Unsupervised Representation Learning - an Invariant Risk Minimization Perspective

TL;DR

This paper introduces an unsupervised framework for invariant risk minimization that learns robust representations from unlabeled data by aligning feature distributions, using methods like PICA and VIAE, and demonstrates effectiveness on synthetic and real datasets.

Contribution

It extends IRM to unlabeled data settings by redefining invariance through feature distribution alignment and introduces two novel methods, PICA and VIAE.

Findings

Effective in capturing invariant structures

Generalizes across environments without labels

Works on synthetic and real datasets

Abstract

We propose a novel unsupervised framework for \emph{Invariant Risk Minimization} (IRM), extending the concept of invariance to settings where labels are unavailable. Traditional IRM methods rely on labeled data to learn representations that are robust to distributional shifts across environments. In contrast, our approach redefines invariance through feature distribution alignment, enabling robust representation learning from unlabeled data. We introduce two methods within this framework: Principal Invariant Component Analysis (PICA), a linear method that extracts invariant directions under Gaussian assumptions, and Variational Invariant Autoencoder (VIAE), a deep generative model that separates environment-invariant and environment-dependent latent factors. Our approach is based on a novel ``unsupervised'' structural causal model and supports environment-conditioned sample-generation and intervention. Empirical evaluations on synthetic dataset, modified versions of MNIST, and CelebA demonstrate the effectiveness of our methods in capturing invariant structure, preserving relevant information, and generalizing across environments without access to labels.