Deep learning-based estimation of time-dependent parameters in Markov models with application to nonlinear regression and SDEs
This provides a versatile tool for parameter estimation in SDE-based models, addressing a domain-specific problem in fields like finance and physics, though it appears incremental as it adapts deep learning to an existing bottleneck.
The paper tackles the problem of estimating time-dependent parameters in Markov processes from discrete samples by developing a deep learning method that reframes parameter approximation as a maximum likelihood optimization problem. Experimental results show the method is validated on multivariate regression and stochastic differential equations (SDEs), with theoretical analysis indicating the real solution is close to SDEs using neural network-derived parameters under specific conditions.
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.