# Independent Vector Analysis: Identification Conditions and Performance Bounds

arXiv: https://arxiv.org/abs/1303.7474 · HTML: https://mlsanity.com/paper/1303.7474/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Mar 2013.

## Built on by (most cited first, 7 of 7)

- [Unpaired Multi-Domain Causal Representation Learning](https://mlsanity.com/paper/2302.00993/) (2023)
- [Multi-View Independent Component Analysis with Shared and Individual Sources](https://mlsanity.com/paper/2210.02083/) (2022)
- [Shared Independent Component Analysis for Multi-Subject Neuroimaging](https://mlsanity.com/paper/2110.13502/) (2021)
- [Identifiable Shared Component Analysis of Unpaired Multimodal Mixtures](https://mlsanity.com/paper/2409.19422/) (2024)
- [Multi-View Causal Discovery without Non-Gaussianity: Identifiability and Algorithms](https://mlsanity.com/paper/2502.20115/) (2025)
- [A 1/R Law for Kurtosis Contrast in Balanced Mixtures](https://mlsanity.com/paper/2602.22334/) (2026)
- [Reservoir Subspace Injection for Online ICA under Top-n Whitening](https://mlsanity.com/paper/2603.02178/) (2026)

## Abstract (arXiv)

Recently, an extension of independent component analysis (ICA) from one to multiple datasets, termed independent vector analysis (IVA), has been the subject of significant research interest. IVA has also been shown to be a generalization of Hotelling's canonical correlation analysis. In this paper, we provide the identification conditions for a general IVA formulation, which accounts for linear, nonlinear, and sample-to-sample dependencies. The identification conditions are a generalization of previous results for ICA and for IVA when samples are independently and identically distributed. Furthermore, a principal aim of IVA is the identification of dependent sources between datasets. Thus, we provide the additional conditions for when the arbitrary ordering of the sources within each dataset is common. Performance bounds in terms of the Cramer-Rao lower bound are also provided for the demixing matrices and interference to source ratio. The performance of two IVA algorithms are compared to the theoretical bounds.