Section: New Results

Sparse covariance inverse estimate for Gaussian Markov Random Field

Participants : Cyril Furtlehner, Jean-Marc Lasgouttes, Victorin Martin.

We investigate the problem of Gaussian Markov random field (GMRF) selection under the constraint that the model is suitable for Gaussian belief propagation (GaBP) inference. We develop a method based on iterative proportional scaling (IPS) to incrementally select optimal GMRF factors, while maintaining GaBP compatibility. Besides the intrinsic sparsity-inducing capability, the proposed method is indeed sufficiently flexible to incorporate various spectral constraints like e.g. walk summability (WS) to insure the compatibility of the solutions with Gaussian Belief Propagation inference. Experimental tests on various datasets with refined $L_0$ or $L_1$ regularized sparse inverse estimate indicate that this approach is competitive and provides us with useful alternatives to traditional sparsity-inducing penalizations norms, giving more freedom in the graph structure selection process with no additional computational cost.