Local Neighborhood Fusion in Locally Constant Gaussian Graphical Models

TL;DR

This paper introduces Neighborhood-Fused Lasso, a novel method for high-dimensional graphical model selection that leverages local constancy, improving accuracy over existing methods by incorporating locality information.

Contribution

It extends node-wise regression with a fusion penalty to utilize local constancy, providing a fast algorithm and theoretical guarantees for improved model selection.

Findings

Outperforms existing methods ignoring locality information

Provides bounds for quadratic prediction error and coefficient estimates

Demonstrates effectiveness through numerical experiments

Abstract

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.