A method for sparse and robust independent component analysis

TL;DR

This paper introduces SICS, a new method for sparse and robust independent component analysis that combines invariant coordinate selection with LASSO penalties and robust scatter matrices, enhancing sparsity and robustness.

Contribution

The paper proposes SICS, a novel approach integrating LASSO and robust scatter matrices into ICS for improved sparse and robust ICA, with theoretical guarantees and practical tools.

Findings

SICS effectively identifies sparse independent components in simulations.

The method demonstrates robustness and sparsity in constructing causal graphs.

A graphical tool aids in selecting optimal sparsity levels.

Abstract

This work presents sparse invariant coordinate selection, SICS, a new method for sparse and robust independent component analysis. SICS is based on classical invariant coordinate selection, which is presented in such a form that a LASSO-type penalty can be applied to promote sparsity. Robustness is achieved by using robust scatter matrices. In the first part of the paper, the background and building blocks: scatter matrices, measures of robustness, ICS and independent component analysis, are carefully introduced. Then the proposed new method and its algorithm are derived and presented. This part also includes consistency and breakdown point results for a general case of sparse ICS-like methods. The performance of SICS in identifying sparse independent component loadings is investigated with multiple simulations. The method is illustrated with an example in constructing sparse causal graphs and we also propose a graphical tool for selecting the appropriate sparsity level in SICS.