Compositional Stochastic Modeling and Probabilistic Programming

TL;DR

This paper explores a continuous-time, compositional approach to stochastic modeling and probabilistic programming, providing a formal operator-algebra semantics that enables systematic development of algorithms for simulation, inference, and model reduction.

Contribution

It introduces a novel continuous-time, operator-algebra framework for probabilistic programming, facilitating systematic algorithm derivation and potential hybrid modeling approaches.

Findings

Operator-algebra semantics for continuous-time stochastic processes

Systematic derivation of simulation and inference algorithms

Potential for hybrid compositional stochastic modeling

Abstract

Probabilistic programming is related to a compositional approach to stochastic modeling by switching from discrete to continuous time dynamics. In continuous time, an operator-algebra semantics is available in which processes proceeding in parallel (and possibly interacting) have summed time-evolution operators. From this foundation, algorithms for simulation, inference and model reduction may be systematically derived. The useful consequences are potentially far-reaching in computational science, machine learning and beyond. Hybrid compositional stochastic modeling/probabilistic programming approaches may also be possible.