Abstract:
Can we develop intelligent systems that learn to disambiguate cause from effect by mere observation or experimentation? Unfortunately, the last several decades of research on causal inference tells us that the answer is "no". Understanding cause and effect requires more than just data; it also requires partial knowledge about latent data generating mechanisms. In order to build intelligent systems, our task then as computational scientists is to design data structures for representing partial causal knowledge, and algorithms for updating that knowledge in light of observations and experiments. In this dissertation, I will explore causal probabilistic programs (CPPs) as one such data structure, and probabilistic inference in multi-world transformations of those programs as the corresponding algorithmic task. Specifically, I will demonstrate that this approach has two distinct advantages over the dominant computational paradigm of causal graphical models; (i) it expands the breadth of compatible assumptions and, (ii) it seamlessly integrates with modern Bayesian modeling and inference technologies to quantify uncertainty in causal structure and causal effects.
In Chapter 3, I discuss my completed work towards this thesis. Specifically, In Section 3.1, I present an application of CPPs for modeling hierarchical relational dependencies with latent confounders using flexible Gaussian process models. In Section 3.2, I present Simulation-Based Identifiability, a gradient-based optimization method for determining if any differentiable and bounded CPP converges to a unique causal conclusion asymptotically. In Section 3.3 I present a prototype software implementation for causal inference using causal probabilistic programming, accommodating a broad class of multi-source observational and experimental data.
In Chapter 4, I discuss two proposed contributions. In Section 4.1, I present a proposal for a pedagogical account of how CPPs induce joint distributions over observed and latent counterfactual random variables, and how the resulting posterior distributions over causal effects capture common motifs in causal inference; including irreducible uncertainty due to structural equivalence, latent confounding, and counterfactual instability. In Section 4.2, I propose an application of CPPs for modeling multi-entity relational settings, again using flexible Gaussian process models. In Chapter 5 I present a proposed timeline for completing this thesis.