Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processes

Neural Information Processing Systems

Predicated on the increasing abundance of electronic health records, we investigate the problem of inferring individualized treatment effects using observational data. Stemming from the potential outcomes model, we propose a novel multi-task learning framework in which factual and counterfactual outcomes are modeled as the outputs of a function in a vector-valued reproducing kernel Hilbert space (vvRKHS). We develop a nonparametric Bayesian method for learning the treatment effects using a multi-task Gaussian process (GP) with a linear coregionalization kernel as a prior over the vvRKHS. The Bayesian approach allows us to compute individualized measures of confidence in our estimates via pointwise credible intervals, which are crucial for realizing the full potential of precision medicine. The impact of selection bias is alleviated via a risk-based empirical Bayes method for adapting the multi-task GP prior, which jointly minimizes the empirical error in factual outcomes and the uncertainty in (unobserved) counterfactual outcomes. We conduct experiments on observational datasets for an interventional social program applied to premature infants, and a left ventricular assist device applied to cardiac patients wait-listed for a heart transplant. In both experiments, we show that our method significantly outperforms the state-of-the-art.

Debiased Bayesian inference for average treatment effects Machine Learning

Bayesian approaches have become increasingly popular in causal inference problems due to their conceptual simplicity, excellent performance and in-built uncertainty quantification ('posterior credible sets'). We investigate Bayesian inference for average treatment effects from observational data, which is a challenging problem due to the missing counterfactuals and selection bias. Working in the standard potential outcomes framework, we propose a data-driven modification to an arbitrary (nonparametric) prior based on the propensity score that corrects for the first-order posterior bias, thereby improving performance. We illustrate our method for Gaussian process (GP) priors using (semi-)synthetic data. Our experiments demonstrate significant improvement in both estimation accuracy and uncertainty quantification compared to the unmodified GP, rendering our approach highly competitive with the state-of-the-art.

Adversarial Balancing-based Representation Learning for Causal Effect Inference with Observational Data Machine Learning

Learning causal effects from observational data greatly benefits a variety of domains such as healthcare, education and sociology. For instance, one could estimate the impact of a policy to decrease unemployment rate. The central problem for causal effect inference is dealing with the unobserved counterfactuals and treatment selection bias. The state-of-the-art approaches focus on solving these problems by balancing the treatment and control groups. However, during the learning and balancing process, highly predictive information from the original covariate space might be lost. In order to build more robust estimators, we tackle this information loss problem by presenting a method called Adversarial Balancing-based representation learning for Causal Effect Inference (ABCEI), based on the recent advances in deep learning. ABCEI uses adversarial learning to balance the distributions of treatment and control group in the latent representation space, without any assumption on the form of the treatment selection/assignment function. ABCEI preserves useful information for predicting causal effects under the regularization of a mutual information estimator. We conduct various experiments on several synthetic and real-world datasets. The experimental results show that ABCEI is robust against treatment selection bias, and matches/outperforms the state-of-the-art approaches.

Matching on Balanced Nonlinear Representations for Treatment Effects Estimation

Neural Information Processing Systems

Estimating treatment effects from observational data is challenging due to the missing counterfactuals. Matching is an effective strategy to tackle this problem. The widely used matching estimators such as nearest neighbor matching (NNM) pair the treated units with the most similar control units in terms of covariates, and then estimate treatment effects accordingly. However, the existing matching estimators have poor performance when the distributions of control and treatment groups are unbalanced. Moreover, theoretical analysis suggests that the bias of causal effect estimation would increase with the dimension of covariates. In this paper, we aim to address these problems by learning low-dimensional balanced and nonlinear representations (BNR) for observational data. In particular, we convert counterfactual prediction as a classification problem, develop a kernel learning model with domain adaptation constraint, and design a novel matching estimator. The dimension of covariates will be significantly reduced after projecting data to a low-dimensional subspace. Experiments on several synthetic and real-world datasets demonstrate the effectiveness of our approach.

Machine Learning Methods Economists Should Know About Machine Learning

We discuss the relevance of the recent Machine Learning (ML) literature for economics and econometrics. First we discuss the differences in goals, methods and settings between the ML literature and the traditional econometrics and statistics literatures. Then we discuss some specific methods from the machine learning literature that we view as important for empirical researchers in economics. These include supervised learning methods for regression and classification, unsupervised learning methods, as well as matrix completion methods. Finally, we highlight newly developed methods at the intersection of ML and econometrics, methods that typically perform better than either off-the-shelf ML or more traditional econometric methods when applied to particular classes of problems, problems that include causal inference for average treatment effects, optimal policy estimation, and estimation of the counterfactual effect of price changes in consumer choice models.