Willard Rafnsson will give a talk based on the paper “Stochastic Lambda Calculus and Monads of Probability Distributions”. Details below.
Willard Rafnsson, Assistant Professor.
A Semantic Domain for Probabilistic Programs
Probabilistic programming is revolutionizing probabilistic reasoning. In a probabilistic programming language, a probabilistic model is defined by a program, and probabilistic inference is handled by the compiler or runtime. This greatly simplifies and scales probabilistic reasoning; models become more readable, explainable, and writable, due to expressive programming language constructs and libraries of models.
In this talk, I present the probability monad as a semantic domain for probabilistic programs. The probability monad leads to simple implementations of queries on models (expectation, sampling, support), and simple proofs of desirable properties (e.g. sampling draws values with appropriate probabilities). Furthermore, the probability monad enables a purely functional model of probabilistic programming; I give a semantics for a stochastic lambda calculus by mapping it to the probability monad. Finally, I will touch on how we are using all of this in the REIDENT project.
This talk is mostly based on (Ramsey & Pfeffer, POPL’02).