Faster independent component analysis by preconditioning with Hessian approximations
This work addresses the need for efficient ICA in observational sciences, offering an incremental improvement in speed and accuracy for processing large multi-channel datasets.
The paper tackles the challenge of performing fast and accurate independent component analysis (ICA) on large real datasets by introducing the Picard algorithm, which uses sparse Hessian approximations to precondition a relative L-BFGS method, resulting in superior performance compared to similar algorithms, especially on real data where the ICA model may not hold.
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.