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Watch a 26-minute conference presentation from POPL 2018 exploring a modular semantic framework for analyzing Bayesian inference algorithms in probabilistic programming languages. Dive into how sophisticated inference algorithms can be conceptualized and analyzed through higher-order functions and inductive types, using quasi-Borel spaces to overcome technical challenges in defining measurable space structures. Learn about semantic structures for representing probabilistic programs and validity criteria for transformations, with practical applications in Sequential Monte Carlo and Markov Chain Monte Carlo methods. Understand the connection between semantic manipulation and measure theory through Kock's synthetic measure theory, including a proof of the quasi-Borel version of the Metropolis-Hastings-Green theorem. Presented by researchers from multiple institutions including the University of Cambridge, University of Oxford, KAIST, and Uber AI Labs, this talk provides deep insights into the theoretical foundations of modern probabilistic programming systems used in data science and machine learning.
