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Documents authored by Cabrera, Benjamin

Document
DOI: 10.4230/LIPIcs.FSTTCS.2020.38
Uncertainty Reasoning for Probabilistic Petri Nets via Bayesian Networks

Authors: Rebecca Bernemann, Benjamin Cabrera, Reiko Heckel, and Barbara König

Published in: LIPIcs, Volume 182, 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)

Abstract
This paper exploits extended Bayesian networks for uncertainty reasoning on Petri nets, where firing of transitions is probabilistic. In particular, Bayesian networks are used as symbolic representations of probability distributions, modelling the observer’s knowledge about the tokens in the net. The observer can study the net by monitoring successful and failed steps. An update mechanism for Bayesian nets is enabled by relaxing some of their restrictions, leading to modular Bayesian nets that can conveniently be represented and modified. As for every symbolic representation, the question is how to derive information - in this case marginal probability distributions - from a modular Bayesian net. We show how to do this by generalizing the known method of variable elimination. The approach is illustrated by examples about the spreading of diseases (SIR model) and information diffusion in social networks. We have implemented our approach and provide runtime results.
Cite as

Rebecca Bernemann, Benjamin Cabrera, Reiko Heckel, and Barbara König. Uncertainty Reasoning for Probabilistic Petri Nets via Bayesian Networks. In 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 182, pp. 38:1-38:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{bernemann_et_al:LIPIcs.FSTTCS.2020.38,
  author =	{Bernemann, Rebecca and Cabrera, Benjamin and Heckel, Reiko and K\"{o}nig, Barbara},
  title =	{{Uncertainty Reasoning for Probabilistic Petri Nets via Bayesian Networks}},
  booktitle =	{40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)},
  pages =	{38:1--38:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-174-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{182},
  editor =	{Saxena, Nitin and Simon, Sunil},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2020.38},
  URN =		{urn:nbn:de:0030-drops-132794},
  doi =		{10.4230/LIPIcs.FSTTCS.2020.38},
  annote =	{Keywords: uncertainty reasoning, probabilistic knowledge, Petri nets, Bayesian networks}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2018.27
Updating Probabilistic Knowledge on Condition/Event Nets using Bayesian Networks

Authors: Benjamin Cabrera, Tobias Heindel, Reiko Heckel, and Barbara König

Published in: LIPIcs, Volume 118, 29th International Conference on Concurrency Theory (CONCUR 2018)

Abstract
The paper extends Bayesian networks (BNs) by a mechanism for dynamic changes to the probability distributions represented by BNs. One application scenario is the process of knowledge acquisition of an observer interacting with a system. In particular, the paper considers condition/event nets where the observer's knowledge about the current marking is a probability distribution over markings. The observer can interact with the net to deduce information about the marking by requesting certain transitions to fire and observing their success or failure. Aiming for an efficient implementation of dynamic changes to probability distributions of BNs, we consider a modular form of networks that form the arrows of a free PROP with a commutative comonoid structure, also known as term graphs. The algebraic structure of such PROPs supplies us with a compositional semantics that functorially maps BNs to their underlying probability distribution and, in particular, it provides a convenient means to describe structural updates of networks.
Cite as

Benjamin Cabrera, Tobias Heindel, Reiko Heckel, and Barbara König. Updating Probabilistic Knowledge on Condition/Event Nets using Bayesian Networks. In 29th International Conference on Concurrency Theory (CONCUR 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 118, pp. 27:1-27:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{cabrera_et_al:LIPIcs.CONCUR.2018.27,
  author =	{Cabrera, Benjamin and Heindel, Tobias and Heckel, Reiko and K\"{o}nig, Barbara},
  title =	{{Updating Probabilistic Knowledge on Condition/Event Nets using Bayesian Networks}},
  booktitle =	{29th International Conference on Concurrency Theory (CONCUR 2018)},
  pages =	{27:1--27:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-087-3},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{118},
  editor =	{Schewe, Sven and Zhang, Lijun},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2018.27},
  URN =		{urn:nbn:de:0030-drops-95659},
  doi =		{10.4230/LIPIcs.CONCUR.2018.27},
  annote =	{Keywords: Petri nets, Bayesian networks, Probabilistic databases, Condition/Event nets, Probabilistic knowledge, Dynamic probability distributions}
}
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