Massive parallelization of projection-based depths

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.