Learning a Common Substructure of Multiple Graphical Gaussian Models
This work addresses the need for robust feature extraction in multi-condition data analysis, with potential applications in fields like sensor monitoring, though it appears incremental in its methodological approach.
The paper tackles the problem of identifying invariant dependency structures across multiple datasets collected under different conditions, proposing a common substructure learning framework based on graphical Gaussian models and demonstrating its performance through simulations and a real-world anomaly detection application.
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.