Related papers: Multiplicative Gaussian Particle Filter
In image reconstruction, an accurate quantification of uncertainty is of great importance for informed decision making. Here, the Bayesian approach to inverse problems can be used: the image is represented through a random function that…
Despite having various attractive qualities such as high prediction accuracy and the ability to quantify uncertainty and avoid over-fitting, Bayesian Matrix Factorization has not been widely adopted because of the prohibitive cost of…
The Gaussian Mixture Probability Hypothesis Density (GM-PHD) filter is an almost exact closed-form approximation to the Bayes-optimal multi-target tracking algorithm. Due to its optimality guarantees and ease of implementation, it has been…
A new method for approximating fractional derivatives of the Gaussian function and Dawson's integral are presented. Unlike previous approaches, which are dominantly based on some discretization of Riemann-Liouville integral using polynomial…
We revisit the replica method for analyzing inference and learning in parametric models, considering situations where the data-generating distribution is unknown or analytically intractable. Instead of assuming idealized distributions to…
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…
Most Kalman filter extensions assume Gaussian noise and when the noise is non-Gaussian, usually other types of filters are used. These filters, such as particle filter variants, are computationally more demanding than Kalman type filters.…
"Particle methods" are sequential Monte Carlo algorithms, typically involving importance sampling, that are used to estimate and sample from joint and marginal densities from a collection of a, presumably increasing, number of random…
We develop an iterative framework for Bayesian inference problems where the posterior distribution may involve computationally intensive models, intractable gradients, significant posterior concentration, and pronounced non-Gaussianity. Our…
We consider chance constrained optimization where it is sought to optimize a function while complying with constraints, both of which are affected by uncertainties. The high computational cost of realistic simulations strongly limits 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…
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…
Bayesian quantum estimation provides a robust framework for quantum technologies, especially in scenarios with limited data and minimal prior information. Yet, its application to continuous-variable Gaussian systems has remained limited and…
The problem of state estimations for electric distribution system is considered. A collaborative filtering approach is proposed in this paper to integrate the slow time-scale smart meter measurements in the distribution system state…
Gaussian processes allow for flexible specification of prior assumptions of unknown dynamics in state space models. We present a procedure for efficient Bayesian learning in Gaussian process state space models, where the representation is…
We develop and analyze a method for stochastic simulation optimization based on Gaussian process models within a trust-region framework. We focus on settings where the variance of the objective function is large, making accurate estimation…
In this paper, we present a novel approach to approximate the gain function of the feedback particle filter (FPF). The exact gain function is the solution of a Poisson equation involving a probability-weighted Laplacian. The numerical…
We derive a Gaussian approximation result for the maximum of a sum of high-dimensional random vectors. Specifically, we establish conditions under which the distribution of the maximum is approximated by that of the maximum of a sum of the…
Recommender systems are often designed based on a collaborative filtering approach, where user preferences are predicted by modelling interactions between users and items. Many common approaches to solve the collaborative filtering task are…
We analyze the dynamics of an algorithm for approximate inference with large Gaussian latent variable models in a student-teacher scenario. To model nontrivial dependencies between the latent variables, we assume random covariance matrices…