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Clustering is part of unsupervised analysis methods that consist in grouping samples into homogeneous and separate subgroups of observations also called clusters. To interpret the clusters, statistical hypothesis testing is often used to…

统计方法学 · 统计学 2022-10-25 Benjamin Hivert , Denis Agniel , Rodolphe Thiébaut , Boris P Hejblum

This paper proposes a novel, nonparametric, interpoint distance-based measure to investigate whether there exist any groups in a set of given data, and if so then, how many groups are prevailing in total. It is a cluster accuracy index…

统计方法学 · 统计学 2026-05-21 Soumita Modak

In this paper we propose a measure of clustering quality or accuracy that is appropriate in situations where it is desirable to evaluate a clustering algorithm by somehow comparing the clusters it produces with ``ground truth' consisting of…

机器学习 · 计算机科学 2013-01-07 Byron E Dom

When scholars suspect units are dependent on each other within clusters but independent of each other across clusters, they employ cluster-robust standard errors (CRSEs). Nevertheless, what to cluster over is sometimes unknown. For…

统计方法学 · 统计学 2025-11-12 Kentaro Fukumoto

This paper presents and analyzes an approach to cluster-based inference for dependent data. The primary setting considered here is with spatially indexed data in which the dependence structure of observed random variables is characterized…

统计理论 · 数学 2022-11-16 Jianfei Cao , Christian Hansen , Damian Kozbur , Lucciano Villacorta

The independence clustering problem is considered in the following formulation: given a set $S$ of random variables, it is required to find the finest partitioning $\{U_1,\dots,U_k\}$ of $S$ into clusters such that the clusters…

机器学习 · 计算机科学 2017-03-21 Daniil Ryabko

Testing the independence between random vectors is a fundamental problem in statistics. Distance correlation, a recently popular dependence measure, is universally consistent for testing independence against all distributions with finite…

统计方法学 · 统计学 2024-08-22 Yuwei Ke , Hok Kan Ling , Yanglei Song

An important aspect of multiple hypothesis testing is controlling the significance level, or the level of Type I error. When the test statistics are not independent it can be particularly challenging to deal with this problem, without…

统计理论 · 数学 2009-03-04 Sandy Clarke , Peter Hall

We show that one single experiment can test simultaneously and independently both the nonclassicality of states and measurements by the violation or fulfillment of classical bounds on the statistics. Nonideal measurements affected by…

量子物理 · 物理学 2011-03-28 Alfredo Luis , Ángel Rivas

Statistical significance testing of differences in values of metrics like recall, precision and balanced F-score is a necessary part of empirical natural language processing. Unfortunately, we find in a set of experiments that many commonly…

计算与语言 · 计算机科学 2007-05-23 Alexander Yeh

Statistically equivalent blocks are not frequently considered in the context of nonparametric two-sample hypothesis testing. Despite the limited exposure, this paper shows that a number of classical nonparametric hypothesis tests can be…

统计方法学 · 统计学 2025-06-11 Chase Holcombe

Hypothesis tests are a crucial statistical tool for data mining and are the workhorse of scientific research in many fields. Here we study differentially private tests of independence between a categorical and a continuous variable. We take…

统计方法学 · 统计学 2019-03-25 Simon Couch , Zeki Kazan , Kaiyan Shi , Andrew Bray , Adam Groce

Distance correlation is a new measure of dependence between random vectors. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but unlike the classical definition of correlation,…

统计理论 · 数学 2008-12-18 Gábor J. Székely , Maria L. Rizzo , Nail K. Bakirov

For testing two random vectors for independence, we consider testing whether the distance of one vector from a center point is independent from the distance of the other vector from a center point by a univariate test. In this paper we…

统计方法学 · 统计学 2016-03-11 Ruth Heller , Yair Heller

A new interpoint distance-based measure is proposed to identify the optimal number of clusters present in a data set. Designed in nonparametric approach, it is independent of the distribution of given data. Interpoint distances between the…

机器学习 · 计算机科学 2022-10-18 Soumita Modak

Distance correlation is a measure of dependence between two paired random vectors or matrices of arbitrary, not necessarily equal, dimensions. Unlike Pearson correlation, the population distance correlation coefficient is zero if and only…

统计方法学 · 统计学 2025-06-19 Kontemeniotis Nikolaos , Vargiakakis Rafail , Tsagris Michail

In general, randomness tests included in a test suite are not independent of each other. This renders it difficult to fix a rational criterion through the whole test suite with an explicit significance level. In this paper, we focus on the…

统计理论 · 数学 2019-08-21 Atsushi Iwasaki

Clustering is the technique to partition data according to their characteristics. Data that are similar in nature belong to the same cluster [1]. There are two types of evaluation methods to evaluate clustering quality. One is an external…

机器学习 · 计算机科学 2024-09-05 Anupriya Vysala , Joseph Gomes

Cluster analysis is a fundamental research issue in statistics and machine learning. In many modern clustering methods, we need to determine whether two subsets of samples come from the same cluster. Since these subsets are usually…

机器学习 · 计算机科学 2025-07-15 Xinying Liu , Lianyu Hu , Mudi Jiang , Simeng Zhang , Jun Lou , Zengyou He

From more critical tests for gravitational (G) hypotheses it has been proved that the relative properties of nonlocal (NL) bodies at rest with respect to an observer depend on the difference of G potential between bodies and observer. The G…

广义相对论与量子宇宙学 · 物理学 2007-05-23 R. A. Vera
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