On Cholesky structures on real symmetric matrices and their applications | Vidéo | Carmin.tv

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On Cholesky structures on real symmetric matrices and their applications

By Hideyuki Ishi

Appears in collection : Mathematical Methods of Modern Statistics 2 / Méthodes mathématiques en statistiques modernes 2

As a generalization of fill-in free property of a sparse positive definite real symmetric matrix with respect to the Cholesky decomposition, we introduce a notion of (quasi-)Cholesky structure for a real vector space of symmetric matrices. The cone of positive definite symmetric matrices in a vector space with a quasi-Cholesky structure admits explicit calculations and rich analysis similar to the ones for Gaussian selsction model associated to a decomposable graph. In particular, we can apply our method to a decomposable graphical model with a vertex pemutation symmetry.

Information about the video

Date of recording 04/06/2020
Date of publication 15/06/2020
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19641103
Cite this video Ishi, Hideyuki (04/06/2020). On Cholesky structures on real symmetric matrices and their applications. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19641103
URL https://dx.doi.org/10.24350/CIRM.V.19641103

Domain(s)

Statistics Theory

Bibliography

HØJSGAARD, Søren et LAURITZEN, Steffen L. Graphical Gaussian models with edge and vertex symmetries. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 2008, vol. 70, no 5, p. 1005-1027. - https://doi.org/10.1111/j.1467-9868.2008.00666.x
ISHI Hideyuki. Homogeneous cones and their applications to statistics, in Modern Methods of Multivariate Statistics, p. 135-154, Hermann, 2014.
LETAC, Gérard, MASSAM, Hélène, et al. Wishart distributions for decomposable graphs. The Annals of Statistics, 2007, vol. 35, no 3, p. 1278-1323. - https://www.jstor.org/stable/25463600
MASSAM, H., LI, Q., et GAO, X. Bayesian precision and covariance matrix estimation for graphical Gaussian models with edge and vertex symmetries. Biometrika, 2018, vol. 105, no 2, p. 371-388. - https://doi.org/10.1093/biomet/asx084

MSC codes

Document(s)

https://www.cirm-math.fr/RepOrga/2146/Slides/Ishi-Slide.pdf

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