Search Results

Documents authored by Stein, Dario

Document
DOI: 10.4230/LIPIcs.CALCO.2023.13
A Category for Unifying Gaussian Probability and Nondeterminism

Authors: Dario Stein and Richard Samuelson

Published in: LIPIcs, Volume 270, 10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023)

Abstract
We introduce categories of extended Gaussian maps and Gaussian relations which unify Gaussian probability distributions with relational nondeterminism in the form of linear relations. Both have crucial and well-understood applications in statistics, engineering, and control theory, but combining them in a single formalism is challenging. It enables us to rigorously describe a variety of phenomena like noisy physical laws, Willems' theory of open systems and uninformative priors in Bayesian statistics. The core idea is to formally admit vector subspaces D ⊆ X as generalized uniform probability distribution. Our formalism represents a first bridge between the literature on categorical systems theory (signal-flow diagrams, linear relations, hypergraph categories) and notions of probability theory.
Cite as

Dario Stein and Richard Samuelson. A Category for Unifying Gaussian Probability and Nondeterminism. In 10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 270, pp. 13:1-13:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{stein_et_al:LIPIcs.CALCO.2023.13,
  author =	{Stein, Dario and Samuelson, Richard},
  title =	{{A Category for Unifying Gaussian Probability and Nondeterminism}},
  booktitle =	{10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023)},
  pages =	{13:1--13:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-287-7},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{270},
  editor =	{Baldan, Paolo and de Paiva, Valeria},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2023.13},
  URN =		{urn:nbn:de:0030-drops-188107},
  doi =		{10.4230/LIPIcs.CALCO.2023.13},
  annote =	{Keywords: systems theory, hypergraph categories, Bayesian inference, category theory, Markov categories}
}
Document
DOI: 10.4230/LIPIcs.CSL.2023.28
Counting and Matching

Authors: Bart Jacobs and Dario Stein

Published in: LIPIcs, Volume 252, 31st EACSL Annual Conference on Computer Science Logic (CSL 2023)

Abstract
Lists, multisets and partitions are fundamental datatypes in mathematics and computing. There are basic transformations from lists to multisets (called "accumulation") and also from lists to partitions (called "matching"). We show how these transformations arise systematically by forgetting/abstracting away certain aspects of information, namely order (transposition) and identity (substitution). Our main result is that suitable restrictions of these transformations are isomorphisms: This reveals fundamental correspondences between elementary datatypes. These restrictions involve "incremental" lists/multisets and "non-crossing" partitions/lists. While the process of forgetting information can be precisely spelled out in the language of category theory, the relevant constructions are very combinatorial in nature. The lists, partitions and multisets in these constructions are counted by Bell numbers and Catalan numbers. One side-product of our main result is a (terminating) rewriting system that turns an arbitrary partition into a non-crossing partition, without improper nestings.
Cite as

Bart Jacobs and Dario Stein. Counting and Matching. In 31st EACSL Annual Conference on Computer Science Logic (CSL 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 252, pp. 28:1-28:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{jacobs_et_al:LIPIcs.CSL.2023.28,
  author =	{Jacobs, Bart and Stein, Dario},
  title =	{{Counting and Matching}},
  booktitle =	{31st EACSL Annual Conference on Computer Science Logic (CSL 2023)},
  pages =	{28:1--28:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-264-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{252},
  editor =	{Klin, Bartek and Pimentel, Elaine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2023.28},
  URN =		{urn:nbn:de:0030-drops-174892},
  doi =		{10.4230/LIPIcs.CSL.2023.28},
  annote =	{Keywords: List, Multiset, Partition, Crossing}
}
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)

Copy BibTex To Clipboard

@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}
}
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact