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 doubly randomized scheme (see, e.g.,~\mbox{%DIFAUXCMD ub_mcmc, ub_grad that involves a novel coupled conditional particle filter (CCPF) on the second level of randomization \mbox{%DIFAUXCMD 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\mbox{%DIFAUXCMD rhee,vihola .
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 doubly randomized scheme, that involves a novel coupled conditional particle filter (CCPF) on the second level of randomization . 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 .
D
doubly randomized scheme
R
(see, e.g.,~\mbox{%DIFAUXCMD ub_mcmc, ub_grad
doubly randomized scheme,
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\mbox{%DIFAUXCMD jacob2
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\& Glynn estimator\mbox{%DIFAUXCMD rhee,vihola
Glynn estimator