Related papers: An error estimate of Gaussian Recursive Filter in …
The expressive power of Bayesian kernel-based methods has led them to become an important tool across many different facets of artificial intelligence, and useful to a plethora of modern application domains, providing both power and…
The state-of-the-art tensor network Kalman filter lifts the curse of dimensionality for high-dimensional recursive estimation problems. However, the required rounding operation can cause filter divergence due to the loss of positive…
Solving Bayesian inference problems approximately with variational approaches can provide fast and accurate results. Capturing correlation within the approximation requires an explicit parametrization. This intrinsically limits this…
We consider the problem of learning time-varying functions in a distributed fashion, where agents collect local information to collaboratively achieve a shared estimate. This task is particularly relevant in control applications, whenever…
We consider a general class of regression models with normally distributed covariates, and the associated nonconvex problem of fitting these models from data. We develop a general recipe for analyzing the convergence of iterative algorithms…
This paper presents a real-time capable algorithm for the learning of Gaussian Processes (GP) for submodels. It extends an existing recursive Gaussian Process (RGP) algorithm which requires a measurable output. In many applications,…
We provide faster algorithms for the problem of Gaussian summation, which occurs in many machine learning methods. We develop two new extensions - an O(Dp) Taylor expansion for the Gaussian kernel with rigorous error bounds and a new error…
We consider estimation of a deterministic unknown parameter vector in a linear model with non-Gaussian noise. In the Gaussian case, dimensionality reduction via a linear matched filter provides a simple low dimensional sufficient statistic…
In this paper, we introduce a new, fast data assimilation algorithm for a 2D linear advection equation with divergence-free coefficients. We first apply the nodal discontinuous Galerkin (DG) method to discretize the advection equation, and…
Reconstructing high-fidelity underwater scenes remains a challenging task due to light absorption, scattering, and limited visibility inherent in aquatic environments. This paper presents an enhanced Gaussian Splatting-based framework that…
Data assimilation involves estimating the state of a system by combining observations from various sources with a background estimate of the state. The weights given to the observations and background state depend on their specified error…
This paper presents a compact, recursive, non-linear, filter, derived from the Gauss-Newton (GNF), which is an algorithm that is based on weighted least squares and the Newton method of local linearisation. The recursive form (RGNF), which…
Representing 3D scenes from multiview images is a core challenge in computer vision and graphics, which requires both precise rendering and accurate reconstruction. Recently, 3D Gaussian Splatting (3DGS) has garnered significant attention…
This paper proposes a novel framework for large-scale scene reconstruction based on 3D Gaussian splatting (3DGS) and aims to address the scalability and accuracy challenges faced by existing methods. For tackling the scalability issue, we…
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…
Practical Bayes filters often assume the state distribution of each time step to be Gaussian for computational tractability, resulting in the so-called Gaussian filters. When facing nonlinear systems, Gaussian filters such as extended…
Positron emission tomography (PET) reconstruction is a critical challenge in molecular imaging, often hampered by noise amplification, structural blurring, and detail loss due to sparse sampling and the ill-posed nature of inverse problems.…
It is well-known that polynomial reproduction is not possible when approximating with Gaussian kernels. Quasi-interpolation schemes have been developed which use a finite number of Gaussians at different scales, which then reproduce…
Matching 3D rigid point clouds in complex environments robustly and accurately is still a core technique used in many applications. This paper proposes a new architecture combining error estimation from sample covariances and dual global…
A method to reconstruct fields, source strengths and physical parameters based on Gaussian process regression is presented for the case where data are known to fulfill a given linear differential equation with localized sources. The…