Massive parallelization of projection-based depths

TL;DR

This paper presents a new parallel algorithm for computing projection-based data depths, achieving significant speedups on GPUs and enabling large-scale high-dimensional data analysis.

Contribution

It introduces a novel parallelization framework using Refined Random Search for projection depths, significantly improving computational efficiency.

Findings

Speedup of up to 7,000 times on GPUs

Improved accuracy and reduced runtime on synthetic data

Availability of implementation in Python library data-depth

Abstract

This article introduces a novel methodology for the massive parallelization of projection-based depths, addressing the computational challenges of data depth in high-dimensional spaces. We propose an algorithmic framework based on Refined Random Search (RRS) and demonstrate significant speedup (up to 7,000 times faster) on GPUs. Empirical results on synthetic data show improved precision and reduced runtime, making the method suitable for large-scale applications. The RRS algorithm (and other depth functions) are available in the Python-library data-depth (https://data-depth.github.io/) with ready-to-use tools to implement and to build upon this work.