A constrained L1 minimization approach for estimating multiple Sparse Gaussian or Nonparanormal Graphical Models

TL;DR

This paper introduces SIMULE, a novel method for jointly estimating multiple sparse graphical models, capable of identifying both shared and context-specific edges, applicable to Gaussian and Nonparanormal data, with theoretical guarantees and superior empirical performance.

Contribution

The paper proposes SIMULE, a constrained L1 minimization approach that efficiently estimates multiple related graphical models, including non-Gaussian data, with proven consistency and improved results.

Findings

SIMULE achieves consistent estimation at rate O(log(Kp)/n_{tot})

Outperforms state-of-the-art multi-sGGM and single-UGM methods on synthetic and biomedical data

Handles both Gaussian and Nonparanormal data effectively

Abstract

Identifying context-specific entity networks from aggregated data is an important task, arising often in bioinformatics and neuroimaging. Computationally, this task can be formulated as jointly estimating multiple different, but related, sparse Undirected Graphical Models (UGM) from aggregated samples across several contexts. Previous joint-UGM studies have mostly focused on sparse Gaussian Graphical Models (sGGMs) and can't identify context-specific edge patterns directly. We, therefore, propose a novel approach, SIMULE (detecting Shared and Individual parts of MULtiple graphs Explicitly) to learn multi-UGM via a constrained L1 minimization. SIMULE automatically infers both specific edge patterns that are unique to each context and shared interactions preserved among all the contexts. Through the L1 constrained formulation, this problem is cast as multiple independent subtasks of linear programming that can be solved efficiently in parallel. In addition to Gaussian data, SIMULE can also handle multivariate Nonparanormal data that greatly relaxes the normality assumption that many real-world applications do not follow. We provide a novel theoretical proof showing that SIMULE achieves a consistent result at the rate O(log(Kp)/n_{tot}). On multiple synthetic datasets and two biomedical datasets, SIMULE shows significant improvement over state-of-the-art multi-sGGM and single-UGM baselines.