Central limit theorems for coupled particle filters

Jasra, Ajay; Yu, Fangyuan

doi:10.1017/apr.2020.27

Cited by 11 publications

(18 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The coupling in point 2 requires a way to resample the indices of the particles so that they have the correct marginals. This topic has been investigated considerably in the literature (see, e.g., [19,30]), and techniques that have been adopted include sampling maximal coupling (e.g., [17]), or using the \BbbL 2 -Wasserstein optimal coupling [2]; in general the latter is found to be better in terms of variance reduction but can only be implemented when d x = 1. We rely upon the maximal coupling in this paper, which has a cost of \scrO (N ) per unit time.…”

Section: Setmentioning

confidence: 99%

Score-Based Parameter Estimation for a Class of Continuous-Time State Space Models

Beskos

Crisan

Jasra³

et al. 2021

SIAM J. Sci. Comput.

Self Cite

View full text Add to dashboard Cite

\bfS \bfC \bfO \bfR \bfE -\bfB \bfA \bfS \bfE \bfD \bfP \bfA \bfR \bfA \bfM \bfE \bfT \bfE \bfR \bfE \bfS \bfT \bfI \bfM \bfA \bfT \bfI \bfO \bfN \bfF \bfO \bfR \bfA \bfC \bfL \bfA \bfS \bfS \bfO \bfF \bfC \bfO \bfN \bfT \bfI \bfN \bfU \bfO \bfU \bfS -\bfT \bfI \bfM \bfE \bfS \bfT \bfA \bfT \bfE \bfS \bfP \bfA \bfC \bfE \bfM \bfO \bfD \bfE \bfL \bfS \ast ALEXANDROS BESKOS \dagger , DAN CRISAN \ddagger , AJAY JASRA \S , NIKOLAS KANTAS \ddagger , \mathrm{\mathrm{\mathrm{ HAMZA RUZAYQAT \S \bfA \bfb \bfs \bft \bfr \bfa \bfc \bft . We consider the problem of parameter estimation for a class of continuous-time state space models (SSMs). In particular, we explore the case of a partially observed diffusion, with data also arriving according to a diffusion process. Based upon a standard identity of the score function, we consider two particle filter based methodologies to estimate the score function. Both methods rely on an online estimation algorithm for the score function, as described, e.g., in [P. Del Moral, A. Doucet, and S. S. Singh, M2AN Math. Model. Numer. Anal., 44 (2010), pp. 947--975], of \scrO (N 2 ) cost, with N \in \BbbN the number of particles. The first approach employs a simple Euler discretization and standard particle smoothers and is of cost \scrO (N 2 + N \Delta - 1 l ) per unit time, where \Delta l = 2 - l , l \in \BbbN 0 , is the time-discretization step. The second approach is new and based upon a novel diffusion bridge construction. It yields a new backward-type Feynman--Kac formula in continuous time for the score function and is presented along with a particle method for its approximation. Considering a time-discretization, the cost is \scrO (N 2 \Delta - 1 l ) per unit time. To improve computational costs, we then consider multilevel methodologies for the score function. We illustrate our parameter estimation method via stochastic gradient approaches in several numerical examples.\bfK \bfe \bfy \bfw \bfo \bfr \bfd \bfs . score function, particle filter, diffusion bridges, parameter estimation \bfA \bfM \bfS \bfs \bfu \bfb \bfj \bfe \bfc \bft \bfc \bfl \bfa \bfs \bfs \bfi fi\bfc \bfa \bft \bfi \bfo \bfn \bfs .

show abstract

Section: Setmentioning

confidence: 99%

Score-Based Parameter Estimation for a Class of Continuous-Time State Space Models

Beskos

Crisan

Jasra³

et al. 2021

SIAM J. Sci. Comput.

Self Cite

View full text Add to dashboard Cite

show abstract

“…We now introduce the CCPF. Although the CCPF is a particular case of the approach in [15], the coupled resampling method (also used in [1]) can perform very well in theory [16]. The basic principle is to generate a coupled particle filter (see, e.g., [16,18]) that runs conditionally on a pair of trajectories (x…”

Section: Ccpf Kernelmentioning

confidence: 99%

“…We consider geometric distribution G(p) with success rate p = 0.6 and p (l) ∝ ∆ 1/2 l (l + 1)(log 2 (2 + l)) 2 as suggested in [14,22]. Then we compare estimator (20) built over these two underlying distributions with Rhee-Glynn estimator (16) for an increased number of particles N . We first compare the mean square error (MSE) satisfied by the estimators, and then visualize how this analysis reflects in a stochastic gradient descent (SGD) procedure to recover unknown parameters.…”

Section: Simulationsmentioning

confidence: 99%

“…For each time series, we perform R = 100 i.i.d. evaluations of the estimators (20) and (16). We consider k = 2 and m = 4, where the method of selecting these parameters is based on the analysis of hitting times τ as described in [22].…”

Section: Algorithm Settingsmentioning

confidence: 99%

“…For OU and GBM, we consider N = {128, 256, 512, 1024}, while for the LM model, we consider N = {362, 512, 724, 1024}. Thus, to compute the MSE given N , we must estimate the variance of both estimators and the bias of the Rhee-Glynn estimator (16) since estimator (20) is unbiased.…”

Section: Algorithm Settingsmentioning

confidence: 99%

See 2 more Smart Citations

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

Ballesio¹,

Jasra²

2021

Preprint

Self Cite

View full text Add to dashboard Cite

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., [13,14]), that involves a novel coupled conditional particle filter (CCPF) on the second level of randomization [15]. 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 [22,23].

show abstract

Unbiased filtering of a class of partially observed diffusions

Jasra

Law

2022

Adv. Appl. Probab.

Self Cite

View full text Add to dashboard Cite

In this article we consider a Monte-Carlo-based method to filter partially observed diffusions observed at regular and discrete times. Given access only to Euler discretizations of the diffusion process, we present a new procedure which can return online estimates of the filtering distribution with no time-discretization bias and finite variance. Our approach is based upon a novel double application of the randomization methods of Rhee and Glynn (Operat. Res.63, 2015) along with the multilevel particle filter (MLPF) approach of Jasra et al. (SIAM J. Numer. Anal.55, 2017). A numerical comparison of our new approach with the MLPF, on a single processor, shows that similar errors are possible for a mild increase in computational cost. However, the new method scales strongly to arbitrarily many processors.

show abstract

Central limit theorems for coupled particle filters

Cited by 11 publications

References 27 publications

Score-Based Parameter Estimation for a Class of Continuous-Time State Space Models

Score-Based Parameter Estimation for a Class of Continuous-Time State Space Models

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

Unbiased filtering of a class of partially observed diffusions

Contact Info

Product

Resources

About