Related papers: Implicit particle filtering for models with partia…
In many signal processing applications it is required to estimate the unobservable state of a dynamic system from its noisy measurements. For linear dynamic systems with Gaussian Mixture (GM) noise distributions, Gaussian Sum Filters (GSF)…
Smoothing in state-space models amounts to computing the conditional distribution of the latent state trajectory, given observations, or expectations of functionals of the state trajectory with respect to this distributions. For models that…
Particle filtering methods can be applied to estimation problems in discrete spaces on bounded domains, to sample from and marginalise over unknown hidden states. As in continuous settings, problems such as particle degradation can arise:…
Nonlinear/non-Gaussian filtering has broad applications in many areas of life sciences where either the dynamic is nonlinear and/or the probability density function of uncertain state is non-Gaussian. In such problems, the accuracy of the…
A hybrid data assimilation algorithm is developed for complex dynamical systems with partial observations. The method starts with applying a spectral decomposition to the entire spatiotemporal fields, followed by creating a machine learning…
This work explores non-negative low-rank matrix factorization based on regularized Poisson models (PF or "Poisson factorization" for short) for recommender systems with implicit-feedback data. The properties of Poisson likelihood allow a…
In Data Assimilation, observations are fused with simulations to obtain an accurate estimate of the state and parameters for a given physical system. Combining data with a model, however, while accurately estimating uncertainty, is…
We propose a novel method for maximum likelihood-based parameter inference in nonlinear and/or non-Gaussian state space models. The method is an iterative procedure with three steps. At each iteration a particle filter is used to estimate…
Particle filtering is a powerful approximation method that applies to state estimation in nonlinear and non-Gaussian dynamical state-space models. Unfortunately, the approximation error depends exponentially on the system dimension. This…
Differentiable programming is revolutionizing computational science by enabling automatic differentiation (AD) of numerical simulations. While first-order gradients are well-established, second-order derivatives (Hessians) for implicit…
Nonlinear non-Gaussian state-space models are ubiquitous in statistics, econometrics, information engineering and signal processing. Particle methods, also known as Sequential Monte Carlo (SMC) methods, provide reliable numerical…
Gaussian mixture filters for nonlinear systems usually rely on severe approximations when calculating mixtures in the prediction and filtering step. Thus, offline approximations of noise densities by Gaussian mixture densities to reduce the…
Data assimilation aims to estimate the states of a dynamical system by optimally combining sparse and noisy observations of the physical system with uncertain forecasts produced by a computational model. The states of many dynamical systems…
Sequential Monte Carlo (SMC), or particle filtering, is widely used in nonlinear state-space systems, but its performance often suffers from poorly approximated proposal and state-transition distributions. This work introduces a…
We consider multiscale stochastic systems that are partially observed at discrete points of the slow time scale. We introduce a particle filter that takes advantage of the multiscale structure of the system to efficiently approximate the…
In this tutorial we consider the non-linear Bayesian filtering of static parameters in a time-dependent model. We outline the theoretical background and discuss appropriate solvers. We focus on particle-based filters and present Sequential…
Particle Metropolis-Hastings (PMH) allows for Bayesian parameter inference in nonlinear state space models by combining Markov chain Monte Carlo (MCMC) and particle filtering. The latter is used to estimate the intractable likelihood. In…
When underlying probability density functions of nonlinear dynamic systems are unknown, the filtering problem is known to be a challenging problem. This paper attempts to make progress on this problem by proposing a new class of filtering…
We discuss how the ideal formalism of Computational Mechanics can be adapted to apply to a non-infinite series of corrupted and correlated data, that is typical of most observed natural time series. Specifically, a simple filter that…
We are interested in the online prediction of the electricity load, within the Bayesian framework of dynamic models. We offer a review of sequential Monte Carlo methods, and provide the calculations needed for the derivation of so-called…