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Documents authored by Hedges, Jules

Document
DOI: 10.4230/LIPIcs.MFCS.2023.24
The Compositional Structure of Bayesian Inference

Authors: Dylan Braithwaite, Jules Hedges, and Toby St Clere Smithe

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract
Bayes' rule tells us how to invert a causal process in order to update our beliefs in light of new evidence. If the process is believed to have a complex compositional structure, we may observe that the inversion of the whole can be computed piecewise in terms of the component processes. We study the structure of this compositional rule, noting that it relates to the lens pattern in functional programming. Working in a suitably general axiomatic presentation of a category of Markov kernels, we see how we can think of Bayesian inversion as a particular instance of a state-dependent morphism in a fibred category. We discuss the compositional nature of this, formulated as a functor on the underlying category and explore how this can used for a more type-driven approach to statistical inference.
Cite as

Dylan Braithwaite, Jules Hedges, and Toby St Clere Smithe. The Compositional Structure of Bayesian Inference. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 24:1-24:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{braithwaite_et_al:LIPIcs.MFCS.2023.24,
  author =	{Braithwaite, Dylan and Hedges, Jules and St Clere Smithe, Toby},
  title =	{{The Compositional Structure of Bayesian Inference}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{24:1--24:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.24},
  URN =		{urn:nbn:de:0030-drops-185584},
  doi =		{10.4230/LIPIcs.MFCS.2023.24},
  annote =	{Keywords: monoidal categories, probabilistic programming, Bayesian inference}
}
Document
DOI: 10.4230/LIPIcs.CSL.2021.30
Compositional Modelling of Network Games

Authors: Elena Di Lavore, Jules Hedges, and Paweł Sobociński

Published in: LIPIcs, Volume 183, 29th EACSL Annual Conference on Computer Science Logic (CSL 2021)

Abstract
The analysis of games played on graph-like structures is of increasing importance due to the prevalence of social networks, both virtual and physical, in our daily life. As well as being relevant in computer science, mathematical analysis and computer simulations of such distributed games are vital methodologies in economics, politics and epidemiology, amongst other fields. Our contribution is to give compositional semantics of a family of such games as a well-behaved mapping, a strict monoidal functor, from a category of open graphs (syntax) to a category of open games (semantics). As well as introducing the theoretical framework, we identify some applications of compositionality.
Cite as

Elena Di Lavore, Jules Hedges, and Paweł Sobociński. Compositional Modelling of Network Games. In 29th EACSL Annual Conference on Computer Science Logic (CSL 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 183, pp. 30:1-30:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{dilavore_et_al:LIPIcs.CSL.2021.30,
  author =	{Di Lavore, Elena and Hedges, Jules and Soboci\'{n}ski, Pawe{\l}},
  title =	{{Compositional Modelling of Network Games}},
  booktitle =	{29th EACSL Annual Conference on Computer Science Logic (CSL 2021)},
  pages =	{30:1--30:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-175-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{183},
  editor =	{Baier, Christel and Goubault-Larrecq, Jean},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2021.30},
  URN =		{urn:nbn:de:0030-drops-134645},
  doi =		{10.4230/LIPIcs.CSL.2021.30},
  annote =	{Keywords: game theory, category theory, network games, open games, open graphs, compositionality}
}
Document
DOI: 10.4230/LIPIcs.TYPES.2014.89
Dialectica Categories and Games with Bidding

Authors: Jules Hedges

Published in: LIPIcs, Volume 39, 20th International Conference on Types for Proofs and Programs (TYPES 2014)

Abstract
This paper presents a construction which transforms categorical models of additive-free propositional linear logic, closely based on de Paiva's dialectica categories and Oliva's functional interpretations of classical linear logic. The construction is defined using dependent type theory, which proves to be a useful tool for reasoning about dialectica categories. Abstractly, we have a closure operator on the class of models: it preserves soundness and completeness and has a monad-like structure. When applied to categories of games we obtain 'games with bidding', which are hybrids of dialectica and game models, and we prove completeness theorems for two specific such models.
Cite as

Jules Hedges. Dialectica Categories and Games with Bidding. In 20th International Conference on Types for Proofs and Programs (TYPES 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 39, pp. 89-110, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{hedges:LIPIcs.TYPES.2014.89,
  author =	{Hedges, Jules},
  title =	{{Dialectica Categories and Games with Bidding}},
  booktitle =	{20th International Conference on Types for Proofs and Programs (TYPES 2014)},
  pages =	{89--110},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-88-0},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{39},
  editor =	{Herbelin, Hugo and Letouzey, Pierre and Sozeau, Matthieu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2014.89},
  URN =		{urn:nbn:de:0030-drops-54937},
  doi =		{10.4230/LIPIcs.TYPES.2014.89},
  annote =	{Keywords: Linear logic, Dialectica categories, categorical semantics, model theory, game semantics, dependent types, functional interpretations}
}
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