Abstract

Bayesian inference tasks and machine learning in general we are often inferring some latent quantity given some observed data and a theory for how this latent quantity generated this data. The idea behind probabilistic programming languages is that this theory of how the data was generated is best expressed as a programming language. In this talk, I will introduce a denotational semantics for one such language based on measures which can be understood as unnormalized probability distributions. I will then introduce an operational semantics based on Markov-Chain Monte Carlo (MCMC) sampling. Finally, I will show that these two semantics are not isomorphic and mappings between the two do not preserve algorithmic performance. I will highlight applications that range from outlier detection to clustering algorithms to predicting who will run a game of tug-of-war.