Probabilistic Programming with Exact Conditions
Dario Stein, Sam Staton · Journal of the ACM · 2023
We spell out the paradigm ofexact conditioningas an intuitive and powerful way of conditioning on observations in probabilistic programs. This is contrasted with likelihood-basedscoringknown from languages such asStan. We study exact conditioning in the cases of discrete and Gaussian probability, presenting prototypical languages for each case and giving semantics to them. We make use of categorical probability (namely Markov and CD categories) to give a general account of exact conditioning, which avoids limits and measure theory, instead focusing on restructuring dataflow and program equations. The correspondence between such categories and a class of programming languages is made precise by defining the internal language of a CD category.