mlsanityData to 7 Oct 2026

Confidence sets for persistence diagrams

arXiv 1303.7117 ↗First posted 28 Mar 2013math.ST cs.CG cs.LGcited by 17

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Abstract (arXiv)

Persistent homology is a method for probing topological properties of point clouds and functions. The method involves tracking the birth and death of topological features (2000) as one varies a tuning parameter. Features with short lifetimes are informally considered to be "topological noise," and those with a long lifetime are considered to be "topological signal." In this paper, we bring some statistical ideas to persistent homology. In particular, we derive confidence sets that allow us to separate topological signal from topological noise.

Key facts. Cited by 17 papers in the map (data through 7 Oct 2026). First posted on arXiv 28 Mar 2013.

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Citing papers per year: 2021: 6; 2022: 3; 2023: 4; 2024: 2; 2025: 2.

17 papers.

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  1. 2021Topological Detection of Trojaned Neural Networkscited by 34
  2. 2023TopP&R: Robust Support Estimation Approach for Evaluating Fidelity and Diversity in Generative Modelscited by 13
  3. 2021Improving Metric Dimensionality Reduction with Distributed Topologycited by 10
  4. 2021Cycle Registration in Persistent Homology with Applications in Topological Bootstrapcited by 8
  5. 2021A Random Persistence Diagram Generatorcited by 6
  6. 2021Augmenting Molecular Deep Generative Models with Topological Data Analysis Representationscited by 6
  7. 2024Hierarchical and Density-based Causal Clusteringcited by 6
  8. 2021Topology Applied to Machine Learning: From Global to Localcited by 4
  9. 2022Topology-Preserving Dimensionality Reduction via Interleaving Optimizationcited by 3
  10. 2022A Topology-Attention ConvLSTM Network and Its Application to EM Imagescited by 2
  11. 2024A distribution-guided Mapper algorithmcited by 2
  12. 2023Stability for Inference with Persistent Homology Rank Functionscited by 1
5 more
  1. 2023Topological data analysis of human vowels: Persistent homologies across representation spacescited by 1
  2. 2023Stronger Coreset Bounds for Kernel Density Estimators via Chainingcited by 1
  3. 2025Topology of Out-of-Distribution Examples in Deep Neural Networkscited by 1
  4. 2022Improved Modeling of Persistence Diagramcited by 0
  5. 2025Topology Structure Optimization of Reservoirs Using GLMY Homologycited by 0