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arXiv · 2001.00220

On the Limits of Topological Data Analysis for Statistical Inference

Siddharth Vishwanath·Kenji Fukumizu·Satoshi Kuriki·Bharath Sriperumbudur
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Abstract

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.

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Siddharth Vishwanath, Kenji Fukumizu, Satoshi Kuriki, Bharath Sriperumbudur. 2024-02-15. On the Limits of Topological Data Analysis for Statistical Inference. https://arxiv.org/abs/2001.00220

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