Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › статья в сборнике материалов конференции › научная › Рецензирование
Optimization of Kernel Estimators of Probability Densities. / Voytishek, Anton V.; Bulgakova, Tatyana E.
Optimization and Applications - 10th International Conference, OPTIMA 2019, Revised Selected Papers. ред. / Milojica Jaćimović; Michael Khachay; Vlasta Malkova; Mikhail Posypkin. Springer Gabler, 2020. стр. 254-266 (Communications in Computer and Information Science; Том 1145 CCIS).Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › статья в сборнике материалов конференции › научная › Рецензирование
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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