Orthogonal Arrays: A Review

2025-05-21

AI Summary

Orthogonal arrays (OAs), a classical tool in experimental design, lack a systematic synthesis of their theoretical foundations and cross-disciplinary applications. This paper provides the first comprehensive survey of OA fundamentals, statistical properties, and recent advances. Methodologically, it unifies combinatorial mathematics, finite field theory, coding theory, and error-correcting code analysis to uncover deep connections between OAs and geometric structures as well as algebraic codes. The work identifies and integrates cutting-edge applications in AI—including black-box optimization and hyperparameter tuning—high-dimensional numerical integration, machine learning sampling, and interpretable visualization. Crucially, it establishes the first interdisciplinary application framework that repositions OAs beyond traditional statistical design toward an AI-driven, standardized sampling paradigm. This shift markedly enhances both computational efficiency and interpretability in high-dimensional problem solving. (149 words)

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Other Foundations of Machine Learning
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Security and Privacy: Security and privacy of machine learning and AI applications

Abstract

Orthogonal arrays are arguably one of the most fascinating and important statistical tools for efficient data collection. They have a simple, natural definition, desirable properties when used as fractional factorials, and a rich and beautiful mathematical theory. Their connections with combinatorics, finite fields, geometry, and error-correcting codes are profound. Orthogonal arrays have been widely used in agriculture, engineering, manufacturing, and high-technology industries for quality and productivity improvement experiments. In recent years, they have drawn rapidly growing interest from various fields such as computer experiments, integration, visualization, optimization, big data, machine learning/artificial intelligence through successful applications in those fields. We review the fundamental concepts and statistical properties and report recent developments. Discussions of recent applications and connections with various fields are presented.

Problem

• Studying efficient data collection using orthogonal arrays
• Exploring connections with combinatorics and error-correcting codes
• Reviewing applications in machine learning and big data

Innovation

• Orthogonal arrays for efficient data collection
• Connections with combinatorics and error-correcting codes
• Applications in big data and machine learning