Independent vector analysis -- an introduction for statisticians

TL;DR

This paper introduces Independent Vector Analysis (IVA), extending ICA to jointly analyze multiple datasets by leveraging dependencies, and discusses its statistical properties and models for the statistics community.

Contribution

It provides an introduction to the IVA model, density models, and classical methods, emphasizing the need for further theoretical research in statistical properties.

Findings

Introduces the IVA model and its density functions

Highlights the gap in understanding IVA's statistical properties

Calls for further theoretical developments in IVA methods

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.