2020/01/01 by Siddharth Vishwanath, Vishwanath, Siddharth, Kenji Fukumizu +5
Computer Science · Mathematics · #55N31 #62F30 #62R40 #Algebraic Topology (math.AT) #Algorithm #Artificial intelligence #Combinatorics #Computer science #Data mining #FOS: Mathematics #Inference #Mathematics #Metric (unit) #Probability (math.PR) #Pure mathematics #Statistic #Statistical inference #Statistics #Statistics Theory (math.ST) #Topological and Geometric Data Analysis #Topological data analysis #Topological space #Topology (electrical circuits)
paper · pdf · doi:10.48550/arxiv.2001.00220
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2020/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 valid statistical inference is possible using topological summary statistics. Additionally, we provide examples of models that demonstrate invariance with respect to topological summaries.