Towards Visually Explaining Statistical Tests with Applications in Biomedical Imaging

TL;DR

The work tackles the interpretability gap in deep two-sample tests by introducing an explainable framework that provides sample-level influence and feature-level gradient-based attributions for population differences in biomedical imaging. It formalizes explanations for statistical decisions, defines a sample-level influence score, and derives a gradient-based attribution method that yields spatial maps reflecting region- and sample-specific contributions to significance. The authors validate the approach on synthetic data and real imaging datasets (dSprites, ADNI MRI, EyePACS diabetic retinopathy), showing biologically meaningful and clinically plausible explanations that align with known disease patterns and biomarkers. This framework enables actionable, label-free population analysis in medical imaging, supporting tasks such as patient stratification, trial enrichment, quality control, and biomarker discovery, with code and supplementary materials provided.

Abstract

Deep neural two-sample tests have recently shown strong power for detecting distributional differences between groups, yet their black-box nature limits interpretability and practical adoption in biomedical analysis. Moreover, most existing post-hoc explainability methods rely on class labels, making them unsuitable for label-free statistical testing settings. We propose an explainable deep statistical testing framework that augments deep two-sample tests with sample-level and feature-level explanations, revealing which individual samples and which input features drive statistically significant group differences. Our method highlights which image regions and which individual samples contribute most to the detected group difference, providing spatial and instance-wise insight into the test's decision. Applied to biomedical imaging data, the proposed framework identifies influential samples and highlights anatomically meaningful regions associated with disease-related variation. This work bridges statistical inference and explainable AI, enabling interpretable, label-free population analysis in medical imaging.

Figures (7)

• Figure 1: Feature-level explanation of population-level statistical significance. Two populations are encoded to embeddings to compute a two-sample statistic $S$, whose gradients are backpropagated to feature maps $A_{k}$ and aggregated via weights $\alpha_{k}$ to produce a spatial attribution map, which is then upsampled and overlaid on the input for visualization.
• Figure 2: Sample-level explainability results on dSprites.
• Figure 3: Sample-level explainability results on Diabetic Retinopathy.
• Figure 4: Qualitative examples illustrating samples with high (left) and low (right) influence scores. High-influence samples exhibit clear and distinctive visual patterns that strongly contribute to group differences, while low-influence samples appear more ambiguous or borderline.
• Figure 5: Representative outliers identified by influence scores for diabetic retinopathy severity levels 0–3. No outliers were observed for severity level 4 under the chosen criterion.

Theorems & Definitions (2)

• Definition 3.1
• Definition 3.2