论文标题
分裂方法的应用用于计算过滤方程解决方案的神经网络表示形式
An application of the splitting-up method for the computation of a neural network representation for the solution for the filtering equations
论文作者
论文摘要
滤波方程控制了一个信号过程的条件分布的演变，给定的部分，可能是嘈杂的观察值。它们的数值近似在许多现实生活应用中起着核心作用，包括数值预测，金融和工程。近似滤波方程解决方案的经典方法之一是使用PDE启发的方法，称为“分裂方法”，由Gyongy，Krylov，Legland等启动，以及其他贡献者。该方法和其他基于PDE的方法具有特殊适用于解决低维问题的适用性。在这项工作中，我们将此方法与神经网络表示结合在一起。新方法用于产生信号过程的不当条件分布的近似值。我们进一步开发了递归归一化程序，以恢复信号过程的归一化条件分布。新方案可以在多个时间步骤中迭代，同时保持其渐近无偏见性能完整。 我们测试了Kalman和Benes滤波器的数值近似结果的神经网络近似值。
The filtering equations govern the evolution of the conditional distribution of a signal process given partial, and possibly noisy, observations arriving sequentially in time. Their numerical approximation plays a central role in many real-life applications, including numerical weather prediction, finance and engineering. One of the classical approaches to approximate the solution of the filtering equations is to use a PDE inspired method, called the splitting-up method, initiated by Gyongy, Krylov, LeGland, among other contributors. This method, and other PDE based approaches, have particular applicability for solving low-dimensional problems. In this work we combine this method with a neural network representation. The new methodology is used to produce an approximation of the unnormalised conditional distribution of the signal process. We further develop a recursive normalisation procedure to recover the normalised conditional distribution of the signal process. The new scheme can be iterated over multiple time steps whilst keeping its asymptotic unbiasedness property intact. We test the neural network approximations with numerical approximation results for the Kalman and Benes filter.
