# Equivariance Allows Handling Multiple Nuisance Variables When Analyzing Pooled Neuroimaging Datasets

arXiv: https://arxiv.org/abs/2203.15234 · HTML: https://mlsanity.com/paper/2203.15234/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 59 references that are in the map.
- First posted on arXiv 29 Mar 2022.

## Builds on (most cited first, 23 of 23)

- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Mitigating Unwanted Biases with Adversarial Learning](https://mlsanity.com/paper/1801.07593/) (2018)
- [Unified Deep Supervised Domain Adaptation and Generalization](https://mlsanity.com/paper/1709.10190/) (2017)
- [Empirical Risk Minimization under Fairness Constraints](https://mlsanity.com/paper/1802.08626/) (2018)
- [Domain Generalization using Causal Matching](https://mlsanity.com/paper/2006.07500/) (2020)
- [Towards Causal Representation Learning](https://mlsanity.com/paper/2102.11107/) (2021)
- [Causality matters in medical imaging](https://mlsanity.com/paper/1912.08142/) (2019)
- [Generalized Source-free Domain Adaptation](https://mlsanity.com/paper/2108.01614/) (2021)
- [Controllable Invariance through Adversarial Feature Learning](https://mlsanity.com/paper/1705.11122/) (2017)
- [Invariant Representations without Adversarial Training](https://mlsanity.com/paper/1805.09458/) (2018)
- [Simple, Robust and Optimal Ranking from Pairwise Comparisons](https://mlsanity.com/paper/1512.08949/) (2015)
- [Adaptive Methods for Real-World Domain Generalization](https://mlsanity.com/paper/2103.15796/) (2021)
- [Competitive Gradient Descent](https://mlsanity.com/paper/1905.12103/) (2019)
- [Patterns, predictions, and actions: A story about machine learning](https://mlsanity.com/paper/2102.05242/) (2021)
- [Alternating Minimization Converges Super-Linearly for Mixed Linear Regression](https://mlsanity.com/paper/2004.10914/) (2020)
- [Learning unbiased features](https://mlsanity.com/paper/1412.5244/) (2014)
- [Latent Variables on Spheres for Autoencoders in High Dimensions](https://mlsanity.com/paper/1912.10233/) (2019)
- [Variational Transport: A Convergent Particle-BasedAlgorithm for Distributional Optimization](https://mlsanity.com/paper/2012.11554/) (2020)
- [Learning Invariant Representations using Inverse Contrastive Loss](https://mlsanity.com/paper/2102.08343/) (2021)
- [When can Multi-Site Datasets be Pooled for Regression? Hypothesis Tests, ℓ2-consistency and Neuroscience Applications](https://mlsanity.com/paper/1709.00640/) (2017)

## Built on by (most cited first, 7 of 7)

- [On the Versatile Uses of Partial Distance Correlation in Deep Learning](https://mlsanity.com/paper/2207.09684/) (2022)
- [Pooling Image Datasets With Multiple Covariate Shift and Imbalance](https://mlsanity.com/paper/2403.02598/) (2024)
- [ManifoldGD: Training-Free Hierarchical Manifold Guidance for Diffusion-Based Dataset Distillation](https://mlsanity.com/paper/2602.23295/) (2026)
- [Is Exchangeability better than I.I.D to handle Data Distribution Shifts while Pooling Data for Data-scarce Medical image segmentation?](https://mlsanity.com/paper/2507.19575/) (2025)
- [Forget Less by Learning from Parents Through Hierarchical Relationships](https://mlsanity.com/paper/2601.01892/) (2026)
- [Beyond Pooling: Matching for Robust Generalization under Data Heterogeneity](https://mlsanity.com/paper/2602.07154/) (2026)
- [Attending to Routers Aids Indoor Wireless Localization](https://mlsanity.com/paper/2602.16762/) (2026)

## Abstract (arXiv)

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.