Related papers: Gaussian filtering and variational approximations …
In this paper, we study porous media flows in heterogeneous stochastic media. We propose an efficient forward simulation technique that is tailored for variational Bayesian inversion. As a starting point, the proposed forward simulation…
In this work, we employ the Bayesian inference framework to solve the problem of estimating the solution and particularly, its derivatives, which satisfy a known differential equation, from the given noisy and scarce observations of the…
We develop and analyze stochastic inexact Gauss-Newton methods for nonlinear least-squares problems and for nonlinear systems ofequations. Random models are formed using suitable sampling strategies for the matrices involved in the…
Within the past two decades, Gaussian process regression has been increasingly used for modeling dynamical systems due to some beneficial properties such as the bias variance trade-off and the strong connection to Bayesian mathematics. As…
Variable clustering is important for explanatory analysis. However, only few dedicated methods for variable clustering with the Gaussian graphical model have been proposed. Even more severe, small insignificant partial correlations due to…
We introduce a variational Bayesian neural network where the parameters are governed via a probability distribution on random matrices. Specifically, we employ a matrix variate Gaussian \cite{gupta1999matrix} parameter posterior…
This paper focuses on Bayesian Optimization in combinatorial spaces. In many applications in the natural science. Broad applications include the study of molecules, proteins, DNA, device structures and quantum circuit designs, a on…
Popular Bayes filters often apply linearization techniques, such as Taylor expansion or stochastic linear regression, to enable the use of the Kalman filter structure, but this can lead to large errors in strongly nonlinear systems. The…
This article proposes a new filtering model for stationary Gaussian Markov statistical experiments, given by diffusion-type difference stochastic equations.
High dimensional time series are endemic in applications of machine learning such as robotics (sensor data), computational biology (gene expression data), vision (video sequences) and graphics (motion capture data). Practical nonlinear…
The nonlinear dynamics of an obliquely oriented wave packet at sea surface is studied both analytically and numerically for various initial parameters of the packet, in connection with the problem of oceanic rogue waves. In the framework of…
In this paper, we study the finite-horizon optimal density steering problem for discrete-time stochastic linear dynamical systems. Specifically, we focus on steering probability densities represented as Gaussian mixture models which are…
We obtain solutions to conservation laws under any random initial conditions that are described by Gaussian stochastic processes (in some cases discretized). We analyze the generalization of Burgers' equation for a smooth flux function…
We propose a nonparametric density estimator based on the Gaussian process (GP) and derive three novel closed form learning algorithms based on Fisher divergence (FD) score matching. The density estimator is formed by multiplying a base…
Gaussian processes are the gold standard for many real-world modeling problems, especially in cases where a model's success hinges upon its ability to faithfully represent predictive uncertainty. These problems typically exist as parts of…
The estimation of non-Gaussian measurement noise models is a significant challenge across various fields. In practical applications, it often faces challenges due to the large number of parameters and high computational complexity. This…
By learning the gradient of smoothed data distributions, diffusion models can iteratively generate samples from complex distributions. The learned score function enables their generalization capabilities, but how the learned score relates…
Several numerical approximation strategies for the expectation-propagation algorithm are studied in the context of large-scale learning: the Laplace method, a faster variant of it, Gaussian quadrature, and a deterministic version of…
Many approximate Bayesian inference methods assume a particular parametric form for approximating the posterior distribution. A multivariate Gaussian distribution provides a convenient density for such approaches; examples include the…
This paper is concerned with numerical algorithms for gain function approximation in the feedback particle filter. The exact gain function is the solution of a Poisson equation involving a probability-weighted Laplacian. The problem is to…