Optimality of Multiple Decision Statistical Procedure for Gaussian Graphical Model Selection

• Published in: Learning and Intelligent Optimization Vol. 11353; pp. 304 - 308
• Main Authors: Kalyagin, Valery A., Koldanov, Alexander P., Koldanov, Petr A., Pardalos, Panos M.
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 01.01.2019; Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: Gaussian graphical models; Multiple Decision; Optimal multiple decision statistical procedures; Unbiased multiple decision statistical procedures
• ISBN: 3030053474; 9783030053475
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-030-05348-2_26

Gaussian graphical model selection is a statistical problem that identifies the Gaussian graphical model from observations. Existing Gaussian graphical model selection methods focus on the error rate for incorrect edge inclusion. However, when comparing statistical procedures, it is also important to take into account the error rate for incorrect edge exclusion. To handle this issue we consider the graphical model selection problem in the framework of multiple decision theory. We show that the statistical procedure based on simultaneous inference with UMPU individual tests is optimal in the class of unbiased procedures.