Vector-Valued Support Vector Regression

Abstract

A vector-valued extension of the support vector regression problem is presented here. The vector-valued variant is developed by extending the notions of the estimator, loss function and regularization functional from the scalar-valued case. A particular emphasis is placed on the class of loss functions chosen which apply the epsilon-insensitive loss function to the rho-norm of the error. The primal and dual optimization problems are derived and the KKT conditions are developed. The general case for the rho-norm is specialized for the 1-, 2- and infinity-norms. It is shown that the vector-valued variant is a true extension of the scalar-valued case. It is then shown that the vector-valued approach results in sparse representations in terms of support vectors as compared to aggregated scalar- valued learning.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Apr 14, 2006
Accession Number
ADA459789

Entities

People

  • Mark Brudnak

Organizations

  • Tank-automotive and Armaments Command

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Applied Computer Science
  • Artificial Intelligence
  • Artificial Intelligence Computing
  • Computational Processes
  • Computer Science
  • Computing-Related Activities
  • Data Science
  • Information Operations
  • Machine Learning
  • Neural Networks
  • Supervised Machine Learning

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Operations Research

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference
  • AI & ML - Machine Learning Algorithms