Statistical Mechanics of Online Learning for Ensemble Teachers

• Miyoshi Seiji

  Department of Electronic Engineering, Kobe City College of Technology

• Okada Masato

  Division of Transdisciplinary Sciences, Graduate School of Frontier Sciences, The University of Tokyo RIKEN Brain Science Institute JST PRESTO

Abstract

We analyze the generalization performance of a student in a model composed of linear perceptrons: a true teacher, ensemble teachers, and the student. Calculating the generalization error of the student analytically using statistical mechanics in the framework of on-line learning, we prove that when the learning rate satisfies η<1, the larger the number K is and the more variety the ensemble teachers have, the smaller the generalization error is. On the other hand, when η>1, the properties are completely reversed. If the variety of the ensemble teachers is rich enough, the direction cosine between the true teacher and the student becomes unity in the limit of η→0 and K→∞. Intuitive interpretations of these results are given.

Journal

• Journal of the Physical Society of Japan

  Journal of the Physical Society of Japan 75 (4), 044002-, 2006

  THE PHYSICAL SOCIETY OF JAPAN

Keywords

• ensemble teachers
• on-line learning
• generalization error
• statistical mechanics
• learning rate

Details

• CRID: 1390282679166594304
• NII Article ID: 210000106085
• NII Article ID: 110004729258
• NII Book ID: AA00704814
• DOI: 10.1143/jpsj.75.044002
• BIBCODE: 2006JPSJ...75d4002M
• ISSN: 13474073
• ISSN: 00319015
• NDL BIB ID: 7882331
• Web Site: http://id.ndl.go.jp/bib/7882331
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I7882331
• Web Site: http://journals.jps.jp/doi/pdf/10.1143/JPSJ.75.044002
• Text Lang: en
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed