DROPS

Document

RANDOM

DOI: 10.4230/LIPIcs.APPROX/RANDOM.2022.1

A Unified Approach to Discrepancy Minimization

Authors: Nikhil Bansal, Aditi Laddha, and Santosh Vempala

Published in: LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)

Abstract

We study a unified approach and algorithm for constructive discrepancy minimization based on a stochastic process. By varying the parameters of the process, one can recover various state-of-the-art results. We demonstrate the flexibility of the method by deriving a discrepancy bound for smoothed instances, which interpolates between known bounds for worst-case and random instances.

Cite as

Nikhil Bansal, Aditi Laddha, and Santosh Vempala. A Unified Approach to Discrepancy Minimization. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 1:1-1:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{bansal_et_al:LIPIcs.APPROX/RANDOM.2022.1,
  author =	{Bansal, Nikhil and Laddha, Aditi and Vempala, Santosh},
  title =	{{A Unified Approach to Discrepancy Minimization}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{1:1--1:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-249-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{245},
  editor =	{Chakrabarti, Amit and Swamy, Chaitanya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.1},
  URN =		{urn:nbn:de:0030-drops-171238},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.1},
  annote =	{Keywords: Discrepancy theory, smoothed analysis}
}

Document

DOI: 10.4230/LIPIcs.SoCG.2021.51

Convergence of Gibbs Sampling: Coordinate Hit-And-Run Mixes Fast

Authors: Aditi Laddha and Santosh S. Vempala

Published in: LIPIcs, Volume 189, 37th International Symposium on Computational Geometry (SoCG 2021)

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.

Cite as

Aditi Laddha and Santosh S. Vempala. Convergence of Gibbs Sampling: Coordinate Hit-And-Run Mixes Fast. In 37th International Symposium on Computational Geometry (SoCG 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 189, pp. 51:1-51:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@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/entities/document/10.4230/LIPIcs.SoCG.2021.51},
  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}
}

Search Results

Documents authored by Laddha, Aditi

A Unified Approach to Discrepancy Minimization

Abstract

Cite as

Convergence of Gibbs Sampling: Coordinate Hit-And-Run Mixes Fast

Abstract

Cite as

Thanks for your feedback!

Could not send message