A Variational Approach to Path Estimation and Parameter Inference of Hidden Diffusion Processes
A Variational Approach to Path Estimation and Parameter Inference of Hidden Diffusion Processes
复制标题
隐扩散过程路径估计和参数推断的变分方法
DOI：
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发表时间：
2015
影响因子：
6
通讯作者：
H. Koeppl
中科院分区：
文献类型：
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作者：
Tobias Sutter;Arnab Ganguly;H. Koeppl
我们考虑一个隐马尔可夫模型，其中由扩散给出的信号过程只能通过一些噪声测量来间接观察到。本文开发了一种变分方法，用于在给定全套观测值的情况下逼近信号过程的隐藏状态。特别是，这会导致信号处理的平滑密度的系统近似。然后，本文演示了如何基于这种隐状态近似的变分方法设计有效的推理方案来估计随机微分方程的未知参数。最后的两个例子说明了所提出方法的有效性和准确性。
We consider a hidden Markov model, where the signal process, given by a diffusion, is only indirectly observed through some noisy measurements. The article develops a variational method for approximating the hidden states of the signal process given the full set of observations. This, in particular, leads to systematic approximations of the smoothing densities of the signal process. The paper then demonstrates how an efficient inference scheme, based on this variational approach to the approximation of the hidden states, can be designed to estimate the unknown parameters of stochastic differential equations. Two examples at the end illustrate the efficacy and the accuracy of the presented method.