Learning Multi-Attribute Differential Graphs with Non-Convex Penalties

TL;DR

This paper introduces a novel approach for estimating differences in multi-attribute Gaussian graphical models using non-convex penalties, providing theoretical guarantees and demonstrating effectiveness through numerical experiments.

Contribution

It proposes a non-convex penalized D-trace loss method for differential graph estimation, with new optimization algorithms and theoretical support for high-dimensional consistency.

Findings

Effective support recovery in high-dimensional settings

Consistent estimation with non-convex penalties

Successful application to synthetic and real data

Abstract

We consider the problem of estimating differences in two multi-attribute Gaussian graphical models (GGMs) which are known to have similar structure, using a penalized D-trace loss function with non-convex penalties. The GGM structure is encoded in its precision (inverse covariance) matrix. Existing methods for multi-attribute differential graph estimation are based on a group lasso penalized loss function. In this paper, we consider a penalized D-trace loss function with non-convex (log-sum and smoothly clipped absolute deviation (SCAD)) penalties. Two proximal gradient descent methods are presented to optimize the objective function. Theoretical analysis establishing sufficient conditions for consistency in support recovery, convexity and estimation in high-dimensional settings is provided. We illustrate our approaches with numerical examples based on synthetic and real data.