Weakest Preexpectation Semantics for Bayesian Inference
Programming Languages
2020-05-20 v1
Abstract
We present a semantics of a probabilistic while-language with soft conditioning and continuous distributions which handles programs diverging with positive probability. To this end, we extend the probabilistic guarded command language (pGCL) with draws from continuous distributions and a score operator. The main contribution is an extension of the standard weakest preexpectation semantics to support these constructs. As a sanity check of our semantics, we define an alternative trace-based semantics of the language, and show that the two semantics are equivalent. Various examples illustrate the applicability of the semantics.
Cite
@article{arxiv.2005.09013,
title = {Weakest Preexpectation Semantics for Bayesian Inference},
author = {Marcin Szymczak and Joost-Pieter Katoen},
journal= {arXiv preprint arXiv:2005.09013},
year = {2020}
}