Deep learning-based estimation of time-dependent parameters in Markov models with application to nonlinear regression and SDEs
Machine Learning
2023-12-15 v1 Machine Learning
Numerical Analysis
Numerical Analysis
Abstract
We present a novel deep learning method for estimating time-dependent parameters in Markov processes through discrete sampling. Departing from conventional machine learning, our approach reframes parameter approximation as an optimization problem using the maximum likelihood approach. Experimental validation focuses on parameter estimation in multivariate regression and stochastic differential equations (SDEs). Theoretical results show that the real solution is close to SDE with parameters approximated using our neural network-derived under specific conditions. Our work contributes to SDE-based model parameter estimation, offering a versatile tool for diverse fields.
Cite
@article{arxiv.2312.08493,
title = {Deep learning-based estimation of time-dependent parameters in Markov models with application to nonlinear regression and SDEs},
author = {Andrzej Kałuża and Paweł M. Morkisz and Bartłomiej Mulewicz and Paweł Przybyłowicz and Martyna Wiącek},
journal= {arXiv preprint arXiv:2312.08493},
year = {2023}
}