# Fast kernel half-space depth for data with non-convex supports

arXiv: https://arxiv.org/abs/2312.14136 · HTML: https://mlsanity.com/paper/2312.14136/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 38 references that are in the map.
- First posted on arXiv 21 Dec 2023.

## Builds on (most cited first, 3 of 3)

- [Anomaly Detection by Robust Statistics](https://mlsanity.com/paper/1707.09752/) (2017)
- [Choosing among notions of multivariate depth statistics](https://mlsanity.com/paper/2004.01927/) (2020)
- [Functional Anomaly Detection: a Benchmark Study](https://mlsanity.com/paper/2201.05115/) (2022)

## Built on by (most cited first, 1 of 1)

- [Data Depth as a Risk](https://mlsanity.com/paper/2507.08518/) (2025)

## Abstract (arXiv)

Data depth is a statistical function that generalizes order and quantiles to the multivariate setting and beyond, with applications spanning over descriptive and visual statistics, anomaly detection, testing, etc. The celebrated halfspace depth exploits data geometry via an optimization program to deliver properties of invariances, robustness, and non-parametricity. Nevertheless, it implicitly assumes convex data supports and requires exponential computational cost. To tackle distribution's multimodality, we extend the halfspace depth in a Reproducing Kernel Hilbert Space (RKHS). We show that the obtained depth is intuitive and establish its consistency with provable concentration bounds that allow for homogeneity testing. The proposed depth can be computed using manifold gradient making faster than halfspace depth by several orders of magnitude. The performance of our depth is demonstrated through numerical simulations as well as applications such as anomaly detection on real data and homogeneity testing.