2023/03/31 by Arnab Auddy, Ming Yuan, Auddy, Arnab +1 · 5 citations
Computer Science · Engineering · #62H12 #62H25 #Blind Source Separation Techniques #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Machine Learning and Algorithms #Methodology (stat.ME) #Sparse and Compressive Sensing Techniques #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2303.18156
openalex publication_date 2023/03/31 · openalex created_date 2023/04/06 · openalex updated_date 2026/07/28
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.