Related papers: Depth for samples of sets with applications to tes…

The paper concerns a new statistical method for assessing dissimilarity of two random sets based on one realisation of each of them. The method focuses on shapes of the components of the random sets, namely on the curvature of their…

This paper concerns a method of testing equality of distribution of random convex compact sets and the way how to use the test to distinguish between two realisations of general random sets. The family of metrics on the space of…

Data depth has been applied as a nonparametric measurement for ranking multivariate samples. In this paper, we focus on homogeneity tests to assess whether two multivariate samples are from the same distribution. There are many data…

This paper reconsiders the problem of testing the equality of two unspecified continuous distributions. The framework, which we propose, allows for readable and insightful data visualisation and helps to understand and quantify how two…

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…

Statistical depth, which measures the center-outward rank of a given sample with respect to its underlying distribution, has become a popular and powerful tool in nonparametric inference. In this paper, we investigate the use of statistical…

Statistical data depth plays an important role in the analysis of multivariate data sets. The main outcome is a center-outward ordering of the observations that can be used both to highlight features of the underlying distribution of the…

We propose novel methodology for testing equality of model parameters between two high-dimensional populations. The technique is very general and applicable to a wide range of models. The method is based on sample splitting: the data is…

We propose a new approach for the problem of relative depth estimation from a single image. Instead of directly regressing over depth scores, we formulate the problem as estimation of a probability distribution over depth and aim to learn…

In this paper, the classification task for a family of sets representing the realisation of some random set models is solved. Both unsupervised and supervised classification methods are utilised using the similarity measure between two…

Using the fact that some depth functions characterize certain family of distribution functions, and under some mild conditions, distribution of the depth is continuous, we have constructed several new multivariate goodness of fit tests…

Data depth has emerged as an invaluable nonparametric measure for the ranking of multivariate samples. The main contribution of depth-based two-sample comparisons is the introduction of the Q statistic (Liu and Singh, 1993), a quality…

We describe a non-parametric, "example-based" method for estimating the depth of an object, viewed in a single photo. Our method consults a database of example 3D geometries, searching for those which look similar to the object in the…

The design of a metric between probability distributions is a longstanding problem motivated by numerous applications in Machine Learning. Focusing on continuous probability distributions on the Euclidean space $\mathbb{R}^d$, we introduce…

Non-deterministic measurements are common in real-world scenarios: the performance of a stochastic optimization algorithm or the total reward of a reinforcement learning agent in a chaotic environment are just two examples in which…

Determining if two histograms are consistent, whether they have been drawn from the same underlying distribution or not, is a common problem in physics. Existing approaches are not only limited in power but also inapplicable to histograms…

Given two networks of differing sizes, it is of interest to test whether the two networks belong to the same distribution. We formalize the notion of "equality of distribution" under the framework of the generalized random dot product…

We discuss a graph-based approach for testing spatial point patterns. This approach falls under the category of data-random graphs, which have been introduced and used for statistical pattern recognition in recent years. Our goal is to test…

A new method based on the rejection sampling for finding statistical tests is proposed. This method is conceptually intuitive, easy to implement, and applicable for arbitrary dimension. To illustrate its potential applicability, three…

Hypothesis testing in high dimensional data is a notoriously difficult problem without direct access to competing models' likelihood functions. This paper argues that statistical divergences can be used to quantify the difference between…