论文标题
关于统计推断的拓扑数据分析的限制
On the Limits of Topological Data Analysis for Statistical Inference
论文作者
论文摘要
拓扑数据分析已成为一种有力的工具，用于提取数据作为多分辨率摘要统计量的指标，几何和拓扑特征，并在数据引起的多个领域中找到了应用程序。在本文中，我们通过统计推断的角度研究了拓扑摘要统计数据的使用。我们研究了\ textIt {有效统计推论}的必要条件，使用{拓扑摘要统计}。此外，我们提供了模型的示例，这些模型证明了有关拓扑摘要的不变性。
Topological data analysis has emerged as a powerful tool for extracting the metric, geometric and topological features underlying the data as a multi-resolution summary statistic, and has found applications in several areas where data arises from complex sources. In this paper, we examine the use of topological summary statistics through the lens of statistical inference. We investigate necessary and sufficient conditions under which \textit{valid statistical inference} is possible using {topological summary statistics}. Additionally, we provide examples of models that demonstrate invariance with respect to topological summaries.
