References

  1. Mario Alvarez-picallo, Dan Ghica, David Sprunger & Fabio Zanasi (2022): Rewriting for Monoidal Closed Categories. In: 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022) 228. Schloss Dagstuhl – Leibniz-Zentrum für Informatik, Dagstuhl Publishing, Germany, pp. 29:1–29:0, doi:10.4230/LIPIcs.FSCD.2022.29.
  2. Richard Baker (1991): “Lebesgue measure” on R^. Proceedings of the American Mathematical Society 113(4), pp. 1023–1029, doi:10.2307/2048779.
  3. V. I. Bogachev (2007): Measure theory. Springer, Berlin; New York, doi:10.1007/978-3-540-34514-5.
  4. Filippo Bonchi, Fabio Gadducci, Aleks Kissinger, Paweł Sobociński & Fabio Zanasi (2016): Rewriting modulo symmetric monoidal structure. In: Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science. ACM, New York NY USA, pp. 710–719, doi:10.1145/2933575.2935316. Available at https://dl.acm.org/doi/10.1145/2933575.2935316.
  5. Matteo Capucci, Bruno Gavranovi\'c, Jules Hedges & Eigil Fjeldgren Rischel (2021): Towards foundations of categorical cybernetics. In: Applied Category Theory Conference (ACT 2021). EPTCS, pp. 235–248. Available at http://arxiv.org/abs/2105.06332.
  6. Matteo Capucci & Bruno Gavranović (2022): Actegories for the Working Amthematician.
  7. Nick Chater, Joshua B Tenenbaum & Alan Yuille (2006): Probabilistic models of cognition: Conceptual foundations. Trends in cognitive sciences 10(7), pp. 287–291, doi:10.1016/j.tics.2006.05.008.
  8. Kenta Cho & Bart Jacobs (2019): Disintegration and Bayesian inversion via string diagrams. Mathematical Structures in Computer Science 29(7), pp. 938–971, doi:10.1017/S0960129518000488.
  9. Kyle Cranmer, Johann Brehmer & Gilles Louppe (2020): The frontier of simulation-based inference. Proceedings of the National Academy of Sciences 117(48), pp. 30055–30062, doi:10.1073/pnas.1912789117.
  10. Swaraj Dash, Younesse Kaddar, Hugo Paquet & Sam Staton (2023): Affine monads and lazy structures for bayesian programming. Proceedings of the ACM on Programming Languages 7(POPL), pp. 1338–1368, doi:10.1145/3571239.
  11. David H. Fremlin (2010): Measure theory. 2: Broad foundations, 2. ed edition. Torres Fremlin, Colchester.
  12. Karl Friston, Thomas FitzGerald, Francesco Rigoli, Philipp Schwartenbeck & Giovanni Pezzulo (2017): Active inference: a process theory. Neural computation 29(1), pp. 1–49, doi:10.1162/NECO_a_00912.
  13. Tobias Fritz (2020): A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics. Advances in Mathematics 370, pp. 107239, doi:10.1016/j.aim.2020.107239.
  14. Tobias Fritz & Andreas Klingler (2023): The d-Separation Criterion in Categorical Probability. Journal of Machine Learning Research 24(46), pp. 1–49.
  15. Tobias Fritz & Wendong Liang (2023): Free gs-Monoidal Categories and Free Markov Categories. Applied Categorical Structures 31(2), pp. 21, doi:10.1007/s10485-023-09717-0.
  16. Giorgio Gallo, Giustino Longo, Stefano Pallottino & Sang Nguyen (1993): Directed hypergraphs and applications. Discrete Applied Mathematics 42(2–3), pp. 177–201, doi:10.1016/0166-218X(93)90045-P.
  17. Michèle Giry (1982): A categorical approach to probability theory. In: B. Banaschewski: Categorical Aspects of Topology and Analysis. Springer Berlin Heidelberg, Berlin, Heidelberg, pp. 68–85, doi:10.1007/BFb0092872.
  18. Chris Heunen, Ohad Kammar, Sam Staton & Hongseok Yang (2017): A convenient category for higher-order probability theory. In: Proceedings - Symposium on Logic in Computer Science, pp. 1–12, doi:10.1109/LICS.2017.8005137. ArXiv: 1701.02547 Citation Key: Heunen2017 ISSN: 10436871.
  19. Kiyosi Itô (1984): An Introduction to Probability Theory. Cambridge University Press, doi:10.1017/9781139171809.
  20. Brenden M Lake, Tomer D Ullman, Joshua B Tenenbaum & Samuel J Gershman (2017): Building machines that learn and think like people. Behavioral and brain sciences 40, pp. e253, doi:10.1017/S0140525X16001837.
  21. Sergey Levine (2018): Reinforcement learning and control as probabilistic inference: Tutorial and review. arXiv preprint arXiv:1805.00909.
  22. Jan-Willem van de Meent, Brooks Paige, Hongseok Yang & Frank Wood (2018): An introduction to probabilistic programming. arXiv preprint arXiv:1809.10756.
  23. Christian A Naesseth, Fredrik Lindsten & Thomas B Schon (2019): Elements of Sequential Monte Carlo. Foundations and Trends in Machine Learning 12(3), pp. 187–306, doi:10.1561/2200000074.
  24. Judea Pearl (2012): The causal foundations of structural equation modeling. Handbook of structural equation modeling, pp. 68–91.
  25. Judea Pearl & Dana Mackenzie (2018): The book of why: the new science of cause and effect. Basic books.
  26. Paolo Perrone (2019): Notes on Category Theory with examples from basic mathematics. arXiv preprint arXiv:1912.10642.
  27. Alexey Radul & Boris Alexeev (2021): The Base Measure Problem and its Solution. In: Proceedings of the 24th International Conference on Artificial Intelligence and Statistics (AISTATS) 2021 130. Proceedings of Machine Learning Research, San Diego, California, pp. 3583–3591.
  28. Marcin Sabok, Sam Staton, Dario Stein & Michael Wolman (2021): Probabilistic programming semantics for name generation. Proceedings of the ACM on Programming Languages 5(POPL), pp. 1–29, doi:10.1145/3434292.
  29. Moritz Schauer & Frank van der Meulen (2023): Compositionality in algorithms for smoothing. arXiv preprint arXiv:2303.13865.
  30. Adam \'Scibior, Ohad Kammar, Matthijs Vákár, Sam Staton, Hongseok Yang, Yufei Cai, Klaus Ostermann, Sean K. Moss, Chris Heunen & Zoubin Ghahramani (2017): Denotational Validation of Higher-Order Bayesian Inference. Proc. ACM Program. Lang. 2(POPL), doi:10.1145/3158148.
  31. Toby St Clere Smithe (2020): Bayesian updates compose optically. arXiv preprint arXiv:2006.01631.
  32. Sam Staton (2017): Commutative Semantics for Probabilistic Programming, pp. 855–879, Lecture Notes in Computer Science 10201. Springer Berlin Heidelberg, Berlin, Heidelberg, doi:10.1007/978-3-662-54434-1_32. Available at https://link.springer.com/10.1007/978-3-662-54434-1_32.
  33. Terence Tao (2011): An introduction to measure theory. Graduate studies in mathematics 126. American Mathematical Society, Providence, R.I, doi:10.1090/gsm/126/02.
  34. Matthijs Vákár & Luke Ong (2018): On S-Finite Measures and Kernels. Available at http://arxiv.org/abs/1810.01837. ArXiv:1810.01837 [math].
  35. Paul Wilson & Fabio Zanasi (2023): Data-Parallel Algorithms for String Diagrams. ArXiv:2305.01041.
  36. Yi Wu, Siddharth Srivastava, Nicholas Hay, Simon Du & Stuart Russell (2018): Discrete-Continuous Mixtures in Probabilistic Programming: Generalized Semantics and Inference Algorithms. In: Proceedings of the 35th International Conference on Machine Learning. PMLR, pp. 5343–5352. Available at https://proceedings.mlr.press/v80/wu18f.html.

Comments and questions to: eptcs@eptcs.org
For website issues: webmaster@eptcs.org