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URN: urn:nbn:de:0030-drops-91344
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On Computing the Total Variation Distance of Hidden Markov Models

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Abstract

We prove results on the decidability and complexity of computing the total variation distance (equivalently, the L_1-distance) of hidden Markov models (equivalently, labelled Markov chains). This distance measures the difference between the distributions on words that two hidden Markov models induce. The main results are: (1) it is undecidable whether the distance is greater than a given threshold; (2) approximation is #P-hard and in PSPACE.

BibTeX - Entry

@InProceedings{kiefer:LIPIcs:2018:9134,
  author =	{Stefan Kiefer},
  title =	{{On Computing the Total Variation Distance of Hidden Markov Models}},
  booktitle =	{45th International Colloquium on Automata, Languages, and  Programming (ICALP 2018)},
  pages =	{130:1--130:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Ioannis Chatzigiannakis and Christos Kaklamanis and D{\'a}niel Marx and Donald Sannella},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9134},
  URN =		{urn:nbn:de:0030-drops-91344},
  doi =		{10.4230/LIPIcs.ICALP.2018.130},
  annote =	{Keywords: Labelled Markov Chains, Hidden Markov Models, Distance, Decidability, Complexity}
}

Keywords: Labelled Markov Chains, Hidden Markov Models, Distance, Decidability, Complexity
Seminar: 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)
Issue date: 2018
Date of publication: 2018


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