A partial orthogonalization method for simulating covariance and concentration graph matrices

Córdoba Sánchez, Irene and Varando, Gherardo and Bielza Lozoya, Maria Concepcion and Larrañaga Mugica, Pedro Maria (2018). A partial orthogonalization method for simulating covariance and concentration graph matrices. In: "9th International Conference on Probabilistic Graphical Models", 11-14 Sep 2018, Praga, República Checa. pp. 61-72.

Description

Title: A partial orthogonalization method for simulating covariance and concentration graph matrices
Author/s:
  • Córdoba Sánchez, Irene
  • Varando, Gherardo
  • Bielza Lozoya, Maria Concepcion
  • Larrañaga Mugica, Pedro Maria
Item Type: Presentation at Congress or Conference (Article)
Event Title: 9th International Conference on Probabilistic Graphical Models
Event Dates: 11-14 Sep 2018
Event Location: Praga, República Checa
Title of Book: Proceedings of Machine Learning Research (PMLR)
Date: 2018
Volume: 72
Subjects:
Freetext Keywords: Concentration graph; Covariance graph; Positive definite matrix simulation; Undirected graphical model; Algorithm validation
Faculty: E.T.S. de Ingenieros Informáticos (UPM)
Department: Inteligencia Artificial
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

Structure learning methods for covariance and concentration graphs are often validated on synthetic models, usually obtained by randomly generating: (i) an undirected graph, and (ii) a compatible symmetric positive definite (SPD) matrix. In order to ensure positive definiteness in (ii), a dominant diagonal is usually imposed. However, the link strengths in the resulting graphical model, determined by off-diagonal entries in the SPD matrix, are in many scenarios extremely weak. Recovering the structure of the undirected graph thus becomes a challenge, and algorithm validation is notably affected. In this paper, we propose an alternative method which overcomes such problem yet yields a compatible SPD matrix. We generate a partially row-wise-orthogonal matrix factor, where pairwise orthogonal rows correspond to missing edges in the undirected graph. In numerical experiments ranging from moderately dense to sparse scenarios, we obtain that, as the dimension increases, the link strength we simulate is stable with respect to the structure sparsity. Importantly, we show in a real validation setting how structure recovery is greatly improved for all learning algorithms when using our proposed method, thereby producing a more realistic comparison framework.

Funding Projects

TypeCodeAcronymLeaderTitle
Government of SpainTIN2016-79684-PUnspecifiedUniversidad Politécnica de MadridAvances en clasificación multidimensional y detección de anomalías con redes bayesianas
Madrid Regional GovernmentS2013/ICE-2845CASI-CAM-CMUnspecifiedConceptos y Aplicaciones de los Sistemas Inteligentes
Government of SpainC080020-09UnspecifiedUniversidad Politécnica de MadridCajal Blue Brain

More information

Item ID: 54636
DC Identifier: http://oa.upm.es/54636/
OAI Identifier: oai:oa.upm.es:54636
Official URL: http://proceedings.mlr.press/v72/cordoba18a/cordoba18a.pdf
Deposited by: Memoria Investigacion
Deposited on: 23 Apr 2019 10:07
Last Modified: 24 Apr 2019 10:36
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