# On Generalization and Computation of Tukey's Depth: Part I

arXiv: https://arxiv.org/abs/2112.08475 · HTML: https://mlsanity.com/paper/2112.08475/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Dec 2021.

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

- [Anomaly detection using data depth: multivariate case](https://mlsanity.com/paper/2210.02851/) (2022)

## Abstract (arXiv)

Tukey's depth offers a powerful tool for nonparametric inference and estimation, but also encounters serious computational and methodological difficulties in modern statistical data analysis. This paper studies how to generalize and compute Tukey-type depths in multi-dimensions. A general framework of influence-driven polished subspace depth, which emphasizes the importance of the underlying influence space and discrepancy measure, is introduced. The new matrix formulation enables us to utilize state-of-the-art optimization techniques to develop scalable algorithms with implementation ease and guaranteed fast convergence. In particular, half-space depth as well as regression depth can now be computed much faster than previously possible, with the support from extensive experiments. A companion paper is also offered to the reader in the same issue of this journal.