Related papers: Approximation of symmetric total variation on poin…
In this paper, we introduce a novel method for comparing 3D point clouds, a critical task in various machine learning applications. By interpreting point clouds as samples from underlying probability density functions, the statistical…
We develop a theory to measure the variance and covariance of probability distributions defined on the nodes of a graph, which takes into account the distance between nodes. Our approach generalizes the usual (co)variance to the setting of…
A simple finite-size scaling theory is proposed here for anisotropic percolation models considering the cluster size distribution function as generalized homogeneous function of the system size and two connectivity lengths. The proposed…
We develop a general framework for the probabilistic analysis of random finite point clouds in the context of topological data analysis. We extend the notion of a barcode of a finite point cloud to compact metric spaces. Such a barcode…
We introduce the price of symmetrisation, a concept that aims to compare fundamental differences (gap and quotient) between values of a given graph invariant for digraphs and the values of the same invariant of the symmetric versions of…
A classical result of variational analysis, known as Attouch theorem, establishes the equivalence between epigraphical convergence of a sequence of proper convex lower semicontinuous functions and graphical convergence of the corresponding…
For a variant of the algorithm in [Pit19] (arXiv:1903.10816) to compute the approximate density or distribution function of a linear mixture of independent random variables known by a finite sample, it is presented a proof of the functional…
We propose a $\Gamma$-convergent discrete approximation of the Mumford-Shah functional. The discrete functionals act on functions defined on stationary stochastic lattices and take into account general finite differences through a…
We give a necessary and sufficient condition for symmetric infinitely divisible distribution to have Gaussian component. The result can be applied to approximation the distribution of finite sums of random variables. Particularly, it shows…
We propose a novel meshless method to compute harmonic maps and conformal maps for surfaces embedded in the Euclidean 3-space, using point cloud data only. Given a surface, or a point cloud approximation, we simply use the standard cubic…
We introduce a novel approach for measuring the total curvature at every triangle of a discrete surface. This method takes advantage of the relationship between per triangle total curvature and the Dirichlet energy of the Gauss map. This…
Discrete point cloud objects lack sufficient shape descriptors of 3D geometries. In this paper, we present a novel method for aggregating hypothetical curves in point clouds. Sequences of connected points (curves) are initially grouped by…
This paper is a survey of methods for solving smooth (strongly) monotone stochastic variational inequalities. To begin with, we give the deterministic foundation from which the stochastic methods eventually evolved. Then we review methods…
Let $F_G(P)$ be a functional defined on the set of all the probability distributions on the vertex set of a graph $G$. We say that $G$ is \emph{symmetric with respect to $F_G(P)$} if the uniform distribution on $V(G)$ maximizes $F_G(P)$.…
We consider the detection and localization of change points in the distribution of an offline sequence of observations. Based on a nonparametric framework that uses a similarity graph among observations, we propose new test statistics when…
Scene graphs have been recently introduced into 3D spatial understanding as a comprehensive representation of the scene. The alignment between 3D scene graphs is the first step of many downstream tasks such as scene graph aided point cloud…
A prevalent problem in general state-space models is the approximation of the smoothing distribution of a state, or a sequence of states, conditional on the observations from the past, the present, and the future. The aim of this paper is…
As artificial intelligence (AI) / machine learning (ML) gain widespread adoption, practitioners are increasingly seeking means to quantify and control the risk these systems incur. This challenge is especially salient when such systems have…
The spin-spin correlation function of the spherical model being precisely at an anisotropic Lifshitz point of arbitrary order is calculated exactly. The results are in agreement with scaling. The scaling function is shown to be universal.…
We formulate a simple algorithm for computing global exact symmetries of closed discrete curves in plane. The method is based on a suitable trigonometric interpolation of vertices of the given polyline and consequent computation of the…