# Towards Visually Explaining Statistical Tests with Applications in Biomedical Imaging

arXiv: https://arxiv.org/abs/2601.13899 · HTML: https://mlsanity.com/paper/2601.13899/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 25 references that are in the map.
- First posted on arXiv 20 Jan 2026.

## Builds on (most cited first, 15 of 15)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Grad-CAM++: Improved Visual Explanations for Deep Convolutional Networks](https://mlsanity.com/paper/1710.11063/) (2017)
- [Estimating Training Data Influence by Tracing Gradient Descent](https://mlsanity.com/paper/2002.08484/) (2020)
- [Revisiting Classifier Two-Sample Tests](https://mlsanity.com/paper/1610.06545/) (2016)
- [Deep k-Nearest Neighbors: Towards Confident, Interpretable and Robust Deep Learning](https://mlsanity.com/paper/1803.04765/) (2018)
- [Learning Deep Kernels for Non-Parametric Two-Sample Tests](https://mlsanity.com/paper/2002.09116/) (2020)
- [Interpretable Distribution Features with Maximum Testing Power](https://mlsanity.com/paper/1605.06796/) (2016)
- [Explaining Latent Representations with a Corpus of Examples](https://mlsanity.com/paper/2110.15355/) (2021)
- [Two-sample Testing Using Deep Learning](https://mlsanity.com/paper/1910.06239/) (2019)
- [Label-Free Explainability for Unsupervised Models](https://mlsanity.com/paper/2203.01928/) (2022)

## Abstract (arXiv)

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.