Optimization of Kernel Estimators of Probability Densities

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Abstract

The constructive kernel algorithm for approximation of probability densities using the given sample values is proposed. This algorithm is based on the approaches of the theory of the numerical functional approximation. The critical analysis of the optimization criterion for the kernel density estimators (based on decrease of upper boundary of mean square error) is conducted. It is shown that the constructive kernel algorithm is nearly equal to the randomized projection-mesh functional numerical algorithm for approximation of the solution of the Fredholm integral equation of the second kind. In connection with this it is proposed to use the criterion of conditional optimization of functional algorithms for the kernel algorithm for approximation of probability densities. This criterion is based on minimization of the algorithm’s cost for the fixed level of error. The corresponding formulae for the conditionally optimal parameters of the kernel algorithm are derived.

Original languageEnglish
Title of host publicationOptimization and Applications - 10th International Conference, OPTIMA 2019, Revised Selected Papers
EditorsMilojica Jaćimović, Michael Khachay, Vlasta Malkova, Mikhail Posypkin
PublisherSpringer Gabler
Pages254-266
Number of pages13
ISBN (Print)9783030386023
DOIs
Publication statusPublished - 1 Jan 2020
Event10th International Conference on Optimization and Applications, OPTIMA 2019 - Petrovac, Montenegro
Duration: 30 Sep 20194 Oct 2019

Publication series

NameCommunications in Computer and Information Science
Volume1145 CCIS
ISSN (Print)1865-0929
ISSN (Electronic)1865-0937

Conference

Conference10th International Conference on Optimization and Applications, OPTIMA 2019
CountryMontenegro
CityPetrovac
Period30.09.201904.10.2019

Keywords

  • Conditional optimization of randomized functional numerical algorithms
  • Kernel estimators for approximation of probability densities
  • Multi-dimensional analogue of the polygon of frequencies method
  • Numerical mesh approximation of functions
  • Optimization

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