Header

UZH-Logo

Maintenance Infos

Online Maximum Likelihood Estimation of the Parameters of Partially Observed Diffusion Processes


Surace, Simone Carlo; Pfister, Jean-Pascal (2017). Online Maximum Likelihood Estimation of the Parameters of Partially Observed Diffusion Processes. arXiv.org 1611.00170, Institute of Neuroinformatics.

Abstract

We revisit the problem of estimating the parameters of a partially observed diffusion process, consisting of a hidden state process and an observed process, with a continuous time parameter. The estimation is to be done online, i.e. the parameter estimate should be updated recursively based on the observation filtration. Here, we use an old but under-exploited representation of the incomplete-data log-likelihood function in terms of the filter of the hidden state from the observations. By performing a stochastic gradient ascent, we obtain a fully recursive algorithm for the time evolution of the parameter estimate. We prove the convergence of the algorithm under suitable conditions regarding the ergodicity of the process consisting of state, filter, and tangent filter. Additionally, our parameter estimation is shown numerically to have the potential of improving suboptimal filters, and can be applied even when the system is not identifiable due to parameter redundancies. Online parameter estimation is a challenging problem that is ubiquitous in fields such as robotics, neuroscience, or finance in order to design adaptive filters and optimal controllers for unknown or changing systems.

Abstract

We revisit the problem of estimating the parameters of a partially observed diffusion process, consisting of a hidden state process and an observed process, with a continuous time parameter. The estimation is to be done online, i.e. the parameter estimate should be updated recursively based on the observation filtration. Here, we use an old but under-exploited representation of the incomplete-data log-likelihood function in terms of the filter of the hidden state from the observations. By performing a stochastic gradient ascent, we obtain a fully recursive algorithm for the time evolution of the parameter estimate. We prove the convergence of the algorithm under suitable conditions regarding the ergodicity of the process consisting of state, filter, and tangent filter. Additionally, our parameter estimation is shown numerically to have the potential of improving suboptimal filters, and can be applied even when the system is not identifiable due to parameter redundancies. Online parameter estimation is a challenging problem that is ubiquitous in fields such as robotics, neuroscience, or finance in order to design adaptive filters and optimal controllers for unknown or changing systems.

Statistics

Citations

2 citations in Microsoft Academic

Downloads

1 download since deposited on 01 Mar 2018
1 download since 12 months
Detailed statistics

Additional indexing

Item Type:Working Paper
Communities & Collections:07 Faculty of Science > Institute of Neuroinformatics
Dewey Decimal Classification:570 Life sciences; biology
Language:English
Date:2017
Deposited On:01 Mar 2018 11:00
Last Modified:31 Jul 2018 05:13
Series Name:arXiv.org
ISSN:2331-8422
OA Status:Green
Free access at:Official URL. An embargo period may apply.
Official URL:https://arxiv.org/abs/1611.00170

Download

Download PDF  'Online Maximum Likelihood Estimation of the Parameters of Partially Observed Diffusion Processes'.
Preview
Content: Published Version
Filetype: PDF
Size: 1MB