Section: New Results

Sparse covariance inverse estimate for Gaussian Markov Random Field

Participants : Cyril Furtlehner, Jean-Marc Lasgouttes.

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.

This work has been presented at ECML/PKDD 2014 [40] . The code for $☆$-IPS has been made available at https://who.rocq.inria.fr/Jean-Marc.Lasgouttes/star-ips/ .