# Non-Independent Components Analysis

arXiv: https://arxiv.org/abs/2206.13668 · HTML: https://mlsanity.com/paper/2206.13668/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jun 2022.

## Built on by (most cited first, 3 of 3)

- [Unpaired Multi-Domain Causal Representation Learning](https://mlsanity.com/paper/2302.00993/) (2023)
- [Parameter identification in linear non-Gaussian causal models under general confounding](https://mlsanity.com/paper/2405.20856/) (2024)
- [Beyond independent component analysis: identifiability and algorithms](https://mlsanity.com/paper/2510.07525/) (2025)

## Abstract (arXiv)

A seminal result in the ICA literature states that for AY = varepsilon, if the components of varepsilon are independent and at most one is Gaussian, then A is identified up to sign and permutation of its rows (Comon, 1994). In this paper we study to which extent the independence assumption can be relaxed by replacing it with restrictions on higher order moment or cumulant tensors of varepsilon. We document new conditions that establish identification for several non-independent component models, e.g. common variance models, and propose efficient estimation methods based on the identification results. We show that in situations where independence cannot be assumed the efficiency gains can be significant relative to methods that rely on independence.