Learning from a mixture of labeled and unlabeled examples with parametric side information

Joel Ratsaby, Santosh S. Venkatesh

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

57 Scopus citations

Abstract

We investigate the tradeoff between labeled and unlabeled sample complexities in learning a classification rule for a parametric two-class problem. In the problem considered, a sample of m labeled examples and n unlabeled examples generated from a two-class, N-variate Gaussian mixture is provided together with side information specifying the parametric form of the probability densities. The class means and a priori class probabilities are, however, unknown parameters. In this framework we use the maximum likelihood estimation method to estimate the unknown parameters and utilize rates of convergence of uniform strong laws to determine the tradeoff between error rate and sample complexity. In particular, we show that for the algorithm used, the misclassification probability deviates from the minimal Bayes error rate by O(N3/5n-1/5) + O(e-cm) where N is the dimension of the feature space, m is the number of labeled examples, n is the number of unlabeled examples, and c is a positive constant.

Original languageEnglish
Title of host publicationProceedings of the 8th Annual Conference on Computational Learning Theory, COLT 1995
PublisherAssociation for Computing Machinery, Inc
Pages412-417
Number of pages6
ISBN (Electronic)0897917235, 9780897917230
DOIs
StatePublished - 5 Jul 1995
Externally publishedYes
Event8th Annual Conference on Computational Learning Theory, COLT 1995 - Santa Cruz, United States
Duration: 5 Jul 19958 Jul 1995

Publication series

NameProceedings of the 8th Annual Conference on Computational Learning Theory, COLT 1995
Volume1995-January

Conference

Conference8th Annual Conference on Computational Learning Theory, COLT 1995
Country/TerritoryUnited States
CitySanta Cruz
Period5/07/958/07/95

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Artificial Intelligence
  • Software

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