Massive parallelization of projection-based depths

2025-06-09

AI Summary

Scalable computation of projection depth for high-dimensional data remains challenging due to inherent computational intractability and poor parallelizability of classical algorithms. To address this, we propose a GPU-accelerated framework based on Refined Random Search (RRS), the first application of RRS to projection depth estimation. Our method enables plug-and-play parallelization for arbitrary projection depth functions, overcoming both time complexity bottlenecks and memory constraints in high dimensions. Leveraging highly optimized CUDA kernels and a Python high-performance wrapper—integrated into the open-source library *data-depth*—our implementation achieves up to 7,000× speedup on synthetic benchmarks while significantly improving estimation accuracy and robustness. This work delivers the first scalable, general-purpose, and open-source massively parallel solution for high-dimensional statistical depth analysis.

Technology Category

• Computer Vision: 3D Computer Vision
• Search and Optimization: Non-convex Optimization
• Machine Learning: Learning with Manifolds

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Security and Privacy: Large-scale security measurements

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.

Problem

• Address computational challenges in high-dimensional data depth
• Propose Refined Random Search for massive parallelization
• Achieve significant speedup and precision on GPUs

Innovation

• Massive parallelization of projection-based depths
• Refined Random Search (RRS) algorithmic framework
• GPU acceleration for significant speedup