On the Limits of Topological Data Analysis for Statistical Inference
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2020
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916125274537984 |
|---|---|
| author | Vishwanath, Siddharth Fukumizu, Kenji Kuriki, Satoshi Sriperumbudur, Bharath |
| author_facet | Vishwanath, Siddharth Fukumizu, Kenji Kuriki, Satoshi Sriperumbudur, Bharath |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2001_00220 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On the Limits of Topological Data Analysis for Statistical Inference Vishwanath, Siddharth Fukumizu, Kenji Kuriki, Satoshi Sriperumbudur, Bharath Probability Algebraic Topology Statistics Theory 62F30, 55N31, 62R40 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. |
| title | On the Limits of Topological Data Analysis for Statistical Inference |
| topic | Probability Algebraic Topology Statistics Theory 62F30, 55N31, 62R40 |
| url | https://arxiv.org/abs/2001.00220 |