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JOURNALS // Proceedings of the Yerevan State University, series Physical and Mathematical Sciences // Archive

Proceedings of the YSU, Physical and Mathematical Sciences, 2021 Volume 55, Issue 1, Pages 29–35 (Mi uzeru829)

Mathematics

Loss functions and descent method

V. K. Ohanyan, H. Z. Zohrabyan

Yerevan State University, Faculty of Mathematics and Mechanics

Abstract: In this paper, we showed that it is possible to use gradient descent method to get minimal error values of loss functions close to their Bayesian estimators. We calculated Bayesian estimators mathematically for different loss functions and tested them using gradient descent algorithm. This algorithm, working on Normal and Poisson distributions showed that it is possible to find minimal error values without having Bayesian estimators. Using Python, we tested the theory on loss functions with known Bayesian estimators as well as another loss functions, getting results proving the theory.

Keywords: Bayesian estimators, gradient descent, loss functions, machine learning.

MSC: 91B30, 91G60, 62C10

Received: 07.04.2021
Revised: 23.04.2021
Accepted: 27.04.2021

Language: English

DOI: 10.46991/PYSU:A/2021.55.1.029



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