Optimal Rates for Regularization Operators in Learning Theory

Abstract

We develop some new error bounds for learning algorithms induced by regularization methods in the regression setting. The hardness of the problem is characterized in terms of the parameters r and s, the first related to the complexity of the target function, the second connected to the effective dimension of the marginal probability measure over the input space. We show, extending previous results, that by a suitable choice of the regularization parameter as a function of the number of the available examples, it is possible attain the optimal minimax rates of convergence for the expected squared loss of the estimators, over the family of priors fulfilling the constraint r + s > 1/2. The setting considers both labelled and unlabelled examples, the latter being crucial for the optimality results on the priors in the range r < 1/2 .

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Document Details

Document Type
Technical Report
Publication Date
Sep 10, 2006
Accession Number
ADA456685

Entities

People

  • Andrea Caponnetto

Organizations

  • Massachusetts Institute of Technology

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Abstracts
  • Algorithms
  • Artificial Intelligence
  • Computations
  • Computer Science
  • Convergence
  • Electric Power
  • Equations
  • Estimators
  • European Communities
  • Inequalities
  • Inverse Problems
  • Learning
  • Probability
  • Random Variables
  • Standards
  • Training

Fields of Study

  • Computer science

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  • Graph Algorithms and Convex Optimization.
  • Neural Network Machine Learning.
  • Systems Analysis and Design

Technology Areas

  • Space