Adaptation for Regularization Operators in Learning Theory

Abstract

We consider learning algorithms induced by regularization methods in the regression setting. We show that previously obtained error bounds for these algorithms using a-priori choices of the regularization parameter, can be attained using a suitable a-posteriori choice based on validation. In particular, these results prove adaptation of the rate of convergence of the estimators to the minimax rate induced by the effective dimension of the problem. We also show universal consistency for this class methods.

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Document Details

Document Type
Technical Report
Publication Date
Sep 10, 2006
Accession Number
ADA456686

Entities

People

  • Andrea Caponnetto
  • Yuan Yao

Organizations

  • Massachusetts Institute of Technology

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Artificial Intelligence
  • Computer Science
  • Construction
  • Convergence
  • Equations
  • Estimators
  • European Communities
  • Inequalities
  • Inverse Problems
  • Learning
  • Numbers
  • Probability
  • Random Variables
  • Real Numbers
  • Sequences
  • Two Dimensional

Fields of Study

  • Computer science

Readers

  • Brain and Cognitive Science; Experimental Psychology; Cognitive Neuroscience
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Statistical inference.