Learning a common substructure of multiple graphical Gaussian models

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.

Anomaly detection in reconstructed quantum states using a machine-learning technique

“…To reflect these two points in a sophisticated manner, we introduce a technique proposed in graphical Gaussian modeling (GGM), which is a research field of data mining. The technique involves efficiently decomposing a set of precision matrices, which are inverse covariance matrices, into their common invariant elements and individually deviated elements [6,9]. Because these techniques are dedicated to the precision matrices, which are typically sparse and positive semi-definite (PSD), it is not applicable to our absolute density matrices, which are often dense and not limited to being PSD.…”

“…Here, we describe an overview of the algorithm, which works up to several qubits or for matrices of size around hundreds. Similar to our previous study [6], we do not work on the problem (2) directly but work on the dual problem instead:…”

“…Such anomalies include dephasing in the quantum states, which is very important in many applications and tasks of quantum information processing. For this purpose, we have developed a new data mining method named 'ED 3 (Erroneous Deviation Detection for Density matrices)' for quantum density matrices by ex-tending a previously reported method [6]. We compare ED 3 and a naive method, in which the erroneous states are distinguished by the trace distance from the average of the states.…”

Meta-Path Graphical Lasso for Learning Heterogeneous Connectivities

“…There are some prior works [6,13,14,20,24] on learning multiple precision matrices simultaneously from multiple different but related sets of observations. All these methods assume that the jointly learned precision matrices (graphs) should share the similar structure.…”

“…All these methods assume that the jointly learned precision matrices (graphs) should share the similar structure. For example, [13] proposed a method to learn common substructures among multiple graphs. [6] used ADMM to estimate multiple precision matrices with pairwise fused lasso penalty and group lasso penalty.…”