A partial orthogonalization method for simulating covariance and concentration graph matrices

Publikation: Bidrag til bog/antologi/rapportKonferencebidrag i proceedingsForskningfagfællebedømt

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.
OriginalsprogEngelsk
TitelProceedings of the 9th International Conference on Probabilistic Graphical Models
RedaktørerVáclav Kratochvíl, Milan Studený
ForlagPMLR
Publikationsdato2018
Sider61-72
StatusUdgivet - 2018
Begivenhed9th International Conference on Probabilistic Graphical Models - Prague, Tjekkiet
Varighed: 11 sep. 201814 sep. 2018

Konference

Konference9th International Conference on Probabilistic Graphical Models
LandTjekkiet
ByPrague
Periode11/09/201814/09/2018
NavnProceedings of Machine Learning Research
Vol/bind72
ISSN1938-7228

ID: 215089091