# Faster independent component analysis by preconditioning with Hessian approximations

## TL;DR

This paper introduces Picard, a preconditioned L-BFGS algorithm for ICA that uses Hessian approximations, significantly improving speed and accuracy on large, real-world datasets.

## Contribution

The paper presents a novel preconditioning approach for ICA using Hessian approximations, enhancing convergence speed and robustness on real data.

## Key findings

- Picard outperforms existing ICA algorithms in speed and accuracy.
- The method is particularly effective on real datasets where ICA assumptions are relaxed.
- Extensive numerical experiments validate the superiority of the proposed approach.

## Abstract

Independent Component Analysis (ICA) is a technique for unsupervised exploration of multi-channel data that is widely used in observational sciences. In its classic form, ICA relies on modeling the data as linear mixtures of non-Gaussian independent sources. The maximization of the corresponding likelihood is a challenging problem if it has to be completed quickly and accurately on large sets of real data. We introduce the Preconditioned ICA for Real Data (Picard) algorithm, which is a relative L-BFGS algorithm preconditioned with sparse Hessian approximations. Extensive numerical comparisons to several algorithms of the same class demonstrate the superior performance of the proposed technique, especially on real data, for which the ICA model does not necessarily hold.