Related papers: A combinatorial interpretation of Gaussian blur
Most object detection methods use bounding boxes to encode and represent the object shape and location. In this work, we explore a fuzzy representation of object regions using Gaussian distributions, which provides an implicit binary…
Whitening is a classical technique in unsupervised learning that can facilitate estimation tasks by standardizing data. An important application is the estimation of latent variable models via the decomposition of tensors built from…
Gravitational lensing occurs as the path of light from distant celestial bodies is distorted due to gravitational attraction by other celestial bodies, whose mass is partly invisible, being so-called dark matter. When observed through a…
Sum-product networks have recently emerged as an attractive representation due to their dual view as a special type of deep neural network with clear semantics and a special type of probabilistic graphical model for which inference is…
The aim of this article is to define some new families of the special numbers. These numbers provide some further motivation for computation of combinatorial sums involving binomial coefficients and the Euler kind numbers of negative order.…
Gaussian Boson Sampling (GBS) is a recently developed paradigm of quantum computing consisting of sending a Gaussian state through a linear interferometer and then counting the number of photons in each output mode. When the system encodes…
Stochastic filtering is defined as the estimation of a partially observed dynamical system. A massive scientific and computational effort is dedicated to the development of numerical methods for approximating the solution of the filtering…
Recently, a novel method for developing filtering algorithms, based on the interconnection of two Bayesian filters and called double Bayesian filtering, has been proposed. In this manuscript we show that the same conceptual approach can be…
Gaussian graphical models (GGMs) are well-established tools for probabilistic exploration of dependence structures using precision matrices. We develop a Bayesian method to incorporate covariate information in this GGMs setup in a nonlinear…
We present a variation of a quantum algorithm for the machine learning task of classification with graph-structured data. The algorithm implements a feature extraction strategy that is based on Gaussian boson sampling (GBS) a near term…
Gaussian curvature is an important geometric property of surfaces, which has been used broadly in mathematical modeling. Due to the full nonlinearity of the Gaussian curvature, efficient numerical methods for models based on it are uncommon…
Conventional approximations to Bayesian inference rely on either approximations by statistics such as mean and covariance or by point particles. Recent advances such as the ensemble Gaussian mixture filter have generalized these notions to…
In the previous article (Found Phys. Lett. {\bf{16}} 325-341), we showed that a reciprocity of the Gauss sums is connected with the wave and particle complementary. In this article, we revise the previous investigation by considering a…
Gaussian process (GP) models provide a powerful tool for prediction but are computationally prohibitive using large data sets. In such scenarios, one has to resort to approximate methods. We derive an approximation based on a composite…
The main purpose of this article is to study higher power mean values of generalized quadratic Gauss sums using estimates for character sums, analytic method and algebraic geometric methods. In this article, we prove two conjectures which…
We present a general form of the iteration and interpolation process used in implicit particle filters. Implicit filters are based on a pseudo-Gaussian representation of posterior densities, and are designed to focus the particle paths so…
This paper addresses the statistical estimation of Gaussian Mixture Models (GMMs) with unknown diagonal covariances from independent and identically distributed samples. We employ the Beurling-LASSO (BLASSO), a convex optimization framework…
This paper investigates Gaussian copula mixture models (GCMM), which are an extension of Gaussian mixture models (GMM) that incorporate copula concepts. The paper presents the mathematical definition of GCMM and explores the properties of…
Motion blur is a frequently observed image artifact, especially under insufficient illumination where exposure time has to be prolonged so as to collect more photons for a bright enough image. Rather than simply removing such blurring…
The mean-shift algorithm is a popular algorithm in computer vision and image processing. It can also be cast as a minimum gamma-divergence estimation. In this paper we focus on the "blurring" mean shift algorithm, which is one version of…