License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CONCUR.2016.23
URN: urn:nbn:de:0030-drops-61737
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6173/
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Dahlqvist, Fredrik ; Danos, Vincent ; Garnier, Ilias

Robustly Parameterised Higher-Order Probabilistic Models

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LIPIcs-CONCUR-2016-23.pdf (0.6 MB)

Abstract

We present a method for constructing robustly parameterised families of higher-order probabilistic models. Parameter spaces and models are represented by certain classes of functors in the category of Polish spaces. Maps from parameter spaces to models (parameterisations) are continuous and natural transformations between such functors. Naturality ensures that parameterised models are invariant by change of granularity -- ie that parameterisations are intrinsic. Continuity ensures that models are robust with respect to their parameterisation. Our method allows one to build models from a set of basic functors among which the Giry probabilistic functor, spaces of cadlag trajectories (in continuous and discrete time), multisets and compact powersets. These functors can be combined by guarded composition, product and coproduct. Parameter spaces range over the polynomial closure of Giry-like functors. Thus we obtain a class of robust parameterised models which includes the Dirichlet process, various point processes (random sequences with values in Polish spaces) and other classical objects of probability theory. By extending techniques developed in prior work, we show how to reduce the questions of existence, uniqueness, naturality, and continuity of a parameterised model to combinatorial questions only involving finite spaces.

BibTeX - Entry

@InProceedings{dahlqvist_et_al:LIPIcs:2016:6173,
  author =	{Fredrik Dahlqvist and Vincent Danos and Ilias Garnier},
  title =	{{Robustly Parameterised Higher-Order Probabilistic Models}},
  booktitle =	{27th International Conference on Concurrency Theory (CONCUR 2016)},
  pages =	{23:1--23:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-017-0},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{59},
  editor =	{Jos{\'e}e Desharnais and Radha Jagadeesan},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6173},
  URN =		{urn:nbn:de:0030-drops-61737},
  doi =		{10.4230/LIPIcs.CONCUR.2016.23},
  annote =	{Keywords: Probability, category theory, Giry monad}
}

Keywords: Probability, category theory, Giry monad
Collection: 27th International Conference on Concurrency Theory (CONCUR 2016)
Issue Date: 2016
Date of publication: 24.08.2016

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