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Bayesian block-diagonal graphical models via the Fiedler prior

Abstract : We study the problem of inferring the conditional independence structure between the entries of a Gaussian random vector. Our focus is on finding groups of independent variables. This can be translated into the estimation of a precision matrix (inverse of the covariance matrix) with a block-diagonal structure. We borrow ideas from spectral graph theory and spectral clustering and propose a novel prior called Fiedler prior showing shrinkage properties towards block-diagonal precision matrices. We compare the shrinkage induced by our prior and the popular Graphical Lasso prior, and compare their performance on a simulated dataset.
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https://hal.inria.fr/hal-03275245
Contributor : Daria Bystrova Connect in order to contact the contributor
Submitted on : Wednesday, June 30, 2021 - 6:47:00 PM
Last modification on : Friday, February 4, 2022 - 3:24:30 AM
Long-term archiving on: : Friday, October 1, 2021 - 7:07:34 PM

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  • HAL Id : hal-03275245, version 1

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Julyan Arbel, Mario Beraha, Daria Bystrova. Bayesian block-diagonal graphical models via the Fiedler prior. SFdS - 52 Journées de Statistique de la Société Francaise de Statistique, Jun 2021, Nice, France. pp.1-6. ⟨hal-03275245⟩

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