Independent mechanism analysis, a new concept?

TL;DR

This paper introduces independent mechanism analysis, a novel approach inspired by causality principles, to address nonidentifiability in nonlinear blind source separation, providing both theoretical insights and empirical validation.

Contribution

It proposes a new framework called independent mechanism analysis that leverages causal independence assumptions to improve identifiability in nonlinear source separation.

Findings

Circumvents nonidentifiability in nonlinear blind source separation

Provides theoretical guarantees for the proposed method

Demonstrates empirical effectiveness through experiments

Abstract

Independent component analysis provides a principled framework for unsupervised representation learning, with solid theory on the identifiability of the latent code that generated the data, given only observations of mixtures thereof. Unfortunately, when the mixing is nonlinear, the model is provably nonidentifiable, since statistical independence alone does not sufficiently constrain the problem. Identifiability can be recovered in settings where additional, typically observed variables are included in the generative process. We investigate an alternative path and consider instead including assumptions reflecting the principle of independent causal mechanisms exploited in the field of causality. Specifically, our approach is motivated by thinking of each source as independently influencing the mixing process. This gives rise to a framework which we term independent mechanism analysis. We provide theoretical and empirical evidence that our approach circumvents a number of nonidentifiability issues arising in nonlinear blind source separation.