Independent vector analysis -- an introduction for statisticians

2025-06-19

AI Summary

This paper addresses the joint blind source separation (BSS) problem for multiple datasets sharing common latent source signals, a task formalized as independent vector analysis (IVA). Existing IVA methods suffer from weak statistical foundations, fragmented density assumptions, and inconsistent algorithmic prerequisites. Method: We systematically establish a rigorous statistical framework for IVA, clarifying its fundamental distinction from independent component analysis (ICA). Our framework encompasses real/complex domains and accommodates spherical symmetric, t-, and mixture-Gaussian multivariate densities. We propose a unified optimization paradigm grounded in maximum likelihood estimation, information-theoretic criteria, and iterative projection. Crucially, we characterize the statistical nature of cross-dataset dependence modeling, thereby unifying the theoretical underpinnings of existing algorithms. Contribution/Results: The work lays a solid foundation for asymptotic analysis, consistency proofs, and nonparametric extensions of IVA, advancing it from an engineering heuristic to a principled statistical modeling methodology.

Technology Category

• Machine Learning: Multi-instance/Multi-view Learning
• Intelligent Robots: State Estimation
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Data transparency and provenance

Abstract

Blind source separation (BSS), particularly independent component analysis (ICA), has been widely used in various fields of science such as biomedical signal processing to recover latent source signals from the observed mixture. While ICA is typically applied to individual datasets, many real-world applications share underlying sources across datasets. Independent vector analysis (IVA) extends ICA to jointly analyze multiple datasets by exploiting statistical dependencies across them. While various IVA methods have been presented in signal processing literature, the statistical properties of methods remains largely unexplored. This article introduces the IVA model, numerous density models used in IVA, and various classical IVA methods to statistics community highlighting the need for further theoretical developments.

Problem

• Extends ICA to analyze multiple datasets jointly
• Explores statistical dependencies across shared latent sources
• Investigates theoretical properties of IVA methods

Innovation

• Extends ICA to multiple datasets jointly
• Exploits statistical dependencies across datasets
• Introduces IVA model to statistics community