# Statistical Testing for Multiple Instance Learning via Selective Inference with Applications to Computational Pathology

arXiv: https://arxiv.org/abs/2609.31712 · HTML: https://mlsanity.com/paper/2609.31712/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 37 of its 70 references that are in the map.
- First posted on arXiv 21 Sep 2026.

## Builds on (most cited first, 30 of 37)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Attention-based Deep Multiple Instance Learning](https://mlsanity.com/paper/1802.04712/) (2018)
- [Attention is not Explanation](https://mlsanity.com/paper/1902.10186/) (2019)
- [Data Efficient and Weakly Supervised Computational Pathology on Whole Slide Images](https://mlsanity.com/paper/2004.09666/) (2020)
- [Attention is not not Explanation](https://mlsanity.com/paper/1908.04626/) (2019)
- [TransMIL: Transformer based Correlated Multiple Instance Learning for Whole Slide Image Classification](https://mlsanity.com/paper/2106.00908/) (2021)
- [Dual-stream Multiple Instance Learning Network for Whole Slide Image Classification with Self-supervised Contrastive Learning](https://mlsanity.com/paper/2011.08939/) (2020)
- [Is Attention Interpretable?](https://mlsanity.com/paper/1906.03731/) (2019)
- [Scaling Vision Transformers to Gigapixel Images via Hierarchical Self-Supervised Learning](https://mlsanity.com/paper/2206.02647/) (2022)
- [DTFD-MIL: Double-Tier Feature Distillation Multiple Instance Learning for Histopathology Whole Slide Image Classification](https://mlsanity.com/paper/2203.12081/) (2022)
- [Multimodal Whole Slide Foundation Model for Pathology](https://mlsanity.com/paper/2411.19666/) (2024)
- [Revisiting Multiple Instance Neural Networks](https://mlsanity.com/paper/1610.02501/) (2016)
- [Exact post-selection inference, with application to the lasso](https://mlsanity.com/paper/1311.6238/) (2013)
- [Multi-scale Domain-adversarial Multiple-instance CNN for Cancer Subtype Classification with Unannotated Histopathological Images](https://mlsanity.com/paper/2001.01599/) (2020)
- [Optimal Inference After Model Selection](https://mlsanity.com/paper/1410.2597/) (2014)
- [Thoracic Disease Identification and Localization with Limited Supervision](https://mlsanity.com/paper/1711.06373/) (2017)
- [Exact Post-Selection Inference for Sequential Regression Procedures](https://mlsanity.com/paper/1401.3889/) (2014)
- [Selective Inference for Hierarchical Clustering](https://mlsanity.com/paper/2012.02936/) (2020)
- [Classifying and Segmenting Microscopy Images Using Convolutional Multiple Instance Learning](https://mlsanity.com/paper/1511.05286/) (2015)
- [Valid Inference Corrected for Outlier Removal](https://mlsanity.com/paper/1711.10635/) (2017)
- [Computing Valid p-value for Optimal Changepoint by Selective Inference using Dynamic Programming](https://mlsanity.com/paper/2002.09132/) (2020)
- [More Powerful Conditional Selective Inference for Generalized Lasso by Parametric Programming](https://mlsanity.com/paper/2105.04920/) (2021)
- [Selective inference for k-means clustering](https://mlsanity.com/paper/2203.15267/) (2022)
- [Quantifying Statistical Significance of Neural Network-based Image Segmentation by Selective Inference](https://mlsanity.com/paper/2010.01823/) (2020)
- [Valid P-Value for Deep Learning-Driven Salient Region](https://mlsanity.com/paper/2301.02437/) (2023)
- [Post Selection Inference with Kernels](https://mlsanity.com/paper/1610.03725/) (2016)
- [Label Cleaning Multiple Instance Learning: Refining Coarse Annotations on Single Whole-Slide Images](https://mlsanity.com/paper/2109.10778/) (2021)
- [Label-free Concept Based Multiple Instance Learning for Gigapixel Histopathology](https://mlsanity.com/paper/2501.02922/) (2025)
- [si4onnx: A Python package for Selective Inference in Deep Learning Models](https://mlsanity.com/paper/2501.17415/) (2025)
- [Inference on the proportion of variance explained in principal component analysis](https://mlsanity.com/paper/2402.16725/) (2024)

## Abstract (arXiv)

Multiple instance learning (MIL) is widely used in computational pathology because it enables weakly supervised analysis of whole-slide images (WSIs) without requiring patch-level annotations. In attention-based MIL, instances with high attention scores are often interpreted as diagnostically important regions and used as visual explanations. However, attention scores alone cannot determine whether selected high-attention instances are significantly different from normal instances, limiting the reliability of attention-based explanations. In this paper, we formulate the evaluation of high-attention instances as a statistical hypothesis testing problem. Specifically, we assess whether a selected high-attention instance significantly deviates from a representative normal reference instance selected based on feature similarity. A major challenge is that both the target instance and the reference instance are selected through data-dependent procedures, rendering standard hypothesis testing invalid. To address this issue, we introduce a selective inference (SI) framework that explicitly accounts for the selection events induced by attention-based instance selection and adaptive reference selection, thereby enabling the computation of valid selective p-values conditional on these events. Experiments demonstrate Type-I error control on synthetic and MNIST-based data and practical applicability to pathological WSIs, with higher statistical power than the conventional over-conditioning approach.