Sufficient Dimension Reduction for Classification Using Principal Optimal Transport Direction

• Activity Number: 262 - Emerging Statistical Theory and Methods in Deep Learning
• Type: Invited
• Date/Time: Wednesday, August 11, 2021 : 1:30 PM to 3:20 PM
• Sponsor: Section for Statistical Programmers and Analysts
• Author(s): Cheng Meng and Jun Yu and Jingyi Zhang and Ping Ma and Wenxuan Zhong*
• Companies: Institute of Statistics and Big Data, Renmin University of China and School of Mathematics and Statistics, Beijing Institute of Technology and Center for Statistical Science, Tsinghua University and University of Georgia and University of Georgia
• Keywords: categorical response; conditional class probability; optimal transport direction; sufficient dimension reduction

Abstract

Sufficient dimension reduction is used pervasively as a supervised dimension reduction approach. Most existing sufficient dimension reduction methods are developed for data with a continuous response and may have an unsatisfactory performance for the categorical response, especially for the binary-response. To address this issue, a novel estimation method of sufficient dimension reduction subspace (SDR subspace) using optimal transport is proposed. The proposed method, named principal optimal transport direction (POTD), estimates the basis of the SDR subspace using the principal directions of the optimal transport coupling between the data respecting different response categories. The proposed method also reveals the relationship among three seemingly irrelevant topics, i.e., sufficient dimension reduction, support vector machine, and optimal transport. The asymptotic properties of POTD are studied and show that in the cases when the class labels contain no error, POTD estimates the SDR subspace exclusively. Empirical studies show POTD outperforms most of the state-of-the-art linear dimension reduction methods.