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.
Keywords
- Correlation matrices
- Random sampling
- Metroplis-Hastings
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Acknowledgements
This work has been partially supported by the Spanish Ministry of Economy, Industry and Competitiveness through the Cajal Blue Brain (C080020-09; the Spanish partner of the EPFL Blue Brain initiative) and TIN2016-79684-P projects; by the Regional Government of Madrid through the S2013/ICE-2845-CASI-CAM-CM project; and by Fundación BBVA grants to Scientific Research Teams in Big Data 2016. I. Córdoba has been supported by the predoctoral grant FPU15/03797 from the Spanish Ministry of Education, Culture and Sports. G. Varando has been partially supported by research grant 13358 from VILLUM FONDEN.
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Córdoba, I., Varando, G., Bielza, C., Larrañaga, P. (2018). A Fast Metropolis-Hastings Method for Generating Random Correlation Matrices. In: Yin, H., Camacho, D., Novais, P., Tallón-Ballesteros, A. (eds) Intelligent Data Engineering and Automated Learning – IDEAL 2018. IDEAL 2018. Lecture Notes in Computer Science(), vol 11314. Springer, Cham. https://doi.org/10.1007/978-3-030-03493-1_13
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DOI: https://doi.org/10.1007/978-3-030-03493-1_13
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