Counterfactual Explanations for Deep Two-Sample Testing
A team of researchers has introduced a method that generates counterfactual explanations for deep two-sample tests, producing sample-level edits that reveal which data features drive statistical differences between groups. The framework combines a diffusion autoencoder with a pretrained deep two-sample test model, optimizing a maximum mean discrepancy (MMD) objective to create minimal, plausible edits. The approach offers a way to make powerful but opaque deep learning-based statistical tests more interpretable, with demonstrated applications in MRI neuroimaging.
Deep two-sample tests have improved upon classical statistical methods for detecting distributional differences in high-dimensional data such as images, but they have offered little insight into what features actually drive those differences. The proposed framework addresses this interpretability gap by generating counterfactual edits — minimal modifications to samples from a source group that move them statistically closer to a target group. The method pairs a diffusion autoencoder with a pretrained deep two-sample test model and optimizes in the test model's representation space using a maximum mean discrepancy objective. Effectiveness is measured by increases in two-sample p-values after editing, indicating the modified source samples are statistically more similar to the target distribution. Minimality of edits is assessed using the LPIPS perceptual similarity metric to ensure changes remain close to the originals. The method was validated on synthetic 2D shape datasets and two MRI cohorts, where localized anatomical changes produced by the framework were consistent with known biological differences between groups. The work represents a step toward making deep statistical testing not only sensitive but also scientifically interpretable.
What's missing
The study does not report results on datasets beyond 2D synthetic shapes and MRI, leaving open questions about generalizability to other high-dimensional domains such as genomics or natural images. It is also unclear whether the counterfactual edits are robust to different choices of pretrained test model or diffusion autoencoder architecture. The paper has not yet undergone formal peer review, as it is a preprint.
What different sources said
- arXiv cs.AICenter
Counterfactual Explanations for Deep Two-Sample Testing
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