Empirical Effective Dimension and Optimal Rates for Regularized Least Squares Algorithm

Abstract

This paper presents an approach to model selection for regularized least-squares on reproducing kernel Hilbert spaces in the semi-supervised setting. The role of effective dimension was recently shown to be crucial in the definition of a rule for the choice of the regularization parameter, attaining asymptotic optimal performances in a minimax sense. The main goal of the present paper is showing how the effective dimension can be replaced by an empirical counterpart while conserving optimality. The empirical effective dimension can be computed from independent unlabelled samples. This makes the approach particularly appealing in the semi-supervised setting.

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Document Details

Document Type
Technical Report
Publication Date
May 27, 2005
Accession Number
ADA466778

Entities

People

  • Alessandro Verri
  • Andrea Caponnetto
  • Ernesto De Vito
  • Lorenzo Rosasco

Organizations

  • Massachusetts Institute of Technology

Tags

Communities of Interest

  • Biomedical
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Artificial Intelligence
  • Banach Space
  • Cognitive Science
  • Computer Science
  • Contracts
  • Convergence
  • Estimators
  • European Communities
  • Hilbert Space
  • Inequalities
  • Learning
  • Military Research
  • Probability
  • Probability Distributions
  • Random Variables
  • Semi-Supervised Learning

Fields of Study

  • Computer science

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Neural Network Machine Learning.

Technology Areas

  • AI & ML
  • AI & ML - Machine Learning Algorithms
  • Space