相关论文: Bi-invariant Dissimilarity Measures for Sample Dis…

In this paper, a novel Bayesian nonparametric test for assessing multivariate normal models is presented. While there are extensive frequentist and graphical methods for testing multivariate normality, it is challenging to find Bayesian…

Two-sample tests for multivariate data and especially for non-Euclidean data are not well explored. This paper presents a novel test statistic based on a similarity graph constructed on the pooled observations from the two samples. It can…

Standard high-dimensional factor models assume that the comovements in a large set of variables could be modeled using a small number of latent factors that affect all variables. In many relevant applications in economics and finance,…

To determine the Lie groups that admit a flat (eventually complete) left invariant semi-Riemannian metric is an open and difficult problem. The main aim of this paper is the study of the flatness of left invariant semi Riemannian metrics on…

We propose the use of a simple intuitive principle for measuring algorithmic classification bias: the significance of the differences in a classifier's error rates across the various demographics is inversely commensurate with the sample…

In this paper we provide the asymptotic theory of the general of $\phi$-divergences measures, which includes the most common divergence measures : Renyi and Tsallis families and the Kullback-Leibler measure. Instead of using the Parzen…

The rapid growth of high-dimensional datasets across various scientific domains has created a pressing need for new statistical methods to compare distributions supported on their underlying structures. Assessing similarity between datasets…

Hotelling's T-squared test is a classical tool to test if the normal mean of a multivariate normal distribution is a specified one or the means of two multivariate normal means are equal. When the population dimension is higher than the…

Datasets containing large samples of time-to-event data arising from several small heterogeneous groups are commonly encountered in statistics. This presents problems as they cannot be pooled directly due to their heterogeneity or analyzed…

Despite of many measures applied for determine the difference between two groups of observations, such as mean value, median value, sample stan- dard deviation and so on, we propose a novel non parametric transformation method based on…

Metrics for rigorously defining a distance between two events have been used to study the properties of the dataspace manifold of particle collider physics. The probability distribution of pairwise distances on this dataspace is unique with…

In this paper we provide the asymptotic theory of the general of $\phi$-divergences measures, which include the most common divergence measures : Renyi and Tsallis families and the Kullback-Leibler measure. We are interested in divergence…

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…

In many applications, we encounter data on Riemannian manifolds such as torus and rotation groups. Standard statistical procedures for multivariate data are not applicable to such data. In this study, we develop goodness-of-fit testing and…

Persistent homology allows us to create topological summaries of complex data. In order to analyse these statistically, we need to choose a topological summary and a relevant metric space in which this topological summary exists. While…

Multiple instance learning (MIL) is concerned with learning from sets (bags) of objects (instances), where the individual instance labels are ambiguous. In this setting, supervised learning cannot be applied directly. Often, specialized MIL…

The paper presents a geometric duality between the spherical squared-Hellinger distance and a hyperbolic isometric invariant of the Poincare disc under the action of the general Mobius group. Motivated by the geometric connection, we…

Suppose that we are interested in the comparison of two independent categorical variables. Suppose also that the population is divided into subpopulations or groups. Notice that the distribution of the target variable may vary across…

Statistical distance measures have found wide applicability in information retrieval tasks that typically involve high dimensional datasets. In order to reduce the storage space and ensure efficient performance of queries, dimensionality…

We consider Lie groups equipped with arbitrary distances. We only assume that the distance is left-invariant and induces the manifold topology. For brevity, we call such object metric Lie groups. Apart from Riemannian Lie groups,…