On the Bayesian Interpretation of Penalized Statistical Estimators

0583574 - ÚTIA 2024 RIV CH eng C - Konferenční příspěvek (zahraniční konf.)
Kalina, Jan - Peštová, B.
On the Bayesian Interpretation of Penalized Statistical Estimators.
Artificial Intelligence and Soft Computing. 22nd International Conference, ICAISC 2023, Proceedings, Part 2. Cham: Springer, 2023 - (Rutkowski, L.; Scherer, R.; Korytkowski, M.; Pedrycz, W.; Tadeusiewicz, R.; Zurada, J.), s. 343-352. Lecture Notes in Computer Science, 14126. ISBN 978-3-031-42507-3.
[ICAISC 2023: International Conference on Artificial Intelligence and Soft Computing /22./. Zakopane (PL), 18.07.2023-22.07.2023]
Grant CEP: GA ČR GA21-05325S
Institucionální podpora: RVO:67985556
Klíčová slova: Bayesian estimation * regularization * penalization * robustness * regression
Obor OECD: Statistics and probability
http://library.utia.cas.cz/separaty/2023/SI/kalina-0583574.pdf

The aim of this work is to search for intuitive interpretations of penalized statistical estimators. Penalized estimates of the parameters of three models obtained by Bayesian reasoning are explained here to correspond to the intuition. First, the paper considers Bayesian estimates of the mean and covariance matrix for the multivariate normal distribution. Second, a connection of a robust regularized version of Mahalanobis distance with Bayesian estimation is discussed. Third, regularization networks, which represent a common nonparametric tool for regression modeling, are presented as Bayesian methods as well. On the whole, selected important multivariate and/or regression models are considered and novel interpretations are formulated.
Trvalý link: https://hdl.handle.net/11104/0351579