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Sooraj Bhat ; Johannes Borgström ; Andrew D. Gordon ; Claudio Russo -Deriving Probability Density Functions from Probabilistic Functional Programs

The probability density function of a probability distribution is afundamental concept in probability theory and a key ingredient in variouswidely used machine learning methods. However, the necessary framework forcompiling probabilistic functional programs to density functions has onlyrecently been developed. In this work, we present a density compiler for aprobabilistic language with failure and both discrete and continuousdistributions, and provide a proof of its soundness. The compiler greatlyreduces the development effort of domain experts, which we demonstrate bysolving inference problems from various scientific applications, such asmodelling the global carbon cycle, using a standard Markov chain Monte Carloframework.

Classifications

• 68N18 - Functional programming and lambda calculus
• 68N19 - Other programming paradigms (object-oriented, sequential, concurrent, automatic, etc.)
• 68N20 - Theory of compilers and interpreters
• 68Q87 - Probability in computer science (algorithm analysis, random structures, phase transitions, etc.)