# Independent Component Analysis by Robust Distance Correlation

arXiv: https://arxiv.org/abs/2505.09425 · HTML: https://mlsanity.com/paper/2505.09425/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 59 references that are in the map.
- First posted on arXiv 14 May 2025.

## Builds on (most cited first, 10 of 10)

- [Independent Component Analysis via Distance Covariance](https://mlsanity.com/paper/1306.4911/) (2013)
- [Model-Based Derivative-Free Optimization Methods and Software](https://mlsanity.com/paper/2210.12018/) (2022)
- [Robustifying Independent Component Analysis by Adjusting for Group-Wise Stationary Noise](https://mlsanity.com/paper/1806.01094/) (2018)
- [Challenges of cellwise outliers](https://mlsanity.com/paper/2302.02156/) (2023)
- [Generalizing Distance Covariance to Measure and Test Multivariate Mutual Dependence](https://mlsanity.com/paper/1709.02532/) (2017)
- [A Pseudo-Euclidean Iteration for Optimal Recovery in Noisy ICA](https://mlsanity.com/paper/1502.04148/) (2015)
- [Robust Sparse Blind Source Separation](https://mlsanity.com/paper/1507.02216/) (2015)
- [A Robustness Analysis of Blind Source Separation](https://mlsanity.com/paper/2303.10104/) (2023)
- [Robust Distance Covariance](https://mlsanity.com/paper/2403.03722/) (2024)
- [RobPy: a Python Package for Robust Statistical Methods](https://mlsanity.com/paper/2411.01954/) (2024)

## Abstract (arXiv)

Independent component analysis (ICA) is a powerful tool for decomposing a multivariate signal or distribution into fully independent sources, not just uncorrelated ones. Unfortunately, most approaches to ICA are not robust against outliers. Here we propose a robust ICA method called RICA, which estimates the components by minimizing a robust measure of dependence between multivariate random variables. The dependence measure used is the distance correlation (dCor). In order to make it more robust we first apply a new transformation called the bowl transform, which is bounded, one-to-one, continuous, and maps far outliers to points close to the origin. This preserves the crucial property that a zero dCor implies independence. RICA estimates the independent sources sequentially, by looking for the component that has the smallest dCor with the remainder. RICA is strongly consistent and has the usual parametric rate of convergence. Its robustness is investigated by a simulation study, in which it generally outperforms its competitors. The method is illustrated on three applications, including the well-known cocktail party problem.