An Introduction to Probabilistic Programming.
This book is a graduate-level introduction to probabilistic programming. It
not only provides a thorough background for anyone wishing to use a
probabilistic programming system, but also introduces the techniques needed to
design and build these systems. It is aimed at people who have an
undergraduate-level understanding of either or, ideally, both probabilistic
machine learning and programming languages.
We start with a discussion of model-based reasoning and explain why
conditioning is a foundational computation central to the fields of
probabilistic machine learning and artificial intelligence. We then introduce a
first-order probabilistic programming language (PPL) whose programs correspond
to graphical models with a known, finite, set of random variables. In the
context of this PPL we introduce fundamental inference algorithms and describe
how they can be implemented.
We then turn to higher-order probabilistic programming languages. Programs in
such languages can define models with dynamic computation graphs, which may not
instantiate the same set of random variables in each execution. Inference
requires methods that generate samples by repeatedly evaluating the program.
Foundational algorithms for this kind of language are discussed in the context
of an interface between program executions and an inference controller.
Finally we consider the intersection of probabilistic and differentiable
programming. We begin with a discussion of automatic differentiation, and how
it can be used to implement efficient inference methods based on Hamiltonian
Monte Carlo. We then discuss gradient-based maximum likelihood estimation in
programs that are parameterized using neural networks, how to amortize
inference using by learning neural approximations to the program posterior, and
how language features impact the design of deep probabilistic programming
systems.
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