Transductive Learning with Multi-class Volume Approximation

Given a hypothesis space, the large volume principle by Vladimir Vapnik prioritizes equivalence classes according to their volume in the hypothesis space. The volume approximation has hitherto been successfully applied to binary learning problems. In this paper, we extend it naturally to a more gene...

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Bibliographic Details
Published inarXiv.org
Main Authors Niu, Gang, Dai, Bo, Marthinus Christoffel du Plessis, Sugiyama, Masashi
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 03.02.2014
Subjects
Approximation
Convexity
Error analysis
Hypotheses
Learning
Mathematical analysis
Optimization
Stability analysis
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Summary:Given a hypothesis space, the large volume principle by Vladimir Vapnik prioritizes equivalence classes according to their volume in the hypothesis space. The volume approximation has hitherto been successfully applied to binary learning problems. In this paper, we extend it naturally to a more general definition which can be applied to several transductive problem settings, such as multi-class, multi-label and serendipitous learning. Even though the resultant learning method involves a non-convex optimization problem, the globally optimal solution is almost surely unique and can be obtained in O(n^3) time. We theoretically provide stability and error analyses for the proposed method, and then experimentally show that it is promising.
ISSN:2331-8422