Deep learning-based estimation of time-dependent parameters in Markov models with application to nonlinear regression and SDEs

Andrzej Kałuża, Paweł M. Morkisz, Bartłomiej Mulewicz, Paweł Przybyłowicz and Martyna Wia̧cek

Applied Mathematics and Computation, 2024, vol. 480, issue C

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.

Keywords: Stochastic differential equations; Markov models; Multivariate regression; Artificial neural networks; Deep learning; Quasi-likelihood function; Maximum likelihood (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:480:y:2024:i:c:s0096300324003679

DOI: 10.1016/j.amc.2024.128906

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