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Activity Number: 311 - Inference, Prediction, and Statistical Learning for Functional Data
Type: Topic-Contributed
Date/Time: Wednesday, August 11, 2021 : 3:30 PM to 5:20 PM
Sponsor: SSC (Statistical Society of Canada)
Abstract #317385
Title: A Reproducing Kernel Hilbert Space Framework for Functional Data Classification
Author(s): Peijun Sang*
Companies: University of Waterloo
Keywords: Functional data classification; Distance-weighted discrimination; Reproducing kernel Hilbert space; Non-asymptotic error bound

We encounter a bottleneck when we try to borrow the strength of classical classifiers to classify functional data. The major issue is that functional data are intrinsically infinite dimensional, thus classical classifiers cannot be applied directly or have poor performance due to curse of dimensionality. To address this concern, we propose to project functional data onto one specific direction, and then a distance-weighted discrimination DWD classifier is built upon the projection score. The projection direction is identified through minimizing an empirical risk function that contains the particular loss function in a DWD classifier, over a reproducing kernel Hilbert space. Hence our proposed classifier can avoid overfitting and enjoy appealing properties of DWD classifiers. This framework is further extended to accommodate functional data classification problems where scalar covariates are involved. In contrast to previous work, we establish a non-asymptotic estimation error bound on the relative misclassification rate.

Authors who are presenting talks have a * after their name.

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