Related papers: Multivariate Gini-type discrepancies
We consider a Markov chain on $\mathbb{R}^d$ with invariant measure $\mu$. We are interested in the rate of convergence of the empirical measures towards the invariant measure with respect to various dual distances, including in particular…
The pairwise comparisons method is a convenient tool used when the relative order of preferences among different concepts (alternatives) needs to be determined. There are several popular implementations of this method, including the…
Cooperative localization is a promising solution to improve the accuracy and overcome the shortcomings of GNSS. Cooperation is often achieved by measuring the distance between users. To optimally integrate a distance measurement between two…
Multidimensional Scaling (MDS) is a classic technique that seeks vectorial representations for data points, given the pairwise distances between them. However, in recent years, data are usually collected from diverse sources or have…
We introduce some new indexes to measure the departure of any multivariate continuous distribution on non-negative orthant from a given reference one such the uncorrelated exponential model, similar to the relative Fisher dispersion indexes…
Quantifying distributional separation across groups is fundamental in statistical learning and scientific discovery, yet most classical discrepancy measures are tailored to two-group comparisons. We generalize the underlap coefficient…
The aim of this paper is to discuss both higher-order asymptotic expansions and skewed approximations for the Bayesian Discrepancy Measure for testing precise statistical hypotheses. In particular, we derive results on third-order…
We define a new family of similarity and distance measures on graphs, and explore their theoretical properties in comparison to conventional distance metrics. These measures are defined by the solution(s) to an optimization problem which…
In this paper, a new measurement to compare two large-scale graphs based on the theory of quantum probability is proposed. An explicit form for the spectral distribution of the corresponding adjacency matrix of a graph is established. Our…
Precision and Recall are two prominent metrics of generative performance, which were proposed to separately measure the fidelity and diversity of generative models. Given their central role in comparing and improving generative models,…
Anomaly detection is a field of intense research. Identifying low probability events in data/images is a challenging problem given the high-dimensionality of the data, especially when no (or little) information about the anomaly is…
Exploiting the geometric nature of statistical divergences, we devise a way to define associated induced uncertainty measures for discrete and finite probability distributions. We also report new uncertainty measures and discuss their…
Comparing $K$-sample distributions is a fundamental problem in data science that arises in a wide variety of fields and applications. In this article, we introduce a maximum-of-differences approach to make such comparisons. Specifically, we…
Generative models are invaluable in many fields of science because of their ability to capture high-dimensional and complicated distributions, such as photo-realistic images, protein structures, and connectomes. How do we evaluate the…
We study a novel class of affine invariant and consistent tests for multivariate normality. The tests are based on a characterization of the standard $d$-variate normal distribution by means of the unique solution of an initial value…
Divergence functions are interesting discrepancy measures. Even though they are not true distances, we can use them to measure how separated two points are. Curiously enough, when they are applied to random variables, they lead to a notion…
Multidimensional scaling (MDS) is a popular technique for mapping a finite metric space into a low-dimensional Euclidean space in a way that best preserves pairwise distances. We overview the theory of classical MDS, along with its…
It has been proposed that complex populations, such as those that arise in genomics studies, may exhibit dependencies among observations as well as among variables. This gives rise to the challenging problem of analyzing unreplicated…
Variable selection is of increasing importance to address the difficulties of high dimensionality in many scientific areas. In this paper, we demonstrate a property for distance covariance, which is incorporated in a novel feature screening…
In several recent works on infinite-dimensional systems of ODEs \cite{cao_derivation_2021,cao_explicit_2021,cao_iterative_2024,cao_sticky_2024}, which arise from the mean-field limit of agent-based models in economics and social sciences…