed characteristics. While estimat…
In this paper, we propose a robust method to estimate the average treatment effects in observational studies when the number of potential confounders is possibly much greater than the sample size. We first use a class of penalized M-estimators for the propensity score and outcome models. We then calibrate the initial estimate of the propensity score by balancing a carefully selected subset of covariates that are predictive of the outcome. Finally, the estimated propensity score is used to construct the inverse probability weighting estimator. We prove that the proposed estimator, which has the…
Eindhoven University of Technology（埃因霍温理工大学）；University at Buffalo（布法罗大学）
Learning causal effects from observational data greatly benefits a variety of domains such as health care, education and sociology. For instance, one could estimate the impact of a new drug on specific individuals to assist the clinic plan and improve the survival rate. In this paper, we focus on studying the problem of estimating Conditional Average Treatment Effect (CATE) from observational data. The challenges for this problem are two-fold: on the one hand, we have to derive a causal estimator to estimate the causal quantity from observational data, where there exists confounding bias; on t…
A key to causal inference with observational data is achieving balance in predictive features associated with each treatment type. Recent literature has explored representation learning to achieve this goal. In this work, we discuss the pitfalls of these strategies - such as a steep trade-off between achieving balance and predictive power - and present a remedy via the integration of balancing weights in causal learning. Specifically, we theoretically link balance to the quality of propensity estimation, emphasize the importance of identifying a proper target population, and elaborate on the c…
Estimating causal effects with propensity scores relies upon the availability of treated and untreated units observed at each value of the estimated propensity score. In settings with strong confounding, limited so-called "overlap" in propensity score distributions can undermine the empirical basis for estimating causal effects and yield erratic finite-sample performance of existing estimators. We propose a Bayesian procedure designed to estimate causal effects in settings where there is limited overlap in propensity score distributions. Our method relies on the posterior predictive treatment …
This paper discusses the fundamental principles of causal inference - the area of statistics that estimates the effect of specific occurrences, treatments, interventions, and exposures on a given outcome from experimental and observational data. We explain the key assumptions required to identify causal effects, and highlight the challenges associated with the use of observational data. We emphasize that experimental thinking is crucial in causal inference. The quality of the data (not necessarily the quantity), the study design, the degree to which the assumptions are met, and the rigor of th…
This paper considers inference of causal structure in a class of graphical models called "conditional DAGs". These are directed acyclic graph (DAG) models with two kinds of variables, primary and secondary. The secondary variables are used to aid in estimation of causal relationships between the primary variables. We give causal semantics for this model class and prove that, under certain assumptions, the direction of causal influence is identifiable from the joint observational distribution of the primary and secondary variables. A score-based approach is developed for estimation of causal st…
In this paper, we focus on estimating the average treatment effect (ATE) of a target population when individual-level data from a source population and summary-level data (e.g., first or second moments of certain covariates) from the target population are available. In the presence of heterogeneous treatment effect, the ATE of the target population can be different from that of the source population when distributions of treatment effect modifiers are dissimilar in these two populations, a phenomenon also known as covariate shift. Many methods have been developed to adjust for covariate shift,…
Researchers are often interested in analyzing conditional treatment effects. One variant of this is "causal moderation," which implies that intervention upon a third (moderator) variable would alter the treatment effect. This study considers the conditions under which causal moderation can be identified and presents a generalized framework for estimating causal moderation effects given randomized treatments and non-randomized moderators. As part of the estimation process, it allows researchers to implement their preferred method of covariate adjustment, including parametric and non-parametric …
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…
In observational study, the propensity score has the central role to estimate causal effects. Since the propensity score is usually unknown, estimating by appropriate procedures is an indispensable step. A point to note that a causal effect estimator might have some bias if a propensity score model was misspecified; valid model construction is important. To overcome the problem, a variety of interesting methods has been proposed. In this paper, we review four methods: using ordinary logistic regression approach; CBPS proposed by Imai and Ratkovic; boosted CART proposed by McCaffrey and colleag…
