Local Neighborhood Fusion in Locally Constant Gaussian Graphical Models

In this paper we penetrate and extend the notion of local constancy in graphical models that has been introduced by Honorio et al. (2009). We propose Neighborhood-Fused Lasso, a method for model selection in high-dimensional graphical models, leveraging locality information. Our approach is based on an extension of the idea of node-wise regression (Meinshausen-B\"{u}hlmann, 2006) by adding a fusion penalty. We propose a fast numerical algorithm for our approach, and provide theoretical and numerical evidence for the fact that our methodology outperforms related approaches that are ignoring the locality information. We further investigate the compatibility issues in our proposed methodology and derive bound for the quadratic prediction error and $l_1$-bounds on the estimated coefficients.