# Diverse, Global and Amortised Counterfactual Explanations for Uncertainty Estimates

arXiv: https://arxiv.org/abs/2112.02646 · HTML: https://mlsanity.com/paper/2112.02646/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 40 references that are in the map.
- First posted on arXiv 5 Dec 2021.

## Builds on (most cited first, 27 of 27)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations](https://mlsanity.com/paper/1905.07697/) (2019)
- [FACE: Feasible and Actionable Counterfactual Explanations](https://mlsanity.com/paper/1909.09369/) (2019)
- [Interpretable Counterfactual Explanations Guided by Prototypes](https://mlsanity.com/paper/1907.02584/) (2019)
- [Explainable Machine Learning in Deployment](https://mlsanity.com/paper/1909.06342/) (2019)
- [Debugging Tests for Model Explanations](https://mlsanity.com/paper/2011.05429/) (2020)
- [Learning Model-Agnostic Counterfactual Explanations for Tabular Data](https://mlsanity.com/paper/1910.09398/) (2019)
- [Preserving Causal Constraints in Counterfactual Explanations for Machine Learning Classifiers](https://mlsanity.com/paper/1912.03277/) (2019)
- [Efficient Search for Diverse Coherent Explanations](https://mlsanity.com/paper/1901.04909/) (2019)
- [Getting a CLUE: A Method for Explaining Uncertainty Estimates](https://mlsanity.com/paper/2006.06848/) (2020)
- [CARLA: A Python Library to Benchmark Algorithmic Recourse and Counterfactual Explanation Algorithms](https://mlsanity.com/paper/2108.00783/) (2021)
- [Explanation by Progressive Exaggeration](https://mlsanity.com/paper/1911.00483/) (2019)
- [On Counterfactual Explanations under Predictive Multiplicity](https://mlsanity.com/paper/2006.13132/) (2020)
- [Counterfactual Explanations in Sequential Decision Making Under Uncertainty](https://mlsanity.com/paper/2107.02776/) (2021)
- [xGEMs: Generating Examplars to Explain Black-Box Models](https://mlsanity.com/paper/1806.08867/) (2018)
- [Explaining Groups of Points in Low-Dimensional Representations](https://mlsanity.com/paper/2003.01640/) (2020)
- [Model-Based Counterfactual Synthesizer for Interpretation](https://mlsanity.com/paper/2106.08971/) (2021)
- [Uncertainty Decomposition in Bayesian Neural Networks with Latent Variables](https://mlsanity.com/paper/1706.08495/) (2017)
- [Synbols: Probing Learning Algorithms with Synthetic Datasets](https://mlsanity.com/paper/2009.06415/) (2020)
- [δ-CLUE: Diverse Sets of Explanations for Uncertainty Estimates](https://mlsanity.com/paper/2104.06323/) (2021)
- [DIVINE: Diverse Influential Training Points for Data Visualization and Model Refinement](https://mlsanity.com/paper/2107.05978/) (2021)
- [MNIST Dataset Classification Utilizing k-NN Classifier with Modified Sliding-window Metric](https://mlsanity.com/paper/1809.06846/) (2018)

## Built on by (most cited first, 19 of 19)

- [Uncertainty Quantification with Pre-trained Language Models: A Large-Scale Empirical Analysis](https://mlsanity.com/paper/2210.04714/) (2022)
- [Explaining Predictive Uncertainty with Information Theoretic Shapley Values](https://mlsanity.com/paper/2306.05724/) (2023)
- [GLOBE-CE: A Translation-Based Approach for Global Counterfactual Explanations](https://mlsanity.com/paper/2305.17021/) (2023)
- [Achieving Diversity in Counterfactual Explanations: a Review and Discussion](https://mlsanity.com/paper/2305.05840/) (2023)
- [Diverse Counterfactual Explanations for Anomaly Detection in Time Series](https://mlsanity.com/paper/2203.11103/) (2022)
- [Global Counterfactual Explanations: Investigations, Implementations and Improvements](https://mlsanity.com/paper/2204.06917/) (2022)
- [Gradient-based Uncertainty Attribution for Explainable Bayesian Deep Learning](https://mlsanity.com/paper/2304.04824/) (2023)
- [Bayesian Hierarchical Models for Counterfactual Estimation](https://mlsanity.com/paper/2301.08833/) (2023)
- [Unveil Sources of Uncertainty: Feature Contribution to Conformal Prediction Intervals](https://mlsanity.com/paper/2505.13118/) (2025)
- [Identifying Drivers of Predictive Aleatoric Uncertainty](https://mlsanity.com/paper/2312.07252/) (2023)
- [X-Fake: Juggling Utility Evaluation and Explanation of Simulated SAR Images](https://mlsanity.com/paper/2407.19436/) (2024)
- [Explaining Predictive Uncertainty by Looking Back at Model Explanations](https://mlsanity.com/paper/2201.03742/) (2022)
- [Explaining and visualizing black-box models through counterfactual paths](https://mlsanity.com/paper/2307.07764/) (2023)
- [When Explanations Compete: Policy-Aware Selection Under Uncertainty](https://mlsanity.com/paper/2410.05479/) (2024)
- [Improving Counterfactual Truthfulness for Molecular Property Prediction through Uncertainty Quantification](https://mlsanity.com/paper/2504.02606/) (2025)
- [DCFO: Density-Based Counterfactuals for Outliers -- Additional Material](https://mlsanity.com/paper/2512.10659/) (2025)
- [Global Graph Counterfactual Explanation: A Subgraph Mapping Approach](https://mlsanity.com/paper/2410.19978/) (2024)
- [Model-Free Counterfactual Subset Selection at Scale](https://mlsanity.com/paper/2502.08326/) (2025)
- [ExDBSCAN: Explaining DBSCAN with Counterfactual Reasoning -- Additional Material](https://mlsanity.com/paper/2605.30225/) (2026)

## Abstract (arXiv)

To interpret uncertainty estimates from differentiable probabilistic models, recent work has proposed generating a single Counterfactual Latent Uncertainty Explanation (CLUE) for a given data point where the model is uncertain, identifying a single, on-manifold change to the input such that the model becomes more certain in its prediction. We broaden the exploration to examine δ-CLUE, the set of potential CLUEs within a δ ball of the original input in latent space. We study the diversity of such sets and find that many CLUEs are redundant; as such, we propose DIVerse CLUE (nabla-CLUE), a set of CLUEs which each propose a distinct explanation as to how one can decrease the uncertainty associated with an input. We then further propose GLobal AMortised CLUE (GLAM-CLUE), a distinct and novel method which learns amortised mappings on specific groups of uncertain inputs, taking them and efficiently transforming them in a single function call into inputs for which a model will be certain. Our experiments show that δ-CLUE, nabla-CLUE, and GLAM-CLUE all address shortcomings of CLUE and provide beneficial explanations of uncertainty estimates to practitioners.