Related papers: Quadratic distances on probabilities: A unified fo…

Stapp claims that, when spatial degrees of freedom are taken into account, Everett quantum mechanics is ambiguous due to a "core basis problem." To examine an aspect of this claim I generalize the ideal measurement model to include…

This paper presents a distance function between sets based on an average of distances between their elements. The distance function is a metric if the sets are non-empty finite subsets of a metric space. It can be applied to produce various…

In the past decades, most work in the area of data analysis and machine learning was focused on optimizing predictive models and getting better results than what was possible with existing models. To what extent the metrics with which such…

How to distribute a set of points uniformly on a spherical surface is a very old problem that still lacks a definite answer. In this work, we introduce a physical measure of uniformity based on the distribution of distances between points,…

We consider the goodness of fit testing problem for linear stochastic differential equation (Ornstein-Uhlenbeck process). The basic hypothesis is supposed to be composite with two-dimensional unknown parameter. We study two goodness of fit…

This article investigates the probabilistic relationship between quantum classification of Boolean functions and their Hamming distance. By integrating concepts from quantum computing, information theory, and combinatorics, we explore how…

Statistical learning theory is the foundation of machine learning, providing theoretical bounds for the risk of models learned from a (single) training set, assumed to issue from an unknown probability distribution. In actual deployment,…

The high energy physics unfolding problem is an important statistical inverse problem in data analysis at the Large Hadron Collider (LHC) at CERN. The goal of unfolding is to make nonparametric inferences about a particle spectrum from…

In the uniformity testing task, an algorithm is provided with samples from an unknown probability distribution over a (known) finite domain, and must decide whether it is the uniform distribution, or, alternatively, if its total variation…

Single-cell omics enable the profiles of cells, which contain large numbers of biological features, to be quantified. Cluster analysis, a dimensionality reduction process, is used to reduce the dimensions of the data to make it…

We investigate a network model based on an infinite regular square lattice embedded in the Euclidean plane where the node connection probability is given by the geometrical distance of nodes. We show that the degree distribution in the…

We introduce fractional flat space, described by a continuous geometry with constant non-integer Hausdorff and spectral dimensions. This is the analogue of Euclidean space, but with anomalous scaling and diffusion properties. The basic tool…

We develop an inferential toolkit for analyzing object-valued responses, which correspond to data situated in general metric spaces, paired with Euclidean predictors within the conformal framework. To this end we introduce conditional…

Discrete partially ordered sets can be turned into distance spaces in several ways. The distance functions may or may not satisfy the triangle inequality, and restriction of the distance to finite chains may or may not coincide with the…

The concepts of similarity and distance are crucial in data mining. We consider the problem of defining the distance between two data sets by comparing summary statistics computed from the data sets. The initial definition of our distance…

Testing independence is of significant interest in many important areas of large-scale inference. Using extreme-value form statistics to test against sparse alternatives and using quadratic form statistics to test against dense alternatives…

A goodness-of-fit test for the fitting of a parametric model to data obtained from a detector with finite resolution and limited acceptance is proposed. The parameters of the model are found by minimization of a statistic that is used for…

We propose two bounded comparison metrics that may be implemented to arbitrary dimensions in regression tasks. One quantifies the structure of uncertainty and the other quantifies the distribution of uncertainty. The structure metric…

We propose a new conditional dependence measure and a statistical test for conditional independence. The measure is based on the difference between analytic kernel embeddings of two well-suited distributions evaluated at a finite set of…

Advances in architectural design, data availability, and compute have driven remarkable progress in semantic segmentation. Yet, these models often rely on relaxed Bayesian assumptions, omitting critical uncertainty information needed for…