Dimension Reduction for Tensor Regression

• Activity Number: 544
• Type: Topic Contributed
• Date/Time: Wednesday, August 6, 2014 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Peng Zeng*+ and Wenxuan Zhong
• Companies: Auburn University and University of Georgia
• Keywords: dimension reduction ; tensor data ; sliced inverse regression

Abstract

As the rapid advance of science and technology in the past decades, data are abundant in a variety of disciplines and become more and more complex in structure. In some applications, the data can be naturally represented in terms of tensors, or multi-way arrays. A motivation example is an optical electronic nose technique, called colorimetric sensor array (CSA). The collected data are 3-dimensional arrays, where the dimensions represent dyes, color, and time, respectively. In traditional statistical analysis, arrays are usually vectorized by stacking up their elements to transform them to vectors. This approach destroys the intrinsic structure of tensors and consequently leads to inefficient analysis. In this talk, we propose a tensor dimension reduction regression model that assumes the response depends on a projection of the tensor predictors through some unknown link function. Fully utilizing the tensor structure, a novel sequential approach, called SIDRA, has been proposed to estimate the parameters. The asymptotic results of the estimates have also been derived. The nice empirical properties of SIDRA will be demonstrated in both simulation study and real examples.