UCLA

Understanding and reasoning about causal relationships is central to modeling the world and making intelligent decisions. At the heart of causal inference lies the identifiability problem, which asks whether a causal query can be uniquely determined from the available information. This dissertation demonstrates the benefits of leveraging additional background knowledge - beyond causal graphs and observational data - to improve the identifiability of causal effects, a widely studied class of causal queries. In particular, we present methods that incorporate background knowledge in the form of parametric constraints on the identifiability problem, including functional dependencies (e.g., legal driving age is a deterministic function of country) and context-specific independencies (e.g., when it is warm outside, whether the heater is on becomes independent of the number of occupants), enabling the identification of causal effects that would otherwise be impossible in the classical setup. We also propose a systematic approach that integrates various forms of constraints into identifiability using tractable arithmetic circuits. Beyond identifiability, we investigate the impact of knowledge, such as functional dependencies, on accelerating the computation of causal queries when causal models are fully specified. This gives rise to the notion of causal treewidth, which establishes tighter complexity bounds for computing marginals and applies directly to queries such as causal effects. We further extend these computational improvements to more sophisticated counterfactual reasoning by bounding its complexity in terms of causal treewidth.