Bayesian Nonparametric Causal Inference: Information Rates and Learning Algorithms

arXiv.org Machine Learning

We investigate the problem of estimating the causal effect of a treatment on individual subjects from observational data, this is a central problem in various application domains, including healthcare, social sciences, and online advertising. Within the Neyman Rubin potential outcomes model, we use the Kullback Leibler (KL) divergence between the estimated and true distributions as a measure of accuracy of the estimate, and we define the information rate of the Bayesian causal inference procedure as the (asymptotic equivalence class of the) expected value of the KL divergence between the estimated and true distributions as a function of the number of samples. Using Fano method, we establish a fundamental limit on the information rate that can be achieved by any Bayesian estimator, and show that this fundamental limit is independent of the selection bias in the observational data. We characterize the Bayesian priors on the potential (factual and counterfactual) outcomes that achieve the optimal information rate. As a consequence, we show that a particular class of priors that have been widely used in the causal inference literature cannot achieve the optimal information rate. On the other hand, a broader class of priors can achieve the optimal information rate. We go on to propose a prior adaptation procedure (which we call the information based empirical Bayes procedure) that optimizes the Bayesian prior by maximizing an information theoretic criterion on the recovered causal effects rather than maximizing the marginal likelihood of the observed (factual) data. Building on our analysis, we construct an information optimal Bayesian causal inference algorithm.


Deep Counterfactual Networks with Propensity-Dropout

arXiv.org Machine Learning

We propose a novel approach for inferring the individualized causal effects of a treatment (intervention) from observational data. Our approach conceptualizes causal inference as a multitask learning problem; we model a subject's potential outcomes using a deep multitask network with a set of shared layers among the factual and counterfactual outcomes, and a set of outcome-specific layers. The impact of selection bias in the observational data is alleviated via a propensity-dropout regularization scheme, in which the network is thinned for every training example via a dropout probability that depends on the associated propensity score. The network is trained in alternating phases, where in each phase we use the training examples of one of the two potential outcomes (treated and control populations) to update the weights of the shared layers and the respective outcome-specific layers. Experiments conducted on data based on a real-world observational study show that our algorithm outperforms the state-of-the-art.


Deep-Treat: Learning Optimal Personalized Treatments From Observational Data Using Neural Networks

AAAI Conferences

We propose a novel approach for constructing effective treatment policies when the observed data is biased and lacks counterfactual information. Learning in settings where the observed data does not contain all possible outcomes for all treatments is difficult since the observed data is typically biased due to existing clinical guidelines. This is an important problem in the medical domain as collecting unbiased data is expensive and so learning from the wealth of existing biased data is a worthwhile task. Our approach separates the problem into two stages: first we reduce the bias by learning a representation map using a novel auto-encoder network---this allows us to control the trade-off between the bias-reduction and the information loss---and then we construct effective treatment policies on the transformed data using a novel feedforward network. Separation of the problem into these two stages creates an algorithm that can be adapted to the problem at hand---the bias-reduction step can be performed as a preprocessing step for other algorithms. We compare our algorithm against state-of-art algorithms on two semi-synthetic datasets and demonstrate that our algorithm achieves a significant improvement in performance.


Learning Representations for Counterfactual Inference

arXiv.org Machine Learning

Observational studies are rising in importance due to the widespread accumulation of data in fields such as healthcare, education, employment and ecology. We consider the task of answering counterfactual questions such as, "Would this patient have lower blood sugar had she received a different medication?". We propose a new algorithmic framework for counterfactual inference which brings together ideas from domain adaptation and representation learning. In addition to a theoretical justification, we perform an empirical comparison with previous approaches to causal inference from observational data. Our deep learning algorithm significantly outperforms the previous state-of-the-art.


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

arXiv.org 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.