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[Wan23] Benjie Wang. Tractable probabilistic models for causal learning and reasoning. Ph.D. thesis, Department of Computer Science, University of Oxford. 2023. [pdf] [bib]
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Abstract. This thesis examines the application of tractable probabilistic modelling principles to causal learning and reasoning. Tractable probabilistic modelling is a promising paradigm that has emerged in recent years, which focuses on probabilistic models that enable exact and efficient probabilistic reasoning. In particular, the framework of probabilistic circuits provides a systematic language of the tractability of models for various inference queries based on their structural properties, with recent proposals pushing the boundaries of expressiveness and tractability. However, not all information about a system can be captured through a probability distribution over observed variables; for example, the causal direction between two variables can be indistinguishable from data alone. Formalizing this, Pearl’s Causal Hierarchy (also known as the information hierarchy) delineates three levels of causal queries, namely, associational, interventional, and counterfactual, that require increasingly greater knowledge of the underlying causal system, represented by a structural causal model and associated causal diagram. Motivated by this, we investigate the possibility of tractable causal modelling; that is, exact and efficient reasoning with respect to classes of causal queries. In particular, we identify three scenarios, separated by the amount of knowledge available to the modeler: namely, when the full causal diagram/model is available, when only the observational distribution and identifiable causal estimand are available, and when there is additionally uncertainty over the causal diagram. In each of the scenarios, we propose probabilistic circuit representations, structural properties, and algorithms that enable efficient and exact causal reasoning. These models are distinguished from tractable probabilistic models in that they can not only answer different probabilistic inference queries, but also causal queries involving different interventions and even different causal diagrams. However, we also identify key limitations that cast doubt on the existence of a fully general tractable causal model. Our contributions also extend the theory of probabilistic circuits by proposing new properties and circuit architectures, which enable the analysis of advanced inference queries including, but not limited to, causal inference estimands.