Supervised classifiers for high-dimensional higher-order data with locally doubly exchangeable covariance structure

• Published in: Communications in statistics. Theory and methods Vol. 46; no. 23; pp. 11612 - 11634
• Main Authors: Pavlenko, Tatjana, Roy, Anuradha
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 02.12.2017; Taylor & Francis Ltd
• Subjects: Class of asymptotically equivalent structure approximations; classification rule; Classifiers; Covariance matrix; graphical Lasso; high-dimensional higher-order data; locally doubly exchangeable covariance structure; Maximum likelihood estimators; Multivariate analysis; Parameter estimation
• ISSN: 0361-0926; 1532-415X; 1532-415X
• DOI: 10.1080/03610926.2016.1275695

We explore the performance accuracy of the linear and quadratic classifiers for high-dimensional higher-order data, assuming that the class conditional distributions are multivariate normal with locally doubly exchangeable covariance structure. We derive a two-stage procedure for estimating the covariance matrix: at the first stage, the Lasso-based structure learning is applied to sparsifying the block components within the covariance matrix. At the second stage, the maximum-likelihood estimators of all block-wise parameters are derived assuming the doubly exchangeable within block covariance structure and a Kronecker product structured mean vector. We also study the effect of the block size on the classification performance in the high-dimensional setting and derive a class of asymptotically equivalent block structure approximations, in a sense that the choice of the block size is asymptotically negligible.