# Robust contrastive learning and nonlinear ICA in the presence of outliers

arXiv: https://arxiv.org/abs/1911.00265 · HTML: https://mlsanity.com/paper/1911.00265/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Nov 2019.

## Built on by (most cited first, 3 of 3)

- [Identifiability of latent-variable and structural-equation models: from linear to nonlinear](https://mlsanity.com/paper/2302.02672/) (2023)
- [Representation learning for maximization of MI, nonlinear ICA and nonlinear subspaces with robust density ratio estimation](https://mlsanity.com/paper/2101.02083/) (2021)
- [Universal hidden monotonic trend estimation with contrastive learning](https://mlsanity.com/paper/2210.09817/) (2022)

## Abstract (arXiv)

Nonlinear independent component analysis (ICA) is a general framework for unsupervised representation learning, and aimed at recovering the latent variables in data. Recent practical methods perform nonlinear ICA by solving a series of classification problems based on logistic regression. However, it is well-known that logistic regression is vulnerable to outliers, and thus the performance can be strongly weakened by outliers. In this paper, we first theoretically analyze nonlinear ICA models in the presence of outliers. Our analysis implies that estimation in nonlinear ICA can be seriously hampered when outliers exist on the tails of the (noncontaminated) target density, which happens in a typical case of contamination by outliers. We develop two robust nonlinear ICA methods based on the γ-divergence, which is a robust alternative to the KL-divergence in logistic regression. The proposed methods are shown to have desired robustness properties in the context of nonlinear ICA. We also experimentally demonstrate that the proposed methods are very robust and outperform existing methods in the presence of outliers. Finally, the proposed method is applied to ICA-based causal discovery and shown to find a plausible causal relationship on fMRI data.