# Hierarchical Optimal Transport for Comparing Histopathology Datasets

arXiv: https://arxiv.org/abs/2204.08324 · HTML: https://mlsanity.com/paper/2204.08324/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 28 references that are in the map.
- First posted on arXiv 18 Apr 2022.

## Builds on (most cited first, 11 of 11)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration](https://mlsanity.com/paper/1705.09634/) (2017)
- [Deep neural network models for computational histopathology: A survey](https://mlsanity.com/paper/1912.12378/) (2019)
- [Geometric Dataset Distances via Optimal Transport](https://mlsanity.com/paper/2002.02923/) (2020)
- [Improving GANs Using Optimal Transport](https://mlsanity.com/paper/1803.05573/) (2018)
- [Hierarchical Optimal Transport for Document Representation](https://mlsanity.com/paper/1906.10827/) (2019)
- [The Information Complexity of Learning Tasks, their Structure and their Distance](https://mlsanity.com/paper/1904.03292/) (2019)
- [Interpretable Survival Prediction for Colorectal Cancer using Deep Learning](https://mlsanity.com/paper/2011.08965/) (2020)
- [An Information-Geometric Distance on the Space of Tasks](https://mlsanity.com/paper/2011.00613/) (2020)

## Built on by (most cited first, 6 of 6)

- [Morphological Prototyping for Unsupervised Slide Representation Learning in Computational Pathology](https://mlsanity.com/paper/2405.11643/) (2024)
- [HASD: Hierarchical Adaption for pathology Slide-level Domain-shift](https://mlsanity.com/paper/2506.23673/) (2025)
- [Generating Synthetic Datasets by Interpolating along Generalized Geodesics](https://mlsanity.com/paper/2306.06866/) (2023)
- [RALAD: Bridging the Real-to-Sim Domain Gap in Autonomous Driving with Retrieval-Augmented Learning](https://mlsanity.com/paper/2501.12296/) (2025)
- [Budget-Constrained Bounds for Mini-Batch Estimation of Optimal Transport](https://mlsanity.com/paper/2210.13630/) (2022)
- [Are "Hierarchical" Visual Representations Hierarchical?](https://mlsanity.com/paper/2311.05784/) (2023)

## Abstract (arXiv)

Scarcity of labeled histopathology data limits the applicability of deep learning methods to under-profiled cancer types and labels. Transfer learning allows researchers to overcome the limitations of small datasets by pre-training machine learning models on larger datasets similar to the small target dataset. However, similarity between datasets is often determined heuristically. In this paper, we propose a principled notion of distance between histopathology datasets based on a hierarchical generalization of optimal transport distances. Our method does not require any training, is agnostic to model type, and preserves much of the hierarchical structure in histopathology datasets imposed by tiling. We apply our method to H&E stained slides from The Cancer Genome Atlas from six different cancer types. We show that our method outperforms a baseline distance in a cancer-type prediction task. Our results also show that our optimal transport distance predicts difficulty of transferability in a tumor vs.normal prediction setting.