Deriving Probability Density Functions from Probabilistic Functional Programs
This work provides a practical tool for domain experts to reduce development effort in probabilistic modeling, though it builds on recent foundational advances and is incremental in implementation.
The authors tackled the problem of compiling probabilistic functional programs to probability density functions, which is essential for machine learning methods but lacked a comprehensive framework. They developed a sound density compiler supporting failure and mixed discrete/continuous distributions, demonstrating its effectiveness by solving inference problems like global carbon cycle modeling using standard MCMC.
The probability density function of a probability distribution is a fundamental concept in probability theory and a key ingredient in various widely used machine learning methods. However, the necessary framework for compiling probabilistic functional programs to density functions has only recently been developed. In this work, we present a density compiler for a probabilistic language with failure and both discrete and continuous distributions, and provide a proof of its soundness. The compiler greatly reduces the development effort of domain experts, which we demonstrate by solving inference problems from various scientific applications, such as modelling the global carbon cycle, using a standard Markov chain Monte Carlo framework.