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

arXiv: https://arxiv.org/abs/2105.11522 · HTML: https://mlsanity.com/paper/2105.11522/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 26 references that are in the map.
- First posted on arXiv 24 May 2021.

## Builds on (most cited first, 2 of 2)

- [On Unbiased Estimation for Discretized Models](https://mlsanity.com/paper/2102.12230/) (2021)
- [Smoothing with Couplings of Conditional Particle Filters](https://mlsanity.com/paper/1701.02002/) (2017)

## Built on by (most cited first, 1 of 1)

- [Constructing unbiased gradient estimators with finite variance for conditional stochastic optimization](https://mlsanity.com/paper/2206.01991/) (2022)

## Abstract (arXiv)

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.