Asymptotics of Gaussian Regularized Least-Squares

Abstract

We consider regularized least-squares (RLS) with a Gaussian kernel. We prove that if we let the Gaussian bandwidth sigma ->infinity while letting the regularization parameter lambda ->0, the RLS solution tends to a polynomial whose order is controlled by the relative rates of decay of 1/sigma(exp2) and lambda : if lambda = sigma (exp- (2k+1)), then, as sigma ->infinity the RLS solution tends to the kth order polynomial with minimal empirical error. We illustrate the result with an example.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 2005
Accession Number
ADA454981

Entities

People

  • Ross Lippert
  • Ryan Rifkin

Organizations

  • Massachusetts Institute of Technology

Tags

Communities of Interest

  • Biomedical

DTIC Thesaurus Topics

  • Abstracts
  • Algorithms
  • Artificial Intelligence
  • Classification
  • Cognitive Science
  • Computer Science
  • Contracts
  • Data Sets
  • Equations
  • Information Science
  • Kernel Functions
  • Lisp Programming Language
  • Polynomials
  • Precision
  • Scalar Functions
  • Supervised Machine Learning
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Linear Algebra
  • Regression Analysis.