B0208
Title: Logistic regression and classification with non-Euclidean covariates
Authors: Zhenhua Lin - National University of Singapore (Singapore) [presenting]
Yinan Lin - National University of Singapore (Singapore)
Abstract: A logistic regression model is introduced for data pairs consisting of a binary response and a covariate residing in a non-Euclidean metric space without vector structures. Based on the proposed model, a binary classifier is also developed for non-Euclidean objects. A maximum likelihood estimator is proposed for the non-Euclidean regression coefficient in the model and provides upper bounds 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. The numerical performance of the proposed estimator and classifier are investigated via simulation studies, and their practical merits via an application to task-related fMRI data are illustrated.
