# Density Level Sets: Asymptotics, Inference, and Visualization

arXiv: https://arxiv.org/abs/1504.05438 · HTML: https://mlsanity.com/paper/1504.05438/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Apr 2015.

## Built on by (most cited first, 11 of 11)

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- [Boundary Estimation from Point Clouds: Algorithms, Guarantees and Applications](https://mlsanity.com/paper/2111.03217/) (2021)
- [Moving Up the Cluster Tree with the Gradient Flow](https://mlsanity.com/paper/2109.08362/) (2021)
- [Optimal subgroup selection](https://mlsanity.com/paper/2109.01077/) (2021)
- [Clustering by Hill-Climbing: Consistency Results](https://mlsanity.com/paper/2202.09023/) (2022)
- [An Asymptotic Equivalence between the Mean-Shift Algorithm and the Cluster Tree](https://mlsanity.com/paper/2111.10298/) (2021)
- [Balanced Hyperbolic Embeddings Are Natural Out-of-Distribution Detectors](https://mlsanity.com/paper/2506.10146/) (2025)
- [Bump hunting through density curvature features](https://mlsanity.com/paper/2208.00174/) (2022)
- [Learning Acceptance Regions for Many Classes with Anomaly Detection](https://mlsanity.com/paper/2209.09963/) (2022)

## Abstract (arXiv)

We derive asymptotic theory for the plug-in estimate for density level sets under Hausdoff loss. Based on the asymptotic theory, we propose two bootstrap confidence regions for level sets. The confidence regions can be used to perform tests for anomaly detection and clustering. We also introduce a technique to visualize high dimensional density level sets by combining mode clustering and multidimensional scaling.