# Confidence sets for persistence diagrams

arXiv: https://arxiv.org/abs/1303.7117 · HTML: https://mlsanity.com/paper/1303.7117/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Mar 2013.

## Built on by (most cited first, 17 of 17)

- [Topological Detection of Trojaned Neural Networks](https://mlsanity.com/paper/2106.06469/) (2021)
- [TopP&R: Robust Support Estimation Approach for Evaluating Fidelity and Diversity in Generative Models](https://mlsanity.com/paper/2306.08013/) (2023)
- [Improving Metric Dimensionality Reduction with Distributed Topology](https://mlsanity.com/paper/2106.07613/) (2021)
- [Cycle Registration in Persistent Homology with Applications in Topological Bootstrap](https://mlsanity.com/paper/2101.00698/) (2021)
- [A Random Persistence Diagram Generator](https://mlsanity.com/paper/2104.07737/) (2021)
- [Augmenting Molecular Deep Generative Models with Topological Data Analysis Representations](https://mlsanity.com/paper/2106.04464/) (2021)
- [Hierarchical and Density-based Causal Clustering](https://mlsanity.com/paper/2411.01250/) (2024)
- [Topology Applied to Machine Learning: From Global to Local](https://mlsanity.com/paper/2103.05796/) (2021)
- [Topology-Preserving Dimensionality Reduction via Interleaving Optimization](https://mlsanity.com/paper/2201.13012/) (2022)
- [A Topology-Attention ConvLSTM Network and Its Application to EM Images](https://mlsanity.com/paper/2202.03430/) (2022)
- [A distribution-guided Mapper algorithm](https://mlsanity.com/paper/2401.12237/) (2024)
- [Stability for Inference with Persistent Homology Rank Functions](https://mlsanity.com/paper/2307.02904/) (2023)
- [Topological data analysis of human vowels: Persistent homologies across representation spaces](https://mlsanity.com/paper/2310.06508/) (2023)
- [Stronger Coreset Bounds for Kernel Density Estimators via Chaining](https://mlsanity.com/paper/2310.08548/) (2023)
- [Topology of Out-of-Distribution Examples in Deep Neural Networks](https://mlsanity.com/paper/2501.12522/) (2025)
- [Improved Modeling of Persistence Diagram](https://mlsanity.com/paper/2205.10907/) (2022)
- [Topology Structure Optimization of Reservoirs Using GLMY Homology](https://mlsanity.com/paper/2509.11612/) (2025)

## 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.