Probabilistic Programming with Stochastic Memoization Implementing Nonparametric Bayesian Inference

Probabilistic programming is a programming language paradigm receiving both government support [1] and the attention of the popular technology press [2]. Probabilistic programming concerns writing programs with segments that can be interpreted as parameter and conditional distributions, yielding statistical findings through nonstandard execution. Mathematica not only has great support for statistics, but has another language feature particular to probabilistic language elements, namely memoization, which is the ability for functions to retain their value for particular function calls across parameters, creating random trials that retain their value. Recent research has found that reasoning about processes instead of given parameters has allowed Bayesian inference to undertake more flexible models that require computational support. This article explains this nonparametric Bayesian inference, shows how Mathematicaʼs capacity for memoization supports probabilistic programming features, and demonstrates this capability through two examples, learning systems of relations and learning arithmetic functions based on output.