# Faster independent component analysis by preconditioning with Hessian approximations

arXiv: https://arxiv.org/abs/1706.08171 · HTML: https://mlsanity.com/paper/1706.08171/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jun 2017.

## Built on by (most cited first, 16 of 16)

- [Independent mechanism analysis, a new concept?](https://mlsanity.com/paper/2106.05200/) (2021)
- [Orthogonal Directions Constrained Gradient Method: from non-linear equality constraints to Stiefel manifold](https://mlsanity.com/paper/2303.09261/) (2023)
- [Evaluating the structure of cognitive tasks with transfer learning](https://mlsanity.com/paper/2308.02408/) (2023)
- [Shared Independent Component Analysis for Multi-Subject Neuroimaging](https://mlsanity.com/paper/2110.13502/) (2021)
- [ICA Lens: Interpreting Language Models Without Training Another Dictionary](https://mlsanity.com/paper/2606.11722/) (2026)
- [MultiView Independent Component Analysis with Delays](https://mlsanity.com/paper/2312.00484/) (2023)
- [Contrast-Free ICA and Causal Inference via Wasserstein Distances to the Gaussian](https://mlsanity.com/paper/2607.12832/) (2026)
- [Adaptive Multi-View ICA: Estimation of noise levels for optimal inference](https://mlsanity.com/paper/2102.10964/) (2021)
- [Second-order Approximation of Minimum Discrimination Information in Independent Component Analysis](https://mlsanity.com/paper/2111.15060/) (2021)
- [Boosting Independent Component Analysis](https://mlsanity.com/paper/2112.06920/) (2021)
- [MVICAD2: Multi-View Independent Component Analysis with Delays and Dilations](https://mlsanity.com/paper/2501.07426/) (2025)
- [Beyond Correlation: Learning Supervised, Sample-Distinct, and Eigenimage-Interpretable Representations](https://mlsanity.com/paper/2507.21136/) (2025)
- [Independent Component Discovery in Temporal Count Data](https://mlsanity.com/paper/2601.21696/) (2026)
- [Linear Independent Component Analysis via Optimal Transport](https://mlsanity.com/paper/2607.14081/) (2026)
- [AMICA-Python: Adaptive Mixture Independent Component Analysis with Anderson Acceleration](https://mlsanity.com/paper/2607.18568/) (2026)
- [Best Practices in EEG Analysis: Preprocessing, Modeling, and Machine Learning](https://mlsanity.com/paper/2609.36609/) (2026)

## Abstract (arXiv)

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.