Jo (Xu), Ritsugen (Liyuan); (2024) Feature Mean Embeddings for Causal Inference. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

In this thesis, we discuss causal inference using a feature mean representation, where probability distributions are represented as expectations of features, and conditional probabilities as conditional feature means. We focus for the most part on causal effect estimation, where our goal is to compute the (conditional) expectation of an outcome given treatment and context (or confounders). We employ a two-stage regression approach: in the first stage, we learn neural net features of the covariates;, in the second stage, we use the expected vector of features to represent the covariate distribution, and thus to compute the causal effects. Our approach avoids the need for sampling or density estimation and thus achieves superior numerical stability, especially when the treatment is continuous or the context is high-dimensional. We show that this approach can be applied to a wide range of causal inference problems, including back-door and front-door adjustment. A similar two-stage regression approach can be used in the case of hidden confounders; including instrumental variable regression, with applications in reinforcement learning; and proxy causal learning, with applications to confounded bandit policy evaluation. All quantities involved in our approach can be estimated from data, and we provide asymptotic convergence guarantees for the estimates. Furthermore, by adaptively learning the features with neural networks, our method can handle the challenging benchmarks involving high-dimensional image observations. We also demonstrate the application of the feature mean representation to approximate Bayesian inference and offline policy evaluation.

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