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
|Semi-symbolic Inference for Efficient Streaming Probabilistic Programming|
Eric Atkinson Massachusetts Institute of Technology, Charles Yuan Massachusetts Institute of Technology, Guillaume Baudart Inria, Louis Mandel IBM Research, Michael Carbin Massachusetts Institute of TechnologyDOI
|Symbolic Execution for Randomized Programs|
Zachary Susag Cornell University, Sumit Lahiri IIT Kanpur, Justin Hsu Cornell University, Subhajit Roy IIT KanpurDOI
|This Is the Moment for Probabilistic Loops|