Probabilistic Programming Interfaces for Random Graphs: Markov Categories, Graphons, and Nominal Sets
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3632903.pdf
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Author(s)
Ackerman, Nate
Freer, Cameron E.
Kaddar, Younesse
Karwowski, Jacek
Moss, Sean
Roy, Daniel
Staton, Sam
Yang, Hongseok
Date Issued
January 5, 2024
Journal
Proceedings of the ACM on Programming Languages
Publisher
ACM
Citation
Ackerman, Nate, Freer, Cameron E., Kaddar, Younesse, Karwowski, Jacek, Moss, Sean et al. 2024. "Probabilistic Programming Interfaces for Random Graphs: Markov Categories, Graphons, and Nominal Sets." Proceedings of the ACM on Programming Languages, 8 (POPL).
Version
Final published version
Abstract
We study semantic models of probabilistic programming languages over graphs, and establish a connection to graphons from graph theory and combinatorics. We show that every well-behaved equational theory for our graph probabilistic programming language corresponds to a graphon, and conversely, every graphon arises in this way.
We provide three constructions for showing that every graphon arises from an equational theory. The first is an abstract construction, using Markov categories and monoidal indeterminates. The second and third are more concrete. The second is in terms of traditional measure theoretic probability, which covers `black-and-white' graphons. The third is in terms of probability monads on the nominal sets of Gabbay and Pitts. Specifically, we use a variation of nominal sets induced by the theory of graphs, which covers Erdős-Rényi graphons. In this way, we build new models of graph probabilistic programming from graphons.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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DOI of Published Version
https://doi.org/10.1145/3632903
