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Some Formal Structures in Probability (Invited Talk)

Author Sam Staton

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LIPIcs.FSCD.2021.4.pdf
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  • 4 pages

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Subject Classification

ACM Subject Classification
  • Theory of computation → Program semantics
  • Mathematics of computing → Nonparametric statistics
Keywords
  • Probabilistic programming

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Abstract

This invited talk will discuss how developments in the Formal Structures for Computation and Deduction can also suggest new directions for the foundations of probability theory. I plan to focus on two aspects: abstraction, and laziness. I plan to highlight two challenges: higher-order random functions, and stochastic memoization.

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Sam Staton. Some Formal Structures in Probability (Invited Talk). In 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 195, pp. 4:1-4:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.FSCD.2021.4

Author Details

Sam Staton
  • University of Oxford, UK

Funding

  • Staton, Sam: Research supported by a Royal Society University Research Fellowship and the ERC BLAST grant.

References

  1. Kenta Cho and B. Jacobs. Disintegration and Bayesian inversion via string diagrams. Math. Struct. Comput. Sci., 29:938-971, 2019. Google Scholar
  2. Fredrik Dahlqvist and Dexter Kozen. Semantics of higher-order probabilistic programs with conditioning. In Proc. POPL 2020, 2020. Google Scholar
  3. Thomas Ehrhard, Michele Pagani, and Christine Tasson. Measurable cones and stable, measurable functions: a model for probabilistic higher-order programming. In Proc. POPL 2018, 2018. Google Scholar
  4. T. Fritz. A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics. Adv. Math., 370, 2020. Google Scholar
  5. N. D. Goodman, V. K. Mansinghka, et al. Church: a language for generative models. In Proceedings of the Twenty-Fourth Conference on Uncertainty in Artificial Intelligence, 2008. Google Scholar
  6. Chris Heunen, Ohad Kammar, Sam Staton, and Hongseok Yang. A convenient category for higher-order probability theory. In Proc. LICS 2017, 2017. Google Scholar
  7. Xiaodong Jia, Bert Lindenhovius, Michael W. Mislove, and Vladimir Zamdzhiev. Commutative monads for probabilistic programming languages. In Proc. LICS 2021, 2021. Google Scholar
  8. P. Jung, J. Lee, S. Staton, and H. Yang. A generalization of hierarchical exchangeability on trees to directed acyclic graphs. Annales Henri Lebesgue, 4, 2021. Google Scholar
  9. Oleg Kiselyov and Chung-chieh Shan. Embedded probabilistic programming. In Proc. DSL 2009, 2009. Google Scholar
  10. Daphne Koller, David McAllester, and Avi Pfeffer. Effective Bayesian inference for stochastic programs. In Proc. AAAI 1997, 1997. Google Scholar
  11. Brian Milch, Bhaskara Marthi, Stuart Russell, David Sontag, Daniel L. Ong, and Andrey Kolobov. BLOG: Probabilistic models with unknown objects. In Introduction to Statistical Relational Learning. MIT Press, 2007. Google Scholar
  12. Peter Orbanz and Daniel M. Roy. Bayesian models of graphs, arrays and other exchangeable random structures. IEEE Trans. Pattern Anal. Mach. Intell., 37(2):437-461, 2015. Google Scholar
  13. Hugo Paquet and Glynn Winskel. Continuous probability distributions in concurrent games. In Proc. MFPS 2018, pages 321-344, 2018. Google Scholar
  14. Marcin Sabok, Sam Staton, Dario Stein, and Michael Wolman. Probabilistic programming semantics for name generation. In Proc. POPL 2021, 2021. Google Scholar
  15. S. Staton, D. Stein, H. Yang, L. Ackerman, C. E. Freer, and D. M. Roy. The Beta-Bernoulli process and algebraic effects. In Proceedings of the 45th International Colloquium on Automata, Languages, and Programming (ICALP), 2018. Google Scholar
  16. S. Staton, H. Yang, N. L.. Ackerman, C. Freer, and D. Roy. Exchangeable random process and data abstraction. In PPS 2017, 2017. Google Scholar
  17. Sam Staton. Commutative semantics for probabilistic programming. In Proc. ESOP 2017, 2017. Google Scholar
  18. Sam Staton. Probabilistic programs as measures. In Foundations of Probabilistic Programming. CUP, 2020. Google Scholar
  19. Sam Staton. LazyPPL, 2021. URL: https://bitbucket.org/samstaton/lazyppl/src/.
  20. Jan-Willem van de Meent, Brooks Paige, Hongseok Yang, and Frank Wood. An introduction to probabilistic programming, 2018. URL: http://arxiv.org/abs/1809.10756.
  21. Frank D. Wood, Cédric Archambeau, Jan Gasthaus, Lancelot James, and Yee Whye Teh. A stochastic memoizer for sequence data. In Proc. ICML 2009, 2009. Google Scholar
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