This is the moment for probabilistic loops

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 algebrai...

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Veröffentlicht in:Proceedings of ACM on programming languages Jg. 6; H. OOPSLA2; S. 1497 - 1525
Hauptverfasser: Moosbrugger, Marcel, Stankovič, Miroslav, Bartocci, Ezio, Kovács, Laura
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York, NY, USA ACM 31.10.2022
Schlagworte:
Computing methodologies
Markov processes
Mathematics of computing
Random walks and Markov chains
Symbolic and algebraic algorithms
Theory of computation
Higher Moments
Distribution Recovery
Linear Recurrences
Probabilistic Programs
ISSN:2475-1421, 2475-1421
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Beschreibung
Zusammenfassung: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.
ISSN:2475-1421
2475-1421
DOI:10.1145/3563341