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.
Fri 9 DecDisplayed time zone: Auckland, Wellington change
15:30 - 17:00 | ProbabilisticOOPSLA at Seminar Room G007 Chair(s): Benjamin Lucien Kaminski Saarland University and University College London | ||
15:30 30mTalk | Semi-symbolic Inference for Efficient Streaming Probabilistic Programming OOPSLA Eric Atkinson Massachusetts Institute of Technology, Charles Yuan Massachusetts Institute of Technology, Guillaume Baudart Inria, Louis Mandel IBM Research, Michael Carbin Massachusetts Institute of Technology DOI | ||
16:00 30mTalk | Symbolic Execution for Randomized Programs OOPSLA Zachary Susag Cornell University, Sumit Lahiri IIT Kanpur, Justin Hsu Cornell University, Subhajit Roy IIT Kanpur DOI | ||
16:30 30mTalk | This Is the Moment for Probabilistic Loops OOPSLA DOI |