A Fast Metropolis-Hastings Method for Generating Random Correlation Matrices

Irene Córdoba; Gherardo Varando; Concha Bielza; Pedro Larrañaga

doi:10.1007/978-3-030-03493-1_13

A Fast Metropolis-Hastings Method for Generating Random Correlation Matrices

Irene Córdoba, Gherardo Varando, Concha Bielza, Pedro Larrañaga

Department of Mathematical Sciences

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 language	English
Title of host publication	Distributions and operators Gerd Grubb : 19th International Conference Madrid, Spain, November 21–23, 2018
Editors	Hujun Yin, David Camacho, Paulo Novais, Antonio J. Tallón-Ballesteros
Number of pages	8
Volume	1
Publisher	Springer
Publication date	2018
Pages	117-124
ISBN (Print)	9783030034924
DOIs	https://doi.org/10.1007/978-3-030-03493-1_13
Publication status	Published - 2018
Event	19th International Conference on Intelligent Data Engineering and Automated Learning, IDEAL 2018 - Madrid, Spain Duration: 21 Nov 2018 → 23 Nov 2018

Conference

Conference	19th International Conference on Intelligent Data Engineering and Automated Learning, IDEAL 2018
Country/Territory	Spain
City	Madrid
Period	21/11/2018 → 23/11/2018

Series	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	11314 LNCS

Keywords

Correlation matrices
Metroplis-Hastings
Random sampling

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10.1007/978-3-030-03493-1_13

Cite this

Córdoba, I., Varando, G., Bielza, C., & Larrañaga, P. (2018). A Fast Metropolis-Hastings Method for Generating Random Correlation Matrices. In H. Yin, D. Camacho, P. Novais, & A. J. Tallón-Ballesteros (Eds.), Distributions and operators Gerd Grubb: 19th International Conference Madrid, Spain, November 21–23, 2018 (Vol. 1, pp. 117-124). Springer. https://doi.org/10.1007/978-3-030-03493-1_13

A Fast Metropolis-Hastings Method for Generating Random Correlation Matrices. / Córdoba, Irene; Varando, Gherardo; Bielza, Concha et al.
Distributions and operators Gerd Grubb: 19th International Conference Madrid, Spain, November 21–23, 2018. ed. / Hujun Yin; David Camacho; Paulo Novais; Antonio J. Tallón-Ballesteros. Vol. 1 Springer, 2018. p. 117-124 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol. 11314 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Book chapter › Research › peer-review

Córdoba, I, Varando, G, Bielza, C & Larrañaga, P 2018, A Fast Metropolis-Hastings Method for Generating Random Correlation Matrices. in H Yin, D Camacho, P Novais & AJ Tallón-Ballesteros (eds), Distributions and operators Gerd Grubb: 19th International Conference Madrid, Spain, November 21–23, 2018. vol. 1, Springer, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11314 LNCS, pp. 117-124, 19th International Conference on Intelligent Data Engineering and Automated Learning, IDEAL 2018, Madrid, Spain, 21/11/2018. https://doi.org/10.1007/978-3-030-03493-1_13

Córdoba I, Varando G, Bielza C, Larrañaga P. A Fast Metropolis-Hastings Method for Generating Random Correlation Matrices. In Yin H, Camacho D, Novais P, Tallón-Ballesteros AJ, editors, Distributions and operators Gerd Grubb: 19th International Conference Madrid, Spain, November 21–23, 2018. Vol. 1. Springer. 2018. p. 117-124. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol. 11314 LNCS). doi: 10.1007/978-3-030-03493-1_13

Córdoba, Irene ; Varando, Gherardo ; Bielza, Concha et al. / A Fast Metropolis-Hastings Method for Generating Random Correlation Matrices. Distributions and operators Gerd Grubb: 19th International Conference Madrid, Spain, November 21–23, 2018. editor / Hujun Yin ; David Camacho ; Paulo Novais ; Antonio J. Tallón-Ballesteros. Vol. 1 Springer, 2018. pp. 117-124 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol. 11314 LNCS).

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A Fast Metropolis-Hastings Method for Generating Random Correlation Matrices

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