A0676
Title: Binary regression and classification with covariates in metric spaces
Authors: Yinan Lin - National University of Singapore (Singapore)
Zhenhua Lin - University of California, Davis (United States) [presenting]
Abstract: Inspired by logistic regression, a regression model is introduced for data tuples consisting of a binary response and a set of covariates residing in a metric space without vector structures. Based on the proposed model, a binary classifier is also developed for metric-space-valued data. A maximum likelihood estimator is proposed for the metric-space valued regression coefficient in the model, and upper bounds are provided on the estimation error under various metric entropy conditions that quantify the complexity of the underlying metric space. Matching lower bounds are derived for the important metric spaces commonly seen in statistics, establishing the optimality of the proposed estimator in such spaces. Similarly, an upper bound on the excess risk of the developed classifier is provided for general metric spaces. A finer upper bound and a matching lower bound, and thus optimality of the proposed classifier, are established for Riemannian manifolds. To the best of knowledge, the proposed regression model and the above minimax bounds are the first of their kind for analyzing a binary response with covariates residing in general metric spaces. The numerical performance of the proposed estimator and classifier is also investigated via simulation studies, and their practical merits are illustrated via an application to task-related fMRI data.
