Large-margin classification with multiple decision rules

Binary classification is a common statistical learning problem in which a model is estimated on a set of covariates for some outcome, indicating the membership of one of two classes. In the literature, there exists a distinction between hard and soft classification. In soft classification, the condi...

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Bibliographic Details
Published in:Statistical analysis and data mining Vol. 9; no. 2; pp. 89 - 105
Main Authors: Kimes, Patrick K., Hayes, David Neil, Marron, J. S., Liu, Yufeng
Format: Journal Article
Language:English
Published: Hoboken Wiley Subscription Services, Inc., A Wiley Company 01.04.2016
Wiley Subscription Services, Inc
Subjects:
Algorithms
Alzheimer's disease
Classification
Cognitive tasks
conditional probability estimation
excess risk bounds
Learning
Magnetic resonance imaging
Medical imaging
Statistical analysis
statistical machine learning
supervised learning
Task complexity
ISSN:1932-1864, 1932-1872
Online Access:Get full text
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Summary:Binary classification is a common statistical learning problem in which a model is estimated on a set of covariates for some outcome, indicating the membership of one of two classes. In the literature, there exists a distinction between hard and soft classification. In soft classification, the conditional class probability is modeled as a function of the covariates. In contrast, hard classification methods only target the optimal prediction boundary. While hard and soft classification methods have been studied extensively, not much work has been performed to compare the actual tasks of hard and soft classification. In this paper, we propose a spectrum of statistical learning problems that span the hard and soft classification tasks based on fitting multiple decision rules to the data. By doing so, we reveal a novel collection of learning tasks of increasing complexity. We study the problems using the framework of large‐margin classifiers and a class of piecewise linear convex surrogates, for which we derive statistical properties and a corresponding sub‐gradient descent algorithm. We conclude by applying our approach to simulation settings and a magnetic resonance imaging (MRI) dataset from the Alzheimer's Disease Neuroimaging Initiative (ADNI) study.
Bibliography:ark:/67375/WNG-THCNZC1F-6
Supporting Information
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ArticleID:SAM11304
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SourceType-Scholarly Journals-1
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content type line 14
ISSN:1932-1864
1932-1872
DOI:10.1002/sam.11304