多变量数据的变点分析：通过测量传输使用多变量基于秩的无分布非参数检验及其在肿瘤微阵列和痴呆中的应用
Change Point Analysis of Multivariate Data: Using Multivariate Rank-based Distribution-free Nonparametric Testing via Measure Transportation with Applications in Tumor Microarrays and Dementia
摘要：
在本文中，我提出了一个通用的算法，通过多变量分布自由的非参数检验的概念的基础上，由测量运输定义的秩的多个变点分析。多元秩和通常的一维秩都有一个重要的性质：它们都是分布自由的。这一发现允许在原假设下创建无分布的非参数检验。这种方法在各种领域的应用，在本文中，我实现了这种算法的微阵列数据集的个人膀胱肿瘤，ECoG快照癫痫患者，并在CASI分数的轨迹的背景下，教育水平和痴呆状态。每个变化点表示认知能力评分多年变化率的变化，表明存在临床前痴呆。在这里，我将估计一个多变量时序观测序列中的变点数量及其位置。本文将研究多个变点问题，在一个广泛的设置中，观察到的分布和数量的变化点是未指定的，而不是假设的时间序列观测遵循参数模型或有一个变点，因为在这一领域的许多作品假设。这里的目标是创建一个算法来检测变化点，同时尽可能少地对数据集进行假设。给出了这种新算法的理论性质以及估计变点的近似数目和位置的条件。该算法也已在GitHub上提供的R包recp中成功实现。本文的一个部分专门介绍此过程的执行以及recp包的使用。
英文摘要：
In this paper, I propose a general algorithm for multiple change point analysis via multivariate distribution-free nonparametric testing based on the concept of ranks that are defined by measure transportation. Multivariate ranks and the usual one-dimensional ranks both share an important property: they are both distribution-free. This finding allows for the creation of nonparametric tests that are distribution-free under the null hypothesis. This method has applications in a variety of fields, and in this paper I implement this algorithm to a microarray dataset for individuals with bladder tumors, an ECoG snapshot for a patient with epilepsy, and in the context of trajectories of CASI scores by education level and dementia status. Each change point denotes a shift in the rate of change of Cognitive Abilities score over years, indicating the existence of preclinical dementia. Here I will estimate the number of change points and each of their locations within a multivariate series of time-ordered observations. This paper will examine the multiple change point question in a broad setting in which the observed distributions and number of change points are unspecified, rather than assume the time series observations follow a parametric model or there is one change point, as many works in this area assume. The objective here is to create an algorithm for change point detection while making as few assumptions about the dataset as possible. Presented are the theoretical properties of this new algorithm and the conditions under which the approximate number of change points and their locations can be estimated. This algorithm has also been successfully implemented in the R package recp, which is available on GitHub. A section of this paper is dedicated to the execution of this procedure, as well as the use of the recp package.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
