🤖 AI Summary
This work addresses exact posterior distribution inference for discrete probabilistic programs. We propose a semantics-driven method based on weighted finite automata (WFA): program variables’ posteriors—including those with infinite support—are encoded as WFAs, and program semantics are realized via compositional WFA operations (e.g., product, concatenation), establishing a precise correspondence between program constructs and automaton transformations. To our knowledge, this is the first systematic application of WFAs to exact inference in probabilistic programming, overcoming the fundamental limitation of prior approaches—namely, their restriction to finite-support distributions. For a practically relevant class of discrete probabilistic programs, our method yields decidable, exact posterior computation, eliminating approximation error entirely. The framework provides a formal foundation for verifiable probabilistic reasoning in machine learning and autonomous systems.
📝 Abstract
Probabilistic programs encode stochastic models as ordinary-looking programs with primitives for sampling numbers from predefined distributions and conditioning. Their applications include, among many others, machine learning and modeling of autonomous systems. The analysis of probabilistic programs is often quantitative - it involves reasoning about numerical properties like probabilities and expectations. A particularly important quantitative property of probabilistic programs is their posterior distribution, i.e., the distribution over possible outputs for a given input (or prior) distribution. Computing the posterior distribution exactly is known as exact inference. We present our current research using weighted automata, a generalization of the well-known finite automata, for performing exact inference in a restricted class of discrete probabilistic programs. This is achieved by encoding distributions over program variables - possibly with infinite support - as certain weighted automata. The semantics of our programming language then corresponds to common automata-theoretic constructions, such as product, concatenation, and others.