Unbiased Estimation of the Gradient of the Log-Likelihood for a Class of Continuous-Time State-Space Models

• URL: http://arxiv.org/abs/2105.11522v1
• Date: Mon, 24 May 2021 20:31:48 GMT
• Title: Unbiased Estimation of the Gradient of the Log-Likelihood for a Class of Continuous-Time State-Space Models
• Authors: Marco Ballesio and Ajay Jasra
• Abstract summary: We consider static parameter estimation for a class of continuous-time state-space models. Our goal is to obtain an unbiased estimate of the gradient of the log-likelihood (score function)
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, we consider static parameter estimation for a class of continuous-time state-space models. Our goal is to obtain an unbiased estimate of the gradient of the log-likelihood (score function), which is an estimate that is unbiased even if the stochastic processes involved in the model must be discretized in time. To achieve this goal, we apply a \emph{doubly randomized scheme} (see, e.g.,~\cite{ub_mcmc, ub_grad}), that involves a novel coupled conditional particle filter (CCPF) on the second level of randomization \cite{jacob2}. Our novel estimate helps facilitate the application of gradient-based estimation algorithms, such as stochastic-gradient Langevin descent. We illustrate our methodology in the context of stochastic gradient descent (SGD) in several numerical examples and compare with the Rhee \& Glynn estimator \cite{rhee,vihola}.

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