License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
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DOI: 10.4230/LIPIcs.ITCS.2021.25
URN: urn:nbn:de:0030-drops-135643
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/13564/
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Feng, Weiming ; He, Kun ; Sun, Xiaoming ; Yin, Yitong

Dynamic Inference in Probabilistic Graphical Models

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LIPIcs-ITCS-2021-25.pdf (0.7 MB)

Abstract

Probabilistic graphical models, such as Markov random fields (MRFs), are useful for describing high-dimensional distributions in terms of local dependence structures. The {probabilistic inference} is a fundamental problem related to graphical models, and sampling is a main approach for the problem. In this paper, we study probabilistic inference problems when the graphical model itself is changing dynamically with time. Such dynamic inference problems arise naturally in today’s application, e.g. multivariate time-series data analysis and practical learning procedures.
We give a dynamic algorithm for sampling-based probabilistic inferences in MRFs, where each dynamic update can change the underlying graph and all parameters of the MRF simultaneously, as long as the total amount of changes is bounded. More precisely, suppose that the MRF has n variables and polylogarithmic-bounded maximum degree, and N(n) independent samples are sufficient for the inference for a polynomial function N(⋅). Our algorithm dynamically maintains an answer to the inference problem using Õ(n N(n)) space cost, and Õ(N(n) + n) incremental time cost upon each update to the MRF, as long as the Dobrushin-Shlosman condition is satisfied by the MRFs. This well-known condition has long been used for guaranteeing the efficiency of Markov chain Monte Carlo (MCMC) sampling in the traditional static setting. Compared to the static case, which requires Ω(n N(n)) time cost for redrawing all N(n) samples whenever the MRF changes, our dynamic algorithm gives a ?^~(min{n, N(n)})-factor speedup. Our approach relies on a novel dynamic sampling technique, which transforms local Markov chains (a.k.a. single-site dynamics) to dynamic sampling algorithms, and an "algorithmic Lipschitz" condition that we establish for sampling from graphical models, namely, when the MRF changes by a small difference, samples can be modified to reflect the new distribution, with cost proportional to the difference on MRF.

BibTeX - Entry

@InProceedings{feng_et_al:LIPIcs.ITCS.2021.25,
  author =	{Weiming Feng and Kun He and Xiaoming Sun and Yitong Yin},
  title =	{{Dynamic Inference in Probabilistic Graphical Models}},
  booktitle =	{12th Innovations in Theoretical Computer Science Conference (ITCS 2021)},
  pages =	{25:1--25:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-177-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{185},
  editor =	{James R. Lee},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/13564},
  URN =		{urn:nbn:de:0030-drops-135643},
  doi =		{10.4230/LIPIcs.ITCS.2021.25},
  annote =	{Keywords: Dynamic inference, probabilistic graphical model, Gibbs sampling, Markov random filed}
}

Keywords: Dynamic inference, probabilistic graphical model, Gibbs sampling, Markov random filed
Collection: 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)
Issue Date: 2021
Date of publication: 04.02.2021

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