Expectation Programming: Adapting Probabilistic Programming Systems to Estimate Expectations Efficiently

Tim Reichelt, Adam Golinski, Luke Ong, Tom Rainforth

Keywords: Probabilistic Programming, Monte Carlo, Integration, Approximate Inference

TL;DR: We introduce the concept of expectation programming which in contrast to conventional probabilistic programming directly targets the estimation of expectations instead of the approximation of conditional distributions.

Abstract: We show that the standard computational pipeline of probabilistic programming systems (PPSs) can be inefficient for estimating expectations and introduce the concept of expectation programming to address this. In expectation programming, the aim of the backend inference engine is to directly estimate expected return values of programs, as opposed to approximating their conditional distributions. This distinction, while subtle, allows us to achieve substantial performance improvements over the standard PPS computational pipeline by tailoring computation to the expectation we care about. We realize a particular instance of our expectation programming concept, Expectation Programming in Turing (EPT), by extending the PPS Turing to allow so-called target-aware inference to be run automatically. We then verify the statistical soundness of EPT theoretically, and show that it provides substantial empirical gains in practice.