Related papers: Implicit particle filtering for models with partia…
Computer simulations of differential equations require a time discretization, which inhibits to identify the exact solution with certainty. Probabilistic simulations take this into account via uncertainty quantification. The construction of…
Particle filters are a widely used Monte Carlo based data assimilation technique that estimates the probability distribution of a system's state conditioned on observations through a collection of weights and particles. A known problem for…
Sequential Bayesian Filtering aims to estimate the current state distribution of a Hidden Markov Model, given the past observations. The problem is well-known to be intractable for most application domains, except in notable cases such as…
Particle filters are key algorithms for object tracking under non-linear, non-Gaussian dynamics. The high computational cost of particle filters, however, hampers their applicability in cases where the likelihood model is costly to…
Recent works on deep non-linear spatially selective filters demonstrate exceptional enhancement performance with computationally lightweight architectures for stationary speakers of known directions. However, to maintain this performance in…
Particle Markov Chain Monte Carlo (PMCMC) is a general computational approach to Bayesian inference for general state space models. Our article scales up PMCMC in terms of the number of observations and parameters by generating the…
In nonlinear state-space models, sequential learning about the hidden state can proceed by particle filtering when the density of the observation conditional on the state is available analytically (e.g. Gordon et al., 1993). This condition…
In the following article we develop a particle filter for approximating Feynman-Kac models with indicator potentials. Examples of such models include approximate Bayesian computation (ABC) posteriors associated with hidden Markov models…
In this work, we develop tracking and estimation techniques relevant to underwater targets. Particularly, we explore particle filtering techniques for target tracking. It is a numerical approximation method for implementing a recursive…
Variational inference for state space models (SSMs) is known to be hard in general. Recent works focus on deriving variational objectives for SSMs from unbiased sequential Monte Carlo estimators. We reveal that the marginal particle filter…
In this paper, we present a sparse grid-based Monte Carlo method for solving high-dimensional semi-linear nonlocal diffusion equations with volume constraints. The nonlocal model is governed by a class of semi-linear partial…
The convolution of a Gaussian and a Cauchy distribution, known as the Voigt distribution, is widely used in spectroscopy and provides a natural framework for modeling heavy-tailed measurement noise. We derive analytical expressions for its…
This paper concerns numerical assessment of Monte Carlo error in particle filters. We show that by keeping track of certain key features of the genealogical structure arising from resampling operations, it is possible to estimate variances…
Bayesian filtering is a well-known problem that aims to estimate plausible states of a dynamical system from observations. Among existing approaches to solve this problem, particle filters are theoretically exact for non-linear dynamics and…
This work leverages recent advances in probabilistic machine learning to discover conservation laws expressed by parametric linear equations. Such equations involve, but are not limited to, ordinary and partial differential,…
Particle discretizations of partial differential equations are advantageous for high-dimensional kinetic models in phase space due to their better scalability than continuum approaches with respect to dimension. Complex processes…
We introduce a new version of particle filter in which the number of "children" of a particle at a given time has a Poisson distribution. As a result, the number of particles is random and varies with time. An advantage of this scheme is…
Exact inference for hidden Markov models requires the evaluation of all distributions of interest - filtering, prediction, smoothing and likelihood - with a finite computational effort. This article provides sufficient conditions for exact…
A common approach to approximating Gaussian log-likelihoods at scale exploits the fact that precision matrices can be well-approximated by sparse matrices in some circumstances. This strategy is motivated by the \emph{screening effect},…
Data assimilation algorithms integrate prior information from numerical model simulations with observed data. Ensemble-based filters, regarded as state-of-the-art, are widely employed for large-scale estimation tasks in disciplines such as…