# Explaining Groups of Points in Low-Dimensional Representations

arXiv: https://arxiv.org/abs/2003.01640 · HTML: https://mlsanity.com/paper/2003.01640/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Mar 2020.

## Built on by (most cited first, 16 of 16)

- [From Anecdotal Evidence to Quantitative Evaluation Methods: A Systematic Review on Evaluating Explainable AI](https://mlsanity.com/paper/2201.08164/) (2022)
- [Finding and Fixing Spurious Patterns with Explanations](https://mlsanity.com/paper/2106.02112/) (2021)
- [GLOBE-CE: A Translation-Based Approach for Global Counterfactual Explanations](https://mlsanity.com/paper/2305.17021/) (2023)
- [Diverse, Global and Amortised Counterfactual Explanations for Uncertainty Estimates](https://mlsanity.com/paper/2112.02646/) (2021)
- [XOmiVAE: an interpretable deep learning model for cancer classification using high-dimensional omics data](https://mlsanity.com/paper/2105.12807/) (2021)
- [Interpretable Machine Learning: Moving From Mythos to Diagnostics](https://mlsanity.com/paper/2103.06254/) (2021)
- [Global Counterfactual Explanations: Investigations, Implementations and Improvements](https://mlsanity.com/paper/2204.06917/) (2022)
- [Explaining Groups of Instances Counterfactually for XAI: A Use Case, Algorithm and User Study for Group-Counterfactuals](https://mlsanity.com/paper/2303.09297/) (2023)
- [Bayesian Hierarchical Models for Counterfactual Estimation](https://mlsanity.com/paper/2301.08833/) (2023)
- [Distributional Counterfactual Explanations With Optimal Transport](https://mlsanity.com/paper/2401.13112/) (2024)
- [A Two-Stage Algorithm for Cost-Efficient Multi-instance Counterfactual Explanations](https://mlsanity.com/paper/2403.01221/) (2024)
- [Unifying Perspectives: Plausible Counterfactual Explanations on Global, Group-wise, and Local Levels](https://mlsanity.com/paper/2405.17642/) (2024)
- [How Well Do Feature-Additive Explainers Explain Feature-Additive Predictors?](https://mlsanity.com/paper/2310.18496/) (2023)
- [VERA: Generating Visual Explanations of Two-Dimensional Embeddings via Region Annotation](https://mlsanity.com/paper/2406.04808/) (2024)
- [POLygraph: Polish Fake News Dataset](https://mlsanity.com/paper/2407.01393/) (2024)
- [DISCOVER: A Solver for Distributional Counterfactual Explanations](https://mlsanity.com/paper/2603.16436/) (2026)

## Abstract (arXiv)

A common workflow in data exploration is to learn a low-dimensional representation of the data, identify groups of points in that representation, and examine the differences between the groups to determine what they represent. We treat this workflow as an interpretable machine learning problem by leveraging the model that learned the low-dimensional representation to help identify the key differences between the groups. To solve this problem, we introduce a new type of explanation, a Global Counterfactual Explanation (GCE), and our algorithm, Transitive Global Translations (TGT), for computing GCEs. TGT identifies the differences between each pair of groups using compressed sensing but constrains those pairwise differences to be consistent among all of the groups. Empirically, we demonstrate that TGT is able to identify explanations that accurately explain the model while being relatively sparse, and that these explanations match real patterns in the data.