Learning Theory for Statistical models with singular points based on algebraic analysis

• WATANABE Sumio

  Advanced Information Processing Division P & I Laboratory, Tokyo Institute of Technology

Bibliographic Information

Other Title

• 代数解析に基づく特異点を持つモデルの学習理論

Abstract

Mathematical foundation for nonlinear and irregular statistical models such as multi-layer neural networks and gauussian mixutures have not been sufficiently established, because the set of true parameters of them is an algeraic variety with singularities. This paper proposes a method to clarify the general learning curves by measuring the depth of the singular points based on the theory for Sato's b-functions.

Journal

• IEICE technical report. Neurocomputing

  IEICE technical report. Neurocomputing 98 (401), 73-80, 1998-11-17

  The Institute of Electronics, Information and Communication Engineers

Keywords

• Irregular statistical model
• Algebraic Analysis
• Algebraic variety
• Sato's b function

Details

• CRID: 1570572702515714688
• NII Article ID: 110003233436
• NII Book ID: AN10091178
• Text Lang: ja
• Data Source:
  • CiNii Articles