APSIPA Transactions on Signal and Information Processing > Vol 7 > Issue 1

Covariance selection quality through detection problem and AUC bounds

Navid Tafaghodi Khajavi, University of Hawaii, USA, navidt@hawaii.edu , Anthony Kuh, University of Hawaii, USA
 
Suggested Citation
Navid Tafaghodi Khajavi and Anthony Kuh (2018), "Covariance selection quality through detection problem and AUC bounds", APSIPA Transactions on Signal and Information Processing: Vol. 7: No. 1, e19. http://dx.doi.org/10.1017/ATSIP.2018.20

Publication Date: 11 Dec 2018
© 2018 Navid Tafaghodi Khajavi and Anthony Kuh
 
Subjects
 
Keywords
Statistical model selectionDetection problemTree approximationArea under the curveCovariance selection
 

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In this article:
I. INTRODUCTION 
II. DETECTION PROBLEM FRAMEWORK 
III. THE ROC CURVE AND THE AUC COMPUTATION 
IV. ANALYTICAL BOUNDS FOR THE AUC 
V. EXAMPLES AND SIMULATION RESULTS 
VI. CONCLUSION 

Abstract

Graphical models are increasingly being used in many complex engineering problems to model the dynamics between states of the graph. These graphs are often very large and approximation models are needed to reduce the computational complexity. This paper considers the problem of quantifying the quality of an approximation model for a graphical model (model selection problem). The model selection often uses a distance measure such as the KullbackÔÇôLeibler (KL) divergence between the original distribution and the model distribution to quantify the quality of the model approximation. We extend and broaden the body of research by formulating the model approximation as a detection problem between the original distribution and the model distribution. We focus on Gaussian random vectors and introduce the Correlation Approximation Matrix (CAM) and use the Area Under the Curve (AUC) for the formulated detection problem. The closeness measures such as the KL divergence, the log-likelihood ratio, and the AUC are functions of the eigenvalues of the CAM. Easily computable upper and lower bounds are found for the AUC. The paper concludes by computing these measures for real and synthetic simulation data. Tree approximations and more complex graphical models are considered for approximation models.

DOI:10.1017/ATSIP.2018.20