Normalising Flow-based Differentiable Particle Filters

• URL: http://arxiv.org/abs/2403.01499v1
• Date: Sun, 3 Mar 2024 12:23:17 GMT
• Title: Normalising Flow-based Differentiable Particle Filters
• Authors: Xiongjie Chen, Yunpeng Li
• Abstract summary: We present a differentiable particle filtering framework that uses (conditional) normalising flows to build its dynamic model, proposal distribution, and measurement model. We derive the theoretical properties of the proposed filters and evaluate the proposed normalising flow-based differentiable particle filters' performance through a series of numerical experiments.
• Score: 19.09640071505051
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recently, there has been a surge of interest in incorporating neural networks into particle filters, e.g. differentiable particle filters, to perform joint sequential state estimation and model learning for non-linear non-Gaussian state-space models in complex environments. Existing differentiable particle filters are mostly constructed with vanilla neural networks that do not allow density estimation. As a result, they are either restricted to a bootstrap particle filtering framework or employ predefined distribution families (e.g. Gaussian distributions), limiting their performance in more complex real-world scenarios. In this paper we present a differentiable particle filtering framework that uses (conditional) normalising flows to build its dynamic model, proposal distribution, and measurement model. This not only enables valid probability densities but also allows the proposed method to adaptively learn these modules in a flexible way, without being restricted to predefined distribution families. We derive the theoretical properties of the proposed filters and evaluate the proposed normalising flow-based differentiable particle filters' performance through a series of numerical experiments.

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 overview of differentiable particle filters for data-adaptive sequential Bayesian inference [19.09640071505051]
  Particle filters (PFs) provide an efficient mechanism for solving non-linear sequential state estimation problems. An emerging trend involves constructing components of particle filters using neural networks and optimising them by gradient descent. Differentiable particle filters are a promising computational tool for performing inference on sequential data in complex, high-dimensional tasks.
  arXiv  Detail & Related papers  (2023-02-19T18:03:53Z)
• 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)
• Understanding the Covariance Structure of Convolutional Filters [86.0964031294896]
  Recent ViT-inspired convolutional networks such as ConvMixer and ConvNeXt use large-kernel depthwise convolutions with notable structure. We first observe that such learned filters have highly-structured covariance matrices, and we find that covariances calculated from small networks may be used to effectively initialize a variety of larger networks.
  arXiv  Detail & Related papers  (2022-10-07T15:59:13Z)
• Continuous-time Particle Filtering for Latent Stochastic Differential Equations [37.51802583388233]
  We propose continuous latent particle filters, an approach that extends particle filtering to the continuous-time domain. We demonstrate how continuous latent particle filters can be used as a generic plug-in replacement for inference techniques relying on a learned variational posterior.
  arXiv  Detail & Related papers  (2022-09-01T01:05:31Z)
• Computational Doob's h-transforms for Online Filtering of Discretely Observed Diffusions [65.74069050283998]
  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.
  arXiv  Detail & Related papers  (2022-06-07T15:03:05Z)
• 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)
• Differentiable Particle Filters through Conditional Normalizing Flow [6.230706386020833]
  Differentiable particle filters provide a flexible mechanism to adaptively train dynamic and measurement models by learning from observed data. In this paper, we utilize conditional normalizing flows to construct proposal distributions for differentiable particle filters. We demonstrate the performance of the proposed conditional normalizing flow-based differentiable particle filters in a visual tracking task.
  arXiv  Detail & Related papers  (2021-07-01T14:31:27Z)
• When is Particle Filtering Efficient for Planning in Partially Observed Linear Dynamical Systems? [60.703816720093016]
  This paper initiates a study on the efficiency of particle filtering for sequential planning. We are able to bound the number of particles needed so that the long-run reward of the policy based on particle filtering is close to that based on exact inference. We believe this technique can be useful in other sequential decision-making problems.
  arXiv  Detail & Related papers  (2020-06-10T17:43:43Z)

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

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.