Learning a Common Substructure of Multiple Graphical Gaussian Models

TL;DR

This paper introduces a framework for identifying common dependency structures across multiple datasets using graphical Gaussian models, with an efficient algorithm and validation through simulations and real-world sensor data.

Contribution

It proposes a novel common substructure learning (CSSL) method for graphical Gaussian models and an efficient optimization algorithm for it.

Findings

CSSL accurately finds invariant dependency structures in synthetic data.

CSSL outperforms existing methods in anomaly detection in automobile sensors.

The proposed algorithm is simple and effective for large-scale problems.

Abstract

Properties of data are frequently seen to vary depending on the sampled situations, which usually changes along a time evolution or owing to environmental effects. One way to analyze such data is to find invariances, or representative features kept constant over changes. The aim of this paper is to identify one such feature, namely interactions or dependencies among variables that are common across multiple datasets collected under different conditions. To that end, we propose a common substructure learning (CSSL) framework based on a graphical Gaussian model. We further present a simple learning algorithm based on the Dual Augmented Lagrangian and the Alternating Direction Method of Multipliers. We confirm the performance of CSSL over other existing techniques in finding unchanging dependency structures in multiple datasets through numerical simulations on synthetic data and through a real world application to anomaly detection in automobile sensors.