Robust Nonlinear ICA.pdf

Key Findings:

Nonlinear ICA is vulnerable to outliers, which can significantly degrade its performance.
A contaminated density model of sources is defined as a mixture of the target and outlier densities.
Theoretical analysis shows that estimation in nonlinear ICA can be seriously hampered when outliers exist on the tails of the target density.
Two robust nonlinear ICA methods are proposed, based on the γ-divergence, which has a favorable robustness property.
The proposed methods are theoretically shown to have desired robustness properties and are experimentally demonstrated to be more robust against outliers than existing methods.

Methodology:

Nonlinear ICA is formulated as a generative model for the data, with the goal of recovering the latent source components.
Logistic regression is used to solve the nonlinear ICA problem, but it is vulnerable to outliers.
The γ-divergence is used as a robust alternative to the KL-divergence in logistic regression.
The proposed methods are based on solving classification problems using the γ-divergence.

Applications:

The proposed robust nonlinear ICA method is applied to ICA-based causal discovery and demonstrates a plausible causal relationship on fMRI data.
Nonlinear ICA has potential applications in causal analysis, transfer learning, and self-supervised learning.

Conclusion:

The proposed robust nonlinear ICA methods are shown to be effective in the presence of outliers and have potential applications in various fields.
* The use of γ-divergence provides a favorable robustness property, making the proposed methods more robust against outliers than existing methods.