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Documents authored by Staton, Sam

Document
Invited Talk
DOI: 10.4230/LIPIcs.FSCD.2021.4
Some Formal Structures in Probability (Invited Talk)

Authors: Sam Staton

Published in: LIPIcs, Volume 195, 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)

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.
Cite as

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)

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@InProceedings{staton:LIPIcs.FSCD.2021.4,
  author =	{Staton, Sam},
  title =	{{Some Formal Structures in Probability}},
  booktitle =	{6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)},
  pages =	{4:1--4:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-191-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{195},
  editor =	{Kobayashi, Naoki},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2021.4},
  URN =		{urn:nbn:de:0030-drops-142421},
  doi =		{10.4230/LIPIcs.FSCD.2021.4},
  annote =	{Keywords: Probabilistic programming}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2021.25
Recursion and Sequentiality in Categories of Sheaves

Authors: Cristina Matache, Sean Moss, and Sam Staton

Published in: LIPIcs, Volume 195, 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)

Abstract
We present a fully abstract model of a call-by-value language with higher-order functions, recursion and natural numbers, as an exponential ideal in a topos. Our model is inspired by the fully abstract models of O'Hearn, Riecke and Sandholm, and Marz and Streicher. In contrast with semantics based on cpo’s, we treat recursion as just one feature in a model built by combining a choice of modular components.
Cite as

Cristina Matache, Sean Moss, and Sam Staton. Recursion and Sequentiality in Categories of Sheaves. In 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 195, pp. 25:1-25:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{matache_et_al:LIPIcs.FSCD.2021.25,
  author =	{Matache, Cristina and Moss, Sean and Staton, Sam},
  title =	{{Recursion and Sequentiality in Categories of Sheaves}},
  booktitle =	{6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)},
  pages =	{25:1--25:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-191-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{195},
  editor =	{Kobayashi, Naoki},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2021.25},
  URN =		{urn:nbn:de:0030-drops-142631},
  doi =		{10.4230/LIPIcs.FSCD.2021.25},
  annote =	{Keywords: Denotational semantics, Full abstraction, Recursion, Sheaf toposes, CPOs}
}
Document
Invited Paper
DOI: 10.4230/LIPIcs.ICALP.2018.3
Probability Theory from a Programming Perspective (Invited Paper)

Authors: Sam Staton

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
A leading idea is to apply techniques from verification and programming theory to machine learning and statistics, to deal with things like compositionality and various notions of correctness and complexity. Probabilistic programming is an example of this. Moreover, this approach leads to new foundational methods in probability theory. This is particularly true in the "non-parametric" aspects, for example in higher-order functions and infinite random graph models.
Cite as

Sam Staton. Probability Theory from a Programming Perspective (Invited Paper). In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, p. 3:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{staton:LIPIcs.ICALP.2018.3,
  author =	{Staton, Sam},
  title =	{{Probability Theory from a Programming Perspective}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{3:1--3:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.3},
  URN =		{urn:nbn:de:0030-drops-90073},
  doi =		{10.4230/LIPIcs.ICALP.2018.3},
  annote =	{Keywords: correctness, complexity, statistics}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2018.141
The Beta-Bernoulli process and algebraic effects

Authors: Sam Staton, Dario Stein, Hongseok Yang, Nathanael L. Ackerman, Cameron E. Freer, and Daniel M. Roy

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
In this paper we use the framework of algebraic effects from programming language theory to analyze the Beta-Bernoulli process, a standard building block in Bayesian models. Our analysis reveals the importance of abstract data types, and two types of program equations, called commutativity and discardability. We develop an equational theory of terms that use the Beta-Bernoulli process, and show that the theory is complete with respect to the measure-theoretic semantics, and also in the syntactic sense of Post. Our analysis has a potential for being generalized to other stochastic processes relevant to Bayesian modelling, yielding new understanding of these processes from the perspective of programming.
Cite as

Sam Staton, Dario Stein, Hongseok Yang, Nathanael L. Ackerman, Cameron E. Freer, and Daniel M. Roy. The Beta-Bernoulli process and algebraic effects. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 141:1-141:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{staton_et_al:LIPIcs.ICALP.2018.141,
  author =	{Staton, Sam and Stein, Dario and Yang, Hongseok and Ackerman, Nathanael L. and Freer, Cameron E. and Roy, Daniel M.},
  title =	{{The Beta-Bernoulli process and algebraic effects}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{141:1--141:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.141},
  URN =		{urn:nbn:de:0030-drops-91456},
  doi =		{10.4230/LIPIcs.ICALP.2018.141},
  annote =	{Keywords: Beta-Bernoulli process, Algebraic effects, Probabilistic programming, Exchangeability}
}
Document
DOI: 10.4230/LIPIcs.TLCA.2015.45
Models for Polymorphism over Physical Dimension

Authors: Robert Atkey, Neil Ghani, Fredrik Nordvall Forsberg, Timothy Revell, and Sam Staton

Published in: LIPIcs, Volume 38, 13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015)

Abstract
We provide a categorical framework for models of a type theory that has special types for physical quantities. The types are indexed by the physical dimensions that they involve. Fibrations are used to organize this index structure in the models of the type theory. We develop some informative models of this type theory: firstly, a model based on group actions, which captures invariance under scaling, and secondly, a way of constructing new models using relational parametricity.
Cite as

Robert Atkey, Neil Ghani, Fredrik Nordvall Forsberg, Timothy Revell, and Sam Staton. Models for Polymorphism over Physical Dimension. In 13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 38, pp. 45-59, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{atkey_et_al:LIPIcs.TLCA.2015.45,
  author =	{Atkey, Robert and Ghani, Neil and Nordvall Forsberg, Fredrik and Revell, Timothy and Staton, Sam},
  title =	{{Models for Polymorphism over Physical Dimension}},
  booktitle =	{13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015)},
  pages =	{45--59},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-87-3},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{38},
  editor =	{Altenkirch, Thorsten},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TLCA.2015.45},
  URN =		{urn:nbn:de:0030-drops-51547},
  doi =		{10.4230/LIPIcs.TLCA.2015.45},
  annote =	{Keywords: Category Theory, Units of Measure, Dimension Types, Type Theory}
}
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