Generalization Bounds and Representation Learning for Estimation of\n Potential Outcomes and Causal Effects

Abstract

Practitioners in diverse fields such as healthcare, economics and education\nare eager to apply machine learning to improve decision making. The cost and\nimpracticality of performing experiments and a recent monumental increase in\nelectronic record keeping has brought attention to the problem of evaluating\ndecisions based on non-experimental observational data. This is the setting of\nthis work. In particular, we study estimation of individual-level causal\neffects, such as a single patient's response to alternative medication, from\nrecorded contexts, decisions and outcomes. We give generalization bounds on the\nerror in estimated effects based on distance measures between groups receiving\ndifferent treatments, allowing for sample re-weighting. We provide conditions\nunder which our bound is tight and show how it relates to results for\nunsupervised domain adaptation. Led by our theoretical results, we devise\nrepresentation learning algorithms that minimize our bound, by regularizing the\nrepresentation's induced treatment group distance, and encourage sharing of\ninformation between treatment groups. We extend these algorithms to\nsimultaneously learn a weighted representation to further reduce treatment\ngroup distances. Finally, an experimental evaluation on real and synthetic data\nshows the value of our proposed representation architecture and regularization\nscheme.\n

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