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Optimization of Kernel Estimators of Probability Densities. / Voytishek, Anton V.; Bulgakova, Tatyana E.

Optimization and Applications - 10th International Conference, OPTIMA 2019, Revised Selected Papers. ed. / Milojica Jaćimović; Michael Khachay; Vlasta Malkova; Mikhail Posypkin. Springer Gabler, 2020. p. 254-266 (Communications in Computer and Information Science; Vol. 1145 CCIS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review

Harvard

Voytishek, AV & Bulgakova, TE 2020, Optimization of Kernel Estimators of Probability Densities. in M Jaćimović, M Khachay, V Malkova & M Posypkin (eds), Optimization and Applications - 10th International Conference, OPTIMA 2019, Revised Selected Papers. Communications in Computer and Information Science, vol. 1145 CCIS, Springer Gabler, pp. 254-266, 10th International Conference on Optimization and Applications, OPTIMA 2019, Petrovac, Montenegro, 30.09.2019. https://doi.org/10.1007/978-3-030-38603-0_19

APA

Voytishek, A. V., & Bulgakova, T. E. (2020). Optimization of Kernel Estimators of Probability Densities. In M. Jaćimović, M. Khachay, V. Malkova, & M. Posypkin (Eds.), Optimization and Applications - 10th International Conference, OPTIMA 2019, Revised Selected Papers (pp. 254-266). (Communications in Computer and Information Science; Vol. 1145 CCIS). Springer Gabler. https://doi.org/10.1007/978-3-030-38603-0_19

Vancouver

Voytishek AV, Bulgakova TE. Optimization of Kernel Estimators of Probability Densities. In Jaćimović M, Khachay M, Malkova V, Posypkin M, editors, Optimization and Applications - 10th International Conference, OPTIMA 2019, Revised Selected Papers. Springer Gabler. 2020. p. 254-266. (Communications in Computer and Information Science). doi: 10.1007/978-3-030-38603-0_19

Author

Voytishek, Anton V. ; Bulgakova, Tatyana E. / Optimization of Kernel Estimators of Probability Densities. Optimization and Applications - 10th International Conference, OPTIMA 2019, Revised Selected Papers. editor / Milojica Jaćimović ; Michael Khachay ; Vlasta Malkova ; Mikhail Posypkin. Springer Gabler, 2020. pp. 254-266 (Communications in Computer and Information Science).

BibTeX

@inproceedings{93f9ee99f0a742aab7f6ef075f1e4ef6,
title = "Optimization of Kernel Estimators of Probability Densities",
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{\textquoteright}s cost for the fixed level of error. The corresponding formulae for the conditionally optimal parameters of the kernel algorithm are derived.",
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",
author = "Voytishek, {Anton V.} and Bulgakova, {Tatyana E.}",
year = "2020",
month = jan,
day = "1",
doi = "10.1007/978-3-030-38603-0_19",
language = "English",
isbn = "9783030386023",
series = "Communications in Computer and Information Science",
publisher = "Springer Gabler",
pages = "254--266",
editor = "Milojica Ja{\'c}imovi{\'c} and Michael Khachay and Vlasta Malkova and Mikhail Posypkin",
booktitle = "Optimization and Applications - 10th International Conference, OPTIMA 2019, Revised Selected Papers",
address = "Germany",
note = "10th International Conference on Optimization and Applications, OPTIMA 2019 ; Conference date: 30-09-2019 Through 04-10-2019",

}

RIS

TY - GEN

T1 - Optimization of Kernel Estimators of Probability Densities

AU - Voytishek, Anton V.

AU - Bulgakova, Tatyana E.

PY - 2020/1/1

Y1 - 2020/1/1

N2 - 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.

AB - 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.

KW - Conditional optimization of randomized functional numerical algorithms

KW - Kernel estimators for approximation of probability densities

KW - Multi-dimensional analogue of the polygon of frequencies method

KW - Numerical mesh approximation of functions

KW - Optimization

UR - http://www.scopus.com/inward/record.url?scp=85078432941&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-38603-0_19

DO - 10.1007/978-3-030-38603-0_19

M3 - Conference contribution

AN - SCOPUS:85078432941

SN - 9783030386023

T3 - Communications in Computer and Information Science

SP - 254

EP - 266

BT - Optimization and Applications - 10th International Conference, OPTIMA 2019, Revised Selected Papers

A2 - Jaćimović, Milojica

A2 - Khachay, Michael

A2 - Malkova, Vlasta

A2 - Posypkin, Mikhail

PB - Springer Gabler

T2 - 10th International Conference on Optimization and Applications, OPTIMA 2019

Y2 - 30 September 2019 through 4 October 2019

ER -

ID: 23259904