Statically bounded-memory delayed sampling for probabilistic streams

Abstract

<jats:p> <jats:italic>Probabilistic programming languages</jats:italic> aid developers performing Bayesian inference. These languages provide programming constructs and tools for probabilistic modeling and automated inference. Prior work introduced a probabilistic programming language, ProbZelus, to extend probabilistic programming functionality to unbounded streams of data. This work demonstrated that the <jats:italic>delayed sampling</jats:italic> inference algorithm could be extended to work in a streaming context. ProbZelus showed that while delayed sampling could be effectively deployed on some programs, depending on the probabilistic model under consideration, delayed sampling is not guaranteed to use a bounded amount of memory over the course of the execution of the program. </jats:p> <jats:p> In this paper, we the present conditions on a probabilistic program’s execution under which delayed sampling will execute in bounded memory. The two conditions are dataflow properties of the core operations of delayed sampling: the <jats:italic>m</jats:italic> <jats:italic>-consumed property</jats:italic> and the <jats:italic>unseparated paths property</jats:italic> . A program executes in bounded memory under delayed sampling if, and only if, it satisfies the <jats:italic>m</jats:italic> -consumed and unseparated paths properties. We propose a static analysis that abstracts over these properties to soundly ensure that any program that passes the analysis satisfies these properties, and thus executes in bounded memory under delayed sampling. </jats:p>