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A model-free soft classification with a functional predictor

Authors
Lee, EugeneShin, Seung Jun
Issue Date
11월-2019
Publisher
KOREAN STATISTICAL SOC
Keywords
functional data; Fisher consistency; support vector machines; probability estimation
Citation
COMMUNICATIONS FOR STATISTICAL APPLICATIONS AND METHODS, v.26, no.6, pp.635 - 644
Indexed
SCOPUS
KCI
Journal Title
COMMUNICATIONS FOR STATISTICAL APPLICATIONS AND METHODS
Volume
26
Number
6
Start Page
635
End Page
644
URI
https://scholar.korea.ac.kr/handle/2021.sw.korea/61989
DOI
10.29220/CSAM.2019.26.6.635
ISSN
2287-7843
Abstract
Class probability is a fundamental target in classification that contains complete classification information. In this article, we propose a class probability estimation method when the predictor is functional. Motivated by Wang et al. (Biometrika, 95, 149-167, 2007), our estimator is obtained by training a sequence of functional weighted support vector machines (FWSVM) with different weights, which can be justified by the Fisher consistency of the hinge loss. The proposed method can be extended to multiclass classification via pairwise coupling proposed by Wu et al. (Journal of Machine Learning Research, 5, 975-1005, 2004). The use of FWSVM makes our method model-free as well as computationally efficient due to the piecewise linearity of the FWSVM solutions as functions of the weight. Numerical investigation to both synthetic and real data show the advantageous performance of the proposed method.
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