Related papers: Natural Gradient Bayesian Filtering: Geometry-Awar…
During the Gaussian Splatting optimization process, the scene's geometry can gradually deteriorate if its structure is not deliberately preserved, especially in non-textured regions such as walls, ceilings, and furniture surfaces. This…
We introduce neural information field filter, a Bayesian state and parameter estimation method for high-dimensional nonlinear dynamical systems given large measurement datasets. Solving such a problem using traditional methods, such as…
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 short note reviews so-called Natural Gradient Descent (NGD) for multivariate Gaussians. The Fisher Information Matrix (FIM) is derived for several different parameterizations of Gaussians. Careful attention is paid to the symmetric…
Consider a space object in an orbit about the earth. An uncertain initial state can be represented as a point cloud which can be propagated to later times by the laws of Newtonian motion. If the state of the object is represented in…
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…
Kalman filtering is a cornerstone of estimation theory, yet learning the optimal filter under unknown and potentially singular noise covariances remains a fundamental challenge. In this paper, we revisit this problem through the lens of…
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…
Convolutional neural networks (CNNs) provide flexible function approximations for a wide variety of applications when the input variables are in the form of images or spatial data. Although CNNs often outperform traditional statistical…
We develop a fast algorithm for Kalman Filter applied to the random walk forecast model. The key idea is an efficient representation of the estimate covariance matrix at each time-step as a weighted sum of two contributions - the process…
Dynamical system state estimation and parameter calibration problems are ubiquitous across science and engineering. Bayesian approaches to the problem are the gold standard as they allow for the quantification of uncertainties and enable…
In this manuscript, a general method for deriving filtering algorithms that involve a network of interconnected Bayesian filters is proposed. This method is based on the idea that the processing accomplished inside each of the Bayesian…
We study the natural gradient method for learning in deep Bayesian networks, including neural networks. There are two natural geometries associated with such learning systems consisting of visible and hidden units. One geometry is related…
Recursive Bayesian filters have been widely deployed in structural system identification where output-only filters are of higher practicality. Unfortunately, the estimation obtained by instantaneous system inversion via filters can be…
Gaussian Processes (GPs) are widely recognized as powerful non-parametric models for regression and classification. Traditional GP frameworks predominantly operate under the assumption that the inputs are either accurately known or subject…
Both experimental and computational methods for the exploration of structure, functionality, and properties of materials often necessitate the search across broad parameter spaces to discover optimal experimental conditions and regions of…
Gaussian process state-space models (GP-SSMs) are a very flexible family of models of nonlinear dynamical systems. They comprise a Bayesian nonparametric representation of the dynamics of the system and additional (hyper-)parameters…
We consider the Bayesian approach to the linear Gaussian inference problem of inferring the initial condition of a linear dynamical system from noisy output measurements taken after the initial time. In practical applications, the large…
Few real-world systems are amenable to truly Bayesian filtering; nonlinearities and non-Gaussian noises can wreak havoc on filters that rely on linearization and Gaussian uncertainty approximations. This article presents the Bayesian…
This paper addresses state estimation of linear systems with special attention on unknown process and measurement noise covariances, aiming to enhance estimation accuracy while preserving the stability guarantee of the Kalman filter. To…