A variational approach to path estimation and parameter inference of hidden diffusion processes
This work addresses parameter inference in hidden diffusion processes, which is incremental as it builds on existing variational approaches for state estimation.
The paper tackles the problem of estimating hidden states and unknown parameters in diffusion processes observed through noisy measurements, developing a variational method that provides systematic approximations of smoothing densities and demonstrates efficacy and accuracy in two examples.
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.