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.

Published at OOPSLA 2022

References in corpus (2)

• Invariant Generation for Multi-Path Loops with Polynomial Assignments
• Automated Generation of Non-Linear Loop Invariants Utilizing Hypergeometric Sequences

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• 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