DROP: Distributionally Robust Optimization for Multi-task Learning in Graphical Models

2026-03-24

AI Summary

This work addresses the vulnerability of Gaussian graphical models in estimating precision matrices under high-dimensional, heavy-tailed, or contaminated data, which often distorts inferred conditional dependence structures. To overcome this limitation, the authors propose DROP, a novel method that, for the first time, integrates distributionally robust optimization into a multi-task node-wise regression framework, augmented with structured sparsity regularization. DROP simultaneously ensures robustness against data perturbations and enforces sparsity while preserving provable theoretical error bounds. Empirical results demonstrate that the method reliably recovers modular network structures even under severe contamination: simulations show markedly reduced false-positive edge rates, and real-world fMRI analyses outperform existing non-robust approaches. The implementation will be made publicly available.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Gaussian Graphical Models (GGMs) are widely used to infer conditional dependence structures in high-dimensional data. However, standard precision matrix estimators are highly sensitive to data contamination, such as extreme outliers and heavy-tailed noise. In this paper, we propose DROP (Distributionally Robust Optimization), a robust estimation method formulated within a multi-task nodewise regression framework. The proposed estimator enforces structural sparsity while resisting the influence of corrupted observations. Theoretically, we establish error bounds for the DROP estimator under general contamination. Through extensive high-dimensional simulations, we demonstrate that DROP consistently controls the rate of false positive edges and outperforms conventional non-robust estimators when data deviate from standard Gaussian assumptions. Furthermore, in a functional MRI (fMRI) application, DROP maintains a stable graph structure and preserves network modularity even when subjected to severe data perturbations, whereas competing methods yield excessively dense networks. To facilitate reproducible research, the DROP R package will be made publicly available on GitHub.

Problem

• Gaussian Graphical Models
• data contamination
• robust estimation
• multi-task learning
• precision matrix

Innovation

• Distributionally Robust Optimization
• Gaussian Graphical Models
• Multi-task Learning
• Robust Estimation
• Structural Sparsity