TU Berlin, Fakultät IV-MAR 4-2, Marchstrasse 23, 10587 Berlin, Germany.
Phys Rev E. 2018 Aug;98(2-1):022109. doi: 10.1103/PhysRevE.98.022109.
We introduce a nonparametric approach for estimating drift and diffusion functions in systems of stochastic differential equations from observations of the state vector. Gaussian processes are used as flexible models for these functions, and estimates are calculated directly from dense data sets using Gaussian process regression. We develop an approximate expectation maximization algorithm to deal with the unobserved, latent dynamics between sparse observations. The posterior over states is approximated by a piecewise linearized process of the Ornstein-Uhlenbeck type and the maximum a posteriori estimation of the drift is facilitated by a sparse Gaussian process approximation.
我们介绍了一种从状态向量的观测中估计随机微分方程系统中的漂移和扩散函数的非参数方法。高斯过程被用作这些函数的灵活模型，并且使用高斯过程回归直接从密集数据集计算估计值。我们开发了一种近似期望最大化算法来处理稀疏观测之间未观察到的潜在动态。状态的后验分布通过 Ornstein-Uhlenbeck 类型的分段线性化过程进行近似，并且通过稀疏高斯过程近似来促进漂移的最大后验估计。
