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Online Gradient Descent for Kernel-Based Maximum Correntropy Criterion.

Baobin Wang1, Ting Hu2

  • 1School of Mathematics and Statistics, South-Central University for Nationalities, Wuhan 430074, China.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary
This summary is machine-generated.

This study analyzes the online gradient descent algorithm using correntropy-induced losses in Reproducing kernel Hilbert spaces (RKHS). Results show a min-max optimal convergence rate for the maximum correntropy criterion (MCC) with a carefully selected scaling parameter.

Keywords:
correntropymaximum correntropy criteriononline algorithmreproducing kernel Hilbert spacesrobustness

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Area of Science:

  • Statistical Learning Theory
  • Machine Learning Algorithms
  • Robust Statistics

Background:

  • Correntropy is a robust generalized correlation measure widely used in practical applications.
  • Online gradient descent is efficient for the maximum correntropy criterion (MCC) but lacks rigorous analysis and error bounds.
  • Reproducing kernel Hilbert spaces (RKHS) provide a powerful framework for kernel-based learning methods.

Purpose of the Study:

  • To provide a theoretical understanding of the online gradient descent algorithm for MCC in RKHS.
  • To establish rigorous error bounds for the algorithm's convergence.
  • To investigate the role of the scaling parameter in algorithm performance.

Main Methods:

  • Analysis of online gradient descent algorithm within the RKHS framework.
  • Utilizing correntropy-induced losses for robust non-parameter estimation.
  • Derivation of convergence rates and error bounds for the MCC.

Main Results:

  • The online gradient descent algorithm for MCC in RKHS is theoretically analyzed.
  • A suitable scaling parameter ensures a min-max optimal convergence rate (up to a logarithmic factor) in regression analysis.
  • The scaling parameter is crucial for achieving both robustness and consistency.

Conclusions:

  • The study offers a theoretical foundation for using online gradient descent with correntropy-induced losses.
  • Optimal convergence rates are achievable, highlighting the importance of parameter selection.
  • The findings contribute to robust and consistent non-parameter estimation in statistical learning.