Single Index Model for Tensor Data: Theory and Application

Abstract

Modern scientific applications are frequently producing data sets where the data are not in the form of vectors but instead higher order tensors. For instance, multi-channel MEG signals in biomedical engineering, gene expression data in bioinformatics and so on. In this dissertation, we combine the semi-parametric model (single index model) with nuclear norm regularization to fit the data with order-2 tensor (matrix). An efficient estimation algorithm is developed. Furthermore, we proved that this algorithm has a good asymptotic property that the estimator of the true parameter B is root-n consistent. In addition to theoretical results, we demonstrate the efficiency of the new method through simulation. One real data set is analyzed by this new method and traditional logistic regression, then the results show that the performance of the new proposed method is better than the performance of logistic regression.