Related papers: A Pseudo-Metric between Probability Distributions …
This article provides an overview on the statistical modeling of complex data as increasingly encountered in modern data analysis. It is argued that such data can often be described as elements of a metric space that satisfies certain…
The paper introduces a new kernel-based Maximum Mean Discrepancy (MMD) statistic for measuring the distance between two distributions given finitely-many multivariate samples. When the distributions are locally low-dimensional, the proposed…
Modeling observations as random distributions embedded within Wasserstein spaces is becoming increasingly popular across scientific fields, as it captures the variability and geometric structure of the data more effectively. However, the…
In this article we present very intuitive, easy to follow, yet mathematically rigorous, approach to the so called data fitting process. Rather than minimizing the distance between measured and simulated data points, we prefer to find such…
We introduce the observable Wasserstein distance, a framework for deriving lower bounds on the Wasserstein distance between probability measures on Polish metric spaces, designed to bypass the computational intractability of exact optimal…
The analysis of samples of random objects that do not lie in a vector space is gaining increasing attention in statistics. An important class of such object data is univariate probability measures defined on the real line. Adopting the…
Applications in data science, shape analysis and object classification frequently require comparison of probability distributions defined on different ambient spaces. To accomplish this, one requires a notion of distance on a given class of…
In this paper, we show that the halfspace depth random variable for samples from a univariate distribution with a notion of center is distributed as a uniform distribution on the interval [0,1/2]. The simplicial depth random variable has a…
This article inspects whether a multivariate distribution is different from a specified distribution or not, and it also tests the equality of two multivariate distributions. In the course of this study, a graphical tool-kit using…
We investigate statistical properties of a likelihood approach to nonparametric estimation of a singular distribution using deep generative models. More specifically, a deep generative model is used to model high-dimensional data that are…
Deep metric learning aims to construct an embedding space where samples of the same class are close to each other, while samples of different classes are far away from each other. Most existing deep metric learning methods attempt to…
Data depth is a concept in multivariate statistics that measures the centrality of a point in a given data cloud in $\IR^d$. If the depth of a point can be represented as the minimum of the depths with respect to all one-dimensional…
This paper defines a new pseudometric for binary relations between finite sets that measures consensus among subsets. The main results are (1) a concise restatement of this pseudometric with an intuitively appealing interpretation via a…
Kernel techniques are among the most popular and flexible approaches in data science allowing to represent probability measures without loss of information under mild conditions. The resulting mapping called mean embedding gives rise to a…
In 1975 John Tukey proposed a multivariate median which is the 'deepest' point in a given data cloud in R^d. Later, in measuring the depth of an arbitrary point z with respect to the data, David Donoho and Miriam Gasko considered…
In this paper, by proposing two new kinds of distributional uncertainty sets, we explore robustness of distortion risk measures against distributional uncertainty. To be precise, we first consider a distributional uncertainty set which is…
Given a probability measure with density, Fermat distances and density-driven metrics are conformal transformations of the Euclidean metric that shrink distances in high density areas and enlarge distances in low density areas. Although…
This paper explores methods for estimating or approximating the total variation distance and the chi-squared divergence of probability measures within topological sample spaces, using independent and identically distributed samples. Our…
With increasing use of digital control it is natural to view control inputs and outputs as stochastic processes assuming values over finite alphabets rather than in a Euclidean space. As control over networks becomes increasingly common,…
Centrality descriptors are widely used to rank nodes according to specific concept(s) of importance. Despite the large number of centrality measures available nowadays, it is still poorly understood how to identify the node which can be…