对比深度学习与统计方法在随机微分方程参数估计中的表现
Comparing statistical and deep learning techniques for parameter estimation of continuous-time stochastic differentiable equations
- 用RNN与最大似然法对比参数估计精度
- RNN在精度上优于传统统计方法，但计算成本更高
- 适合对模型精度敏感的金融或物理建模研究者
随机微分方程（如Ornstein-Uhlenbeck过程）长期用于建模股票价格、温度波动等现实世界的概率事件。传统统计方法如最大似然估计（MLE）、卡尔曼滤波、逆变量法等被广泛用于参数估计。随着深度学习技术的发展，循环神经网络（RNN）被认为可能提供更精确的估计器。本文通过一系列实验，比较了统计方法（MLE）与深度学习模型（RNN）在Ornstein-Uhlenbeck过程参数估计上的准确性和计算开销，验证了RNN在精度上的优势，同时揭示其更高的计算成本。
原文摘要 · Abstract (English)
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.
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