A partial orthogonalization method for simulating covariance and concentration graph matrices
Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
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.
Original language | English |
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Title of host publication | Proceedings of the 9th International Conference on Probabilistic Graphical Models |
Editors | Václav Kratochvíl, Milan Studený |
Publisher | PMLR |
Publication date | 2018 |
Pages | 61-72 |
Publication status | Published - 2018 |
Event | 9th International Conference on Probabilistic Graphical Models - Prague, Czech Republic Duration: 11 Sep 2018 → 14 Sep 2018 |
Conference
Conference | 9th International Conference on Probabilistic Graphical Models |
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Land | Czech Republic |
By | Prague |
Periode | 11/09/2018 → 14/09/2018 |
Series | Proceedings of Machine Learning Research |
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Volume | 72 |
ISSN | 1938-7228 |
ID: 215089091