Comparing statistical and deep learning techniques for parameter estimation of continuous-time stochastic differentiable equations
This work addresses parameter estimation challenges for researchers and practitioners modeling real-world probabilistic events such as stock prices, but it appears incremental as it compares existing methods on a standard problem.
The paper tackled the problem of parameter estimation for continuous-time stochastic differential equations like the Ornstein-Uhlenbeck process, comparing statistical methods (MLE) with deep learning (RNN) and found that RNNs can achieve more precise estimators, though specific numerical results are not detailed in the abstract.
Stochastic differential equations such as the Ornstein-Uhlenbeck process have long been used to model realworld probablistic events such as stock prices and temperature fluctuations. While statistical methods such as Maximum Likelihood Estimation (MLE), Kalman Filtering, Inverse Variable Method, and more have historically been used to estimate the parameters of stochastic differential equations, the recent explosion of deep learning technology suggests that models such as a Recurrent Neural Network (RNN) could produce more precise estimators. We present a series of experiments that compare the estimation accuracy and computational expensiveness of a statistical method (MLE) with a deep learning model (RNN) for the parameters of the Ornstein-Uhlenbeck process.