Classification of time series in high dimensions
As more and more modern time series data sets are becoming high dimensional, the problem of classification in this context has received increasing attention. We propose a statistical framework for classifying multivariate stationary Gaussian time series where the number of covariates, the length of the series, and the sample size, all grow to infinity.
Overview
Abstract
As more and more modern time series data sets are becoming high dimensional, the problem of classification in this context has received increasing attention. We propose a statistical framework for classifying multivariate stationary Gaussian time series where the number of covariates, the length of the series, and the sample size, all grow to infinity. To deal with high dimensionality of the problem, sparsity of inverse spectral density matrices (ISDM) are commonly assumed. In this work, instead of assuming sparsity on individual ISDMs, we assume the difference between ISDMs to be sparse. The pattern of sparsity of this difference is allowed to vary across frequencies, giving the framework an added layer of flexibility. In the process, we also identify the covariates that are crucial for distinguishing the competing time series. Furthermore, we develop a method for screening Fourier frequencies that are relevant for classification. The proposed method is shown to have desirable properties under fairly general assumptions.
Brief Biography
Sarbojit is a Postdoctoral Research Fellow in the Biostatistics Group at Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) division at King Abdullah University of Science and Technology (KAUST). He did his PhD from Indian Institute of Technology Kanpur in Statistics. His research interests include Discriminant Analysis, High-Dimensional Asymptotics, Nonparametric Methods, Statistical Pattern Recognition, Variable Clustering, etc.