Equivariance Allows Handling Multiple Nuisance Variables When Analyzing Pooled Neuroimaging Datasets

TL;DR

This paper introduces an equivariant representation learning approach combined with causal inference principles to effectively analyze pooled neuroimaging datasets affected by multiple nuisance variables, improving statistical power.

Contribution

The paper presents a novel method that leverages equivariant neural networks and causal inference to handle multiple nuisance variables in pooled datasets, surpassing invariant methods.

Findings

Enables analysis with multiple nuisance variables.

Reduces data loss by avoiding sample removal.

Improves statistical power in neuroimaging studies.

Abstract

Pooling multiple neuroimaging datasets across institutions often enables improvements in statistical power when evaluating associations (e.g., between risk factors and disease outcomes) that may otherwise be too weak to detect. When there is only a {\em single} source of variability (e.g., different scanners), domain adaptation and matching the distributions of representations may suffice in many scenarios. But in the presence of {\em more than one} nuisance variable which concurrently influence the measurements, pooling datasets poses unique challenges, e.g., variations in the data can come from both the acquisition method as well as the demographics of participants (gender, age). Invariant representation learning, by itself, is ill-suited to fully model the data generation process. In this paper, we show how bringing recent results on equivariant representation learning (for studying symmetries in neural networks) instantiated on structured spaces together with simple use of classical results on causal inference provides an effective practical solution. In particular, we demonstrate how our model allows dealing with more than one nuisance variable under some assumptions and can enable analysis of pooled scientific datasets in scenarios that would otherwise entail removing a large portion of the samples.