This Is the Moment for Probabilistic Loops

Abstract

We present a novel static analysis technique to derive higher moments for program variables for a large class of probabilistic loops with potentially uncountable state spaces. Our approach is fully automatic, meaning it does not rely on externally provided invariants or templates. We employ algebraic techniques based on linear recurrences and introduce program transformations to simplify probabilistic programs while preserving their statistical properties. We develop power reduction techniques to further simplify the polynomial arithmetic of probabilistic programs and define the theory of moment-computable probabilistic loops for which higher moments can precisely be computed. Our work has applications towards recovering probability distributions of random variables and computing tail probabilities. The empirical evaluation of our results demonstrates the applicability of our work on many challenging examples.

arXiv commentPublished at OOPSLA 2022

References in corpus (5)

• Scaling Exact Inference for Discrete Probabilistic Programs
• Invariant Generation for Multi-Path Loops with Polynomial Assignments
• SPPL: Probabilistic Programming with Fast Exact Symbolic Inference
• Synthesizing Probabilistic Invariants via Doob's Decomposition
• Automated Generation of Non-Linear Loop Invariants Utilizing Hypergeometric Sequences

Cited by in corpus (9)

• Inference of Probabilistic Programs with Moment-Matching Gaussian Mixtures
• Exact Recursive Probabilistic Programming
• Strong Invariants Are Hard: On the Hardness of Strongest Polynomial Invariants for (Probabilistic) Programs
• Exact and Approximate Moment Derivation for Probabilistic Loops With Non-Polynomial Assignments
• Guaranteed Bounds on Posterior Distributions of Discrete Probabilistic Programs with Loops
• Bluebell: An Alliance of Relational Lifting and Independence For Probabilistic Reasoning
• Polar: An Algebraic Analyzer for (Probabilistic) Loops
• Moment-based Density Elicitation with Applications in Probabilistic Loops
• Algebraic and Algorithmic Methods for Computing Polynomial Loop Invariants