Abstract

In this tutorial I will present a semantics for probabilistic programs in terms of linear operators. Mathematically, this is the natural universe in which to talk about probabilistic transition systems – both discrete and continuous – and it therefore makes sense to target this universe when defining a denotational semantics for probabilistic programming languages. I will describe how both higher-order functions and Bayesian inference can be interpreted in this framework. The focus of the tutorial will be on the discrete case which amounts to manipulating matrices, but I will also sketch some of the mathematics behind the general case. The linear operator semantics of probabilistic programs is originally due to Dexter Kozen, and the recent developments that I will describe in this talk are joint work with him too. If time permits, I will also mention some ongoing work on the operational semantics of probabilistic programs.