LARGE-DIMENSIONAL INDEPENDENT COMPONENT ANALYSIS: STATISTICAL OPTIMALITY AND COMPUTATIONAL TRACTABILITY

• 成果类型: Article
• 署名作者: Auddy, Arnab; Yuan, Ming
• 署名单位: University System of Ohio; Ohio State University; Columbia University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/24-AOS2419
• 发表日期: 2025
• 页码: 477-505
• 关键词: blind separation; tensor decompositions; algorithms; mixture; bounds

摘要

In this paper, we investigate the optimal statistical performance and the impact of computational constraints for independent component analysis (ICA). Our goal is twofold. On the one hand, we characterize the precise role of dimensionality on sample complexity and statistical accuracy, and how computational consideration may affect them. In particular, we show that the optimal sample complexity is linear in dimensionality, and interestingly, the commonly used sample kurtosis-based approaches are necessarily suboptimal. However, the optimal sample complexity becomes quadratic, up to a logarithmic factor, in the dimension if we restrict ourselves to estimates that can be computed with low-degree polynomial algorithms. On the other hand, we develop computationally tractable estimates that attain both the optimal sample complexity and minimax optimal rates of convergence. We study the asymptotic properties of the proposed estimates and establish their asymptotic normality that can be readily used for statistical inferences. Our method is fairly easy to implement and numerical experiments are presented to further demonstrate its practical merits.