GMRF Estimation under Topological and Spectral Constraints

Victorin Martin 1 Cyril Furtlehner 2 Yufei Han 3 Jean-Marc Lasgouttes 4
2 TAO - Machine Learning and Optimisation
CNRS - Centre National de la Recherche Scientifique : UMR8623, Inria Saclay - Ile de France, UP11 - Université Paris-Sud - Paris 11, LRI - Laboratoire de Recherche en Informatique
Abstract : We investigate the problem of Gaussian Markov random field selection under a non-analytic constraint: the estimated models must be compatible with a fast inference algorithm, namely the Gaussian belief propagation algorithm. To address this question, we introduce the *-IPS framework, based on iterative proportional scaling, which incrementally selects candidate links in a greedy manner. Besides its intrinsic sparsity-inducing ability, this algorithm is flexible enough to incorporate various spectral constraints, like e.g. walk summability, and topological constraints, like short loops avoidance. Experimental tests on various datasets, including traffic data from San Francisco Bay Area, indicate that this approach can deliver, with reasonable computational cost, a broad range of efficient inference models, which are not accessible through penalization with traditional sparsity-inducing norms.
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Victorin Martin, Cyril Furtlehner, Yufei Han, Jean-Marc Lasgouttes. GMRF Estimation under Topological and Spectral Constraints. 7th European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, Sep 2014, Nancy, France. pp.370-385, ⟨10.1007/978-3-662-44851-9_24⟩. ⟨hal-01065607⟩

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