Church: a language for generative models

TL;DR

Church is a universal probabilistic programming language based on Lisp, enabling concise descriptions of complex stochastic models and supporting exact and approximate inference methods.

Contribution

Introduction of Church, a novel probabilistic language with unique features like the stochastic memoizer, for modeling and inference in complex generative processes.

Findings

Demonstrated expressiveness with examples like Bayesian networks and non-parametric models

Showed implementation of exact and approximate inference techniques

Validated Church's capability to model diverse stochastic processes

Abstract

We introduce Church, a universal language for describing stochastic generative processes. Church is based on the Lisp model of lambda calculus, containing a pure Lisp as its deterministic subset. The semantics of Church is defined in terms of evaluation histories and conditional distributions on such histories. Church also includes a novel language construct, the stochastic memoizer, which enables simple description of many complex non-parametric models. We illustrate language features through several examples, including: a generalized Bayes net in which parameters cluster over trials, infinite PCFGs, planning by inference, and various non-parametric clustering models. Finally, we show how to implement query on any Church program, exactly and approximately, using Monte Carlo techniques.