Change Point Analysis of Multivariate Data: Using Multivariate Rank-based Distribution-free Nonparametric Testing via Measure Transportation with Applications in Tumor Microarrays and Dementia
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基于测度运输多元秩的分布无关非参数变点分析
- 研究问题
- 对于分布形式和变点数量均未知的多变量时间有序观测，如何尽量减少参数假设，同时估计多个变点的数量与位置？
- 方法与思路
- 作者利用测度运输定义多元秩，构造零假设下分布无关的非参数检验并形成变点算法，展示肿瘤、脑电及认知轨迹应用。
- 材料陈述的贡献
- 摘要称给出算法理论性质及变点数量、位置可近似估计的条件，并报告算法已实现于R包recp，提供使用说明。
- 阅读关注点
- 应核对多元秩的构造、分布无关性所需条件、序列依赖处理，以及分布改变与认知轨迹变化速率之间的解释关系。
- 阅读边界
- 这是 arXiv 预印本，同行评审与期刊接收均未核实；摘要未列出理论条件和误差界，分布无关表述不能理解为无需任何假设。
原文摘要
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.