TY - GEN

T1 - A partial orthogonalization method for simulating covariance and concentration graph matrices

AU - Córdoba, Irene

AU - Varando, Gherardo

AU - Bielza, Concha

AU - Larranaga, Pedro

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

M3 - Article in proceedings

T3 - Proceedings of Machine Learning Research

SP - 61

EP - 72

BT - Proceedings of the 9th International Conference on Probabilistic Graphical Models

A2 - Kratochvíl, Václav

A2 - Studený, Milan

PB - PMLR

T2 - 9th International Conference on Probabilistic Graphical Models

Y2 - 11 September 2018 through 14 September 2018

ER -