Unsupervised Invariant Risk Minimization

We propose a novel unsupervised framework for 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 disentangles environment-invariant and environment-dependent latent factors. Our approach is grounded in a novel class of unsupervised structural causal models and supports environment-conditioned sample generation and transfer. Empirical evaluations on synthetic benchmarks, 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.