Researchers propose a counterfactual explanation framework for deep two-sample testing that generates interpretable edits to show which data features drive statistical differences between groups. The method combines diffusion autoencoders with deep learning models to produce plausible sample transformations that reduce distributional discrepancies, validated on synthetic data and MRI cohorts.
This research addresses a critical interpretability gap in modern statistical testing. Classical two-sample tests struggle with high-dimensional structured data like images, and while recent deep learning approaches improve sensitivity, they provide no actionable insight into what features cause detected differences. The proposed counterfactual framework bridges this gap by generating minimal, plausible edits that transform observations from one group toward another while explicitly reducing the test statistic's measured discrepancy.
The technical contribution combines diffusion autoencoders with pretrained deep two-sample test models, optimizing maximum mean discrepancy in learned representation spaces. This approach grounds explanations in the same statistical framework that detected differences, ensuring internal consistency. Validation across synthetic 2D shapes and real MRI data demonstrates consistent increases in p-values for edited samples, indicating genuine distributional shifts.
For scientific practitioners, this work transforms black-box statistical testing into an interpretable tool. Researchers analyzing medical imaging, genomic data, or other high-dimensional domains can now understand which specific features distinguish cohorts. The MRI results showing localized anatomical changes consistent with known differences validate the method's biological plausibility.
The framework's importance extends beyond statistics into machine learning interpretability broadly. As deep learning models drive decision-making in healthcare, finance, and other critical domains, methods that explain model behavior become increasingly essential. Future applications could extend counterfactual explanations to other statistical tests and multimodal data, strengthening the interpretability-performance tradeoff fundamental to responsible AI deployment.
- →Counterfactual explanations make deep two-sample tests interpretable by showing which features drive detected group differences
- →The method combines diffusion autoencoders with deep learning models to generate minimal, plausible transformations
- →Validation on MRI data reveals localized anatomical changes consistent with known cohort differences
- →Results demonstrate increased p-values for edited samples, confirming genuine distributional shifts toward target groups
- →This work advances machine learning interpretability in high-dimensional scientific applications