# Efficient Search for Diverse Coherent Explanations

arXiv: https://arxiv.org/abs/1901.04909 · HTML: https://mlsanity.com/paper/1901.04909/

## Key facts

- Cited by 111 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jan 2019.

## Built on by (most cited first, 30 of 111)

- [Deep Neural Networks and Tabular Data: A Survey](https://mlsanity.com/paper/2110.01889/) (2021)
- [AI Transparency in the Age of LLMs: A Human-Centered Research Roadmap](https://mlsanity.com/paper/2306.01941/) (2023)
- [CARLA: A Python Library to Benchmark Algorithmic Recourse and Counterfactual Explanation Algorithms](https://mlsanity.com/paper/2108.00783/) (2021)
- [If Only We Had Better Counterfactual Explanations: Five Key Deficits to Rectify in the Evaluation of Counterfactual XAI Techniques](https://mlsanity.com/paper/2103.01035/) (2021)
- [Counterfactuals and Causability in Explainable Artificial Intelligence: Theory, Algorithms, and Applications](https://mlsanity.com/paper/2103.04244/) (2021)
- [Beyond Trivial Counterfactual Explanations with Diverse Valuable Explanations](https://mlsanity.com/paper/2103.10226/) (2021)
- [CLEAR: Generative Counterfactual Explanations on Graphs](https://mlsanity.com/paper/2210.08443/) (2022)
- [Optimal Counterfactual Explanations in Tree Ensembles](https://mlsanity.com/paper/2106.06631/) (2021)
- [Cycle-Consistent Counterfactuals by Latent Transformations](https://mlsanity.com/paper/2203.15064/) (2022)
- [DualCF: Efficient Model Extraction Attack from Counterfactual Explanations](https://mlsanity.com/paper/2205.06504/) (2022)
- [ReLAX: Reinforcement Learning Agent eXplainer for Arbitrary Predictive Models](https://mlsanity.com/paper/2110.11960/) (2021)
- [Amortized Generation of Sequential Algorithmic Recourses for Black-box Models](https://mlsanity.com/paper/2106.03962/) (2021)
- [Counterfactual Shapley Additive Explanations](https://mlsanity.com/paper/2110.14270/) (2021)
- [VCNet: A self-explaining model for realistic counterfactual generation](https://mlsanity.com/paper/2212.10847/) (2022)
- [Diverse, Global and Amortised Counterfactual Explanations for Uncertainty Estimates](https://mlsanity.com/paper/2112.02646/) (2021)
- [Counterfactual Plans under Distributional Ambiguity](https://mlsanity.com/paper/2201.12487/) (2022)
- [Finding Regions of Counterfactual Explanations via Robust Optimization](https://mlsanity.com/paper/2301.11113/) (2023)
- [Rational Shapley Values](https://mlsanity.com/paper/2106.10191/) (2021)
- [Directive Explanations for Actionable Explainability in Machine Learning Applications](https://mlsanity.com/paper/2102.02671/) (2021)
- [Counterfactual Explanations for Oblique Decision Trees: Exact, Efficient Algorithms](https://mlsanity.com/paper/2103.01096/) (2021)
- [Efficient XAI Techniques: A Taxonomic Survey](https://mlsanity.com/paper/2302.03225/) (2023)
- [MACE: An Efficient Model-Agnostic Framework for Counterfactual Explanation](https://mlsanity.com/paper/2205.15540/) (2022)
- [Counterfactual Explanations for Misclassified Images: How Human and Machine Explanations Differ](https://mlsanity.com/paper/2212.08733/) (2022)
- [Distributionally Robust Recourse Action](https://mlsanity.com/paper/2302.11211/) (2023)
- [Feature-based Learning for Diverse and Privacy-Preserving Counterfactual Explanations](https://mlsanity.com/paper/2209.13446/) (2022)
- [Achieving Diversity in Counterfactual Explanations: a Review and Discussion](https://mlsanity.com/paper/2305.05840/) (2023)
- [Probabilistically Plausible Counterfactual Explanations with Normalizing Flows](https://mlsanity.com/paper/2405.17640/) (2024)
- [Multi-objective Explanations of GNN Predictions](https://mlsanity.com/paper/2111.14651/) (2021)
- [Diverse Counterfactual Explanations for Anomaly Detection in Time Series](https://mlsanity.com/paper/2203.11103/) (2022)
- [Personalized Algorithmic Recourse with Preference Elicitation](https://mlsanity.com/paper/2205.13743/) (2022)

## Abstract (arXiv)

This paper proposes new search algorithms for counterfactual explanations based upon mixed integer programming. We are concerned with complex data in which variables may take any value from a contiguous range or an additional set of discrete states. We propose a novel set of constraints that we refer to as a "mixed polytope" and show how this can be used with an integer programming solver to efficiently find coherent counterfactual explanations i.e. solutions that are guaranteed to map back onto the underlying data structure, while avoiding the need for brute-force enumeration. We also look at the problem of diverse explanations and show how these can be generated within our framework.