Incremental analysis for probabilistic programs

Abstract

This paper presents Icpp, a new data-flow-based InCremental analysis for Probabilistic Programs, to infer their posterior probability distributions in response to small yet frequent changes to probabilistic knowledge, i.e., prior probability distributions and observations. Unlike incremental analyses for usual programs, which emphasize code changes, such as statement additions and deletions, Icpp focuses on changes made to probabilistic knowledge, the key feature in probabilistic programming. The novelty of Icpp lies in capturing the correlation between prior and posterior probability distributions by reasoning about the probabilistic dependence of each data-flow fact, so that any posterior probability affected by newly changed probabilistic knowledge can be incrementally updated in a sparse manner without recomputing it from scratch, thereby allowing the previously computed results to be reused. We have evaluated Icpp with a set of probabilistic programs. Our results show that Icpp is an order of magnitude faster than the state-of-the-art data-flow-based inference in analyzing probabilistic programs under small yet frequent changes to probabilistic knowledge, with an average analysis overhead of around 0.1 s in response to a single change.