Zeitler, Jakob; (2025) Elements of Partial Identification: Theory and Applications. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

This thesis tackles both exact and approximate partial identification by fo- cusing on challenges such scalability and joint observations of marginals with the Causal Marginal Polytope (Section 6), while handling multi-dimensional continuous treatments with an approximate but useful approach such as Stochastic Causal Programming (SCP, Section 8). It is an expansion on the fundamental work by (J. M. Robins 1989, A. Balke and J. Pearl 1994, Manski 1990) First, we build a foundation for the reader by explaining the interconnected motivations of science, causal inference and partial identifica- tion. We also provide historical background for causal inference and partial identification to put into context a detailed chapter on three ways to define partial identification (Section 5). Using this foundation, we then explore the construction, empirical results and benefits of the Causal Marginal Polytope. This leads into a chapter on Algorithmic Recourse showcasing practical appli- cations of partial identification, to which both the Causal Marginal Polytope and SCP can be applied to. We conclude with a comparison study of SCP and the generative adversarial network framework for bounding, explicating the benefits of a more data-efficient and numerically stable bounding approach for continuous domains. We conclude with a brief discussion of further work, most notably with extensions of the presented methods to the healthcare domain.

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