Automatic inference for higher-order probabilistic programs

Probabilistic models used in quantitative sciences have historically co-evolved with methods for performing inference: specific modeling assumptions are made not because they are appropriate to the application domain, but because they are required to leverage existing software packages or inference methods. The intertwined nature of modeling and computational concerns leaves much of the promise of probabilistic modeling out of reach for data scientists, forcing practitioners to turn to off-the-shelf solutions. The emerging field of probabilistic programming aims to reduce the technical and cognitive overhead for writing and designing novel probabilistic models, by introducing a specialized programming language as an abstraction barrier between modeling and inference. The aim of this thesis is to develop inference algorithms that scale well and are applicable to broad model families. We focus particularly on methods that can be applied to models written in general-purpose higher-order probabilistic programming languages, where programs may make use of recursion, arbitrary deterministic simulation, and higher-order functions to create more accurate models of an application domain. In a probabilistic programming system, probabilistic models are defined using a modeling language; a backend implements generic inference methods applicable to any model written in this language. Probabilistic programs — models — can be written without concern for how inference will later be performed. We begin by considering several existing probabilistic programming languages, their design choices, and tradeoffs. We then demonstrate how programs written in higher-order languages can be used to define coherent probability models, describing possible approaches to inference, and providing explicit algorithms for efficient implementations of both classic and novel inference methods based on and extending sequential Monte Carlo. This is followed by an investigation into the use of variational inference methods within higher-order probabilistic programming languages, with application to policy learning, adaptive importance sampling, and amortization of inference.