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Analysis of Kernel Matrices via the von Neumann Entropy and Its Relation to RVM Performances.

Lluís A Belanche-Muñoz1, Małgorzata Wiejacha2

  • 1Department of Computer Science, Universitat Politècnica de Catalunya, 08034 Barcelona, Catalonia, Spain.

Entropy (Basel, Switzerland)
|January 21, 2023
PubMed
Summary

This study analyzes kernel matrices for kernelized relevance vector machines (RVMs) using an entropic approach. It identifies key kernel properties for better generalization and proposes an efficient heuristic for optimal modeling with limited computational resources.

Keywords:
generalization errorrelevance vector machinesvon Neumann entropy

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Area of Science:

  • Data Science
  • Machine Learning
  • Computational Statistics

Background:

  • Kernel methods are crucial for complex data science problems.
  • Kernel function selection and understanding performance differences remain challenging.
  • High computational costs hinder traditional model selection for kernel methods.

Purpose of the Study:

  • To analyze kernel matrices from an entropic perspective for kernelized relevance vector machines (RVMs).
  • To identify kernel properties that enhance model generalization and fitting ability.
  • To develop an efficient heuristic for optimal modeling with reduced computational load.

Main Methods:

  • Exploration of kernel matrices using an entropic standpoint.
  • Analysis of kernel properties related to generalization power and fitting ability.
  • Derivation of a heuristic for efficient kernelized RVM analysis.

Main Results:

  • Identified desirable properties of kernel matrices for improved RVM performance.
  • Established a link between kernel matrix properties and model fitting ability.
  • Developed a heuristic to achieve near-optimal modeling results efficiently.

Conclusions:

  • The entropic analysis provides insights into kernel matrix properties for RVMs.
  • The derived heuristic offers a computationally efficient approach to kernel design and parameter selection.
  • This work facilitates effective modeling with limited computational resources.