Caron, Alberto; (2023) Bayesian Learning in the Counterfactual World. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

Recent years have witnessed a surging interest towards the use of machine learning tools for causal inference. In contrast to the usual large data settings where the primary goal is prediction, many disciplines, such as health, economic and social sciences, are instead interested in causal questions. Learning individualized responses to an intervention is a crucial task in many applied fields (e.g., precision medicine, targeted advertising, precision agriculture, etc.) where the ultimate goal is to design optimal and highly-personalized policies based on individual features. In this work, I thus tackle the problem of estimating causal effects of an intervention that are heterogeneous across a population of interest and depend on an individual set of characteristics (e.g., a patient's clinical record, user's browsing history, etc..) in high-dimensional observational data settings. This is done by utilizing Bayesian Nonparametric or Probabilistic Machine Learning tools that are specifically adjusted for the causal setting and have desirable uncertainty quantification properties, with a focus on the issues of interpretability/explainability and inclusion of domain experts' prior knowledge. I begin by introducing terminology and concepts from causality and causal reasoning in the first chapter. Then I include a literature review of some of the state-of-the-art regression-based methods for heterogeneous treatment effects estimation, with an attempt to build a unifying taxonomy and lay down the finite-sample empirical properties of these models. The chapters forming the core of the dissertation instead present some novel methods addressing existing issues in individualized causal effects estimation: Chapter 3 develops both a Bayesian tree ensemble method and a deep learning architecture to tackle interpretability, uncertainty coverage and targeted regularization; Chapter 4 instead introduces a novel multi-task Deep Kernel Learning method particularly suited for multi-outcome | multi-action scenarios. The last chapter concludes with a discussion.

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