A Fast Metropolis-Hastings Method for Generating Random Correlation Matrices

Irene Córdoba, Gherardo Varando, Concha Bielza, Pedro Larrañaga

1 Citation (Scopus)

Abstract

We propose a novel Metropolis-Hastings algorithm to sample uniformly from the space of correlation matrices. Existing methods in the literature are based on elaborated representations of a correlation matrix, or on complex parametrizations of it. By contrast, our method is intuitive and simple, based the classical Cholesky factorization of a positive definite matrix and Markov chain Monte Carlo theory. We perform a detailed convergence analysis of the resulting Markov chain, and show how it benefits from fast convergence, both theoretically and empirically. Furthermore, in numerical experiments our algorithm is shown to be significantly faster than the current alternative approaches, thanks to its simple yet principled approach.
Original languageEnglish
Title of host publicationDistributions and operators Gerd Grubb : 19th International Conference Madrid, Spain, November 21–23, 2018
EditorsHujun Yin, David Camacho, Paulo Novais, Antonio J. Tallón-Ballesteros
Number of pages8
Volume1
PublisherSpringer
Publication date2018
Pages117-124
ISBN (Print)9783030034924
DOIs
Publication statusPublished - 2018
Event19th International Conference on Intelligent Data Engineering and Automated Learning, IDEAL 2018 - Madrid, Spain
Duration: 21 Nov 201823 Nov 2018

Conference

Conference19th International Conference on Intelligent Data Engineering and Automated Learning, IDEAL 2018
Country/TerritorySpain
CityMadrid
Period21/11/201823/11/2018
SeriesLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11314 LNCS

Keywords

  • Correlation matrices
  • Metroplis-Hastings
  • Random sampling

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