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URN: urn:nbn:de:0030-drops-138503
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Convergence of Gibbs Sampling: Coordinate Hit-And-Run Mixes Fast

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Abstract

The Gibbs Sampler is a general method for sampling high-dimensional distributions, dating back to 1971. In each step of the Gibbs Sampler, we pick a random coordinate and re-sample that coordinate from the distribution induced by fixing all the other coordinates. While it has become widely used over the past half-century, guarantees of efficient convergence have been elusive. We show that for a convex body K in ℝⁿ with diameter D, the mixing time of the Coordinate Hit-and-Run (CHAR) algorithm on K is polynomial in n and D. We also give a lower bound on the mixing rate of CHAR, showing that it is strictly worse than hit-and-run and the ball walk in the worst case.

BibTeX - Entry

@InProceedings{laddha_et_al:LIPIcs.SoCG.2021.51,
  author =	{Laddha, Aditi and Vempala, Santosh S.},
  title =	{{Convergence of Gibbs Sampling: Coordinate Hit-And-Run Mixes Fast}},
  booktitle =	{37th International Symposium on Computational Geometry (SoCG 2021)},
  pages =	{51:1--51:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-184-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{189},
  editor =	{Buchin, Kevin and Colin de Verdi\`{e}re, \'{E}ric},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/13850},
  URN =		{urn:nbn:de:0030-drops-138503},
  doi =		{10.4230/LIPIcs.SoCG.2021.51},
  annote =	{Keywords: Gibbs Sampler, Coordinate Hit and run, Mixing time of Markov Chain}
}

Keywords: Gibbs Sampler, Coordinate Hit and run, Mixing time of Markov Chain
Seminar: 37th International Symposium on Computational Geometry (SoCG 2021)
Issue date: 2021
Date of publication: 02.06.2021


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