FastICA with Learned Scores from the Empirical Characteristic Function

TL;DR

This paper introduces a method to improve FastICA by learning the nonlinear function directly from data, maintaining efficiency and robustness across various source distributions.

Contribution

It proposes a data-driven approach to estimate the nonlinear function in FastICA, eliminating the need for manual guessing and enhancing performance.

Findings

Separation error remains close to optimal across different source types.

Method retains FastICA-like runtime efficiency.

Robustness to heavy-tailed and discrete sources is improved.

Abstract

Independent component analysis (ICA) estimates a demixing matrix that can recover statistically independent sources from linear mixtures. FastICA is a popular ICA algorithm due to its efficiency, but its performance strongly depends on a user-chosen nonlinear function matched to the source distribution. When the source distribution is unknown, this function must be guessed at, and incorrect guesses can lead to significant drops in performance. We remove the need to guess by estimating a suitable function directly from the observed data. Our experiments show that the separation error stays close to the best fixed choice across synthetic mixtures comprising heavy-tailed or discrete sources while retaining a FastICA-like runtime.