Related papers: Computational Doob's h-transforms for Online Filtering of Discretely Observed Diffusions

Computational Doob's h-transforms for Online Filtering of Discretely Observed Diffusions

URL: http://arxiv.org/abs/2206.03369v2
Date: Tue, 30 May 2023 17:10:40 GMT
Title: Computational Doob's h-transforms for Online Filtering of Discretely Observed Diffusions
Authors: Nicolas Chopin, Andras Fulop, Jeremy Heng, Alexandre H. Thiery
Abstract summary: We propose a computational framework to approximate Doob's $h$-transforms. The proposed approach can be orders of magnitude more efficient than state-of-the-art particle filters.
Score: 65.74069050283998
License: http://creativecommons.org/licenses/by/4.0/
Abstract: This paper is concerned with online filtering of discretely observed nonlinear diffusion processes. Our approach is based on the fully adapted auxiliary particle filter, which involves Doob's $h$-transforms that are typically intractable. We propose a computational framework to approximate these $h$-transforms by solving the underlying backward Kolmogorov equations using nonlinear Feynman-Kac formulas and neural networks. The methodology allows one to train a locally optimal particle filter prior to the data-assimilation procedure. Numerical experiments illustrate that the proposed approach can be orders of magnitude more efficient than state-of-the-art particle filters in the regime of highly informative observations, when the observations are extreme under the model, or if the state dimension is large.

Related papers

Closed-form Filtering for Non-linear Systems [83.91296397912218]
We propose a new class of filters based on Gaussian PSD Models, which offer several advantages in terms of density approximation and computational efficiency. We show that filtering can be efficiently performed in closed form when transitions and observations are Gaussian PSD Models. Our proposed estimator enjoys strong theoretical guarantees, with estimation error that depends on the quality of the approximation and is adaptive to the regularity of the transition probabilities.
arXiv Detail & Related papers (2024-02-15T08:51:49Z)
Nonlinear Filtering with Brenier Optimal Transport Maps [4.745059103971596]
This paper is concerned with the problem of nonlinear filtering, i.e., computing the conditional distribution of the state of a dynamical system. Conventional sequential importance resampling (SIR) particle filters suffer from fundamental limitations, in scenarios involving degenerate likelihoods or high-dimensional states. In this paper, we explore an alternative method, which is based on estimating the Brenier optimal transport (OT) map from the current prior distribution of the state to the posterior distribution at the next time step.
arXiv Detail & Related papers (2023-10-21T01:34:30Z)
An Ensemble Score Filter for Tracking High-Dimensional Nonlinear Dynamical Systems [10.997994515823798]
We propose an ensemble score filter (EnSF) for solving high-dimensional nonlinear filtering problems. Unlike existing diffusion models that train neural networks to approximate the score function, we develop a training-free score estimation. EnSF provides surprising performance, compared with the state-of-the-art Local Ensemble Transform Kalman Filter method.
arXiv Detail & Related papers (2023-09-02T16:48:02Z)
Low-rank extended Kalman filtering for online learning of neural networks from streaming data [71.97861600347959]
We propose an efficient online approximate Bayesian inference algorithm for estimating the parameters of a nonlinear function from a potentially non-stationary data stream. The method is based on the extended Kalman filter (EKF), but uses a novel low-rank plus diagonal decomposition of the posterior matrix. In contrast to methods based on variational inference, our method is fully deterministic, and does not require step-size tuning.
arXiv Detail & Related papers (2023-05-31T03:48:49Z)
Unsupervised Learning of Sampling Distributions for Particle Filters [80.6716888175925]
We put forward four methods for learning sampling distributions from observed measurements. Experiments demonstrate that learned sampling distributions exhibit better performance than designed, minimum-degeneracy sampling distributions.
arXiv Detail & Related papers (2023-02-02T15:50:21Z)
Deep Learning for the Benes Filter [91.3755431537592]
We present a new numerical method based on the mesh-free neural network representation of the density of the solution of the Benes model. We discuss the role of nonlinearity in the filtering model equations for the choice of the domain of the neural network.
arXiv Detail & Related papers (2022-03-09T14:08:38Z)
Innovative And Additive Outlier Robust Kalman Filtering With A Robust Particle Filter [68.8204255655161]
We propose CE-BASS, a particle mixture Kalman filter which is robust to both innovative and additive outliers, and able to fully capture multi-modality in the distribution of the hidden state. Furthermore, the particle sampling approach re-samples past states, which enables CE-BASS to handle innovative outliers which are not immediately visible in the observations, such as trend changes.
arXiv Detail & Related papers (2020-07-07T07:11:09Z)
Multiplicative Gaussian Particle Filter [18.615555573235987]
We propose a new sampling-based approach for approximate inference in filtering problems. Instead of approximating conditional distributions with a finite set of states, as done in particle filters, our approach approximates the distribution with a weighted sum of functions from a set of continuous functions.
arXiv Detail & Related papers (2020-02-29T09:19:38Z)

This list is automatically generated from the titles and abstracts of the papers in this site.