Probing the Robustness of Independent Mechanism Analysis for Representation Learning

TL;DR

This paper investigates the robustness of Independent Mechanism Analysis (IMA) in representation learning, demonstrating its effectiveness even when assumptions are violated, and contrasting it with standard regularization methods.

Contribution

It provides the first systematic analysis of IMA's robustness to assumption violations, showing its advantages over standard regularizers in recovering true latent sources.

Findings

IMA regularization improves source recovery under assumption violations.

Standard regularizers do not perform as well as IMA in these scenarios.

Unregularized maximum likelihood often deviates from IMA principles.

Abstract

One aim of representation learning is to recover the original latent code that generated the data, a task which requires additional information or inductive biases. A recently proposed approach termed Independent Mechanism Analysis (IMA) postulates that each latent source should influence the observed mixtures independently, complementing standard nonlinear independent component analysis, and taking inspiration from the principle of independent causal mechanisms. While it was shown in theory and experiments that IMA helps recovering the true latents, the method's performance was so far only characterized when the modeling assumptions are exactly satisfied. Here, we test the method's robustness to violations of the underlying assumptions. We find that the benefits of IMA-based regularization for recovering the true sources extend to mixing functions with various degrees of violation of the IMA principle, while standard regularizers do not provide the same merits. Moreover, we show that unregularized maximum likelihood recovers mixing functions which systematically deviate from the IMA principle, and provide an argument elucidating the benefits of IMA-based regularization.