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Preprints, Working Papers, ... Year : 2023

Density-Based Semantics for Reactive Probabilistic Programming

Abstract

Synchronous languages are now a standard industry tool for critical embedded systems. Designers write high-level specifications by composing streams of values using block diagrams. These languages have been extended with Bayesian reasoning to program state-space models which compute a stream of distributions given a stream of observations. However, the semantics of probabilistic models is only defined for scheduled equations-a significant limitation compared to dataflow synchronous languages and block diagrams which do not require any ordering. In this paper we propose two schedule agnostic semantics for a probabilistic synchronous language. The key idea is to interpret probabilistic expressions as a stream of un-normalized density functions which maps random variable values to a result and positive score. The co-iterative semantics interprets programs as state machines and equations are computed using a fixpoint operator. The relational semantics directly manipulates streams and is thus a better fit to reason about program equivalence. We use the relational semantics to prove the correctness of a program transformation required to run an optimized inference algorithm for state-space models with constant parameters.
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Dates and versions

hal-04488216 , version 1 (04-03-2024)

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Guillaume Baudart, Louis Mandel, Christine Tasson. Density-Based Semantics for Reactive Probabilistic Programming. 2024. ⟨hal-04488216⟩
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