# Model-Agnostic Counterfactual Explanations for Consequential Decisions

arXiv: https://arxiv.org/abs/1905.11190 · HTML: https://mlsanity.com/paper/1905.11190/

## Key facts

- Cited by 204 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 May 2019.

## Built on by (most cited first, 30 of 204)

- [Deep Neural Networks and Tabular Data: A Survey](https://mlsanity.com/paper/2110.01889/) (2021)
- [Benchmarking and Survey of Explanation Methods for Black Box Models](https://mlsanity.com/paper/2102.13076/) (2021)
- [OpenXAI: Towards a Transparent Evaluation of Model Explanations](https://mlsanity.com/paper/2206.11104/) (2022)
- [CF-GNNExplainer: Counterfactual Explanations for Graph Neural Networks](https://mlsanity.com/paper/2102.03322/) (2021)
- [Counterfactual Explanations Can Be Manipulated](https://mlsanity.com/paper/2106.02666/) (2021)
- [Towards Robust and Reliable Algorithmic Recourse](https://mlsanity.com/paper/2102.13620/) (2021)
- [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)
- [Which Explanation Should I Choose? A Function Approximation Perspective to Characterizing Post Hoc Explanations](https://mlsanity.com/paper/2206.01254/) (2022)
- [NICE: An Algorithm for Nearest Instance Counterfactual Explanations](https://mlsanity.com/paper/2104.07411/) (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)
- [Explaining Black-Box Algorithms Using Probabilistic Contrastive Counterfactuals](https://mlsanity.com/paper/2103.11972/) (2021)
- [Exploring Counterfactual Explanations Through the Lens of Adversarial Examples: A Theoretical and Empirical Analysis](https://mlsanity.com/paper/2106.09992/) (2021)
- [Towards the Unification and Robustness of Perturbation and Gradient Based Explanations](https://mlsanity.com/paper/2102.10618/) (2021)
- [Probabilistically Robust Recourse: Navigating the Trade-offs between Costs and Robustness in Algorithmic Recourse](https://mlsanity.com/paper/2203.06768/) (2022)
- [Counterfactual Explanations in Sequential Decision Making Under Uncertainty](https://mlsanity.com/paper/2107.02776/) (2021)
- [Optimal Counterfactual Explanations in Tree Ensembles](https://mlsanity.com/paper/2106.06631/) (2021)
- [Explaining Predictive Uncertainty with Information Theoretic Shapley Values](https://mlsanity.com/paper/2306.05724/) (2023)
- [GeCo: Quality Counterfactual Explanations in Real Time](https://mlsanity.com/paper/2101.01292/) (2021)
- [On the Privacy Risks of Algorithmic Recourse](https://mlsanity.com/paper/2211.05427/) (2022)
- [Interpretable Data-Based Explanations for Fairness Debugging](https://mlsanity.com/paper/2112.09745/) (2021)
- [How Well do Feature Visualizations Support Causal Understanding of CNN Activations?](https://mlsanity.com/paper/2106.12447/) (2021)
- [To trust or not to trust an explanation: using LEAF to evaluate local linear XAI methods](https://mlsanity.com/paper/2106.00461/) (2021)
- [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)
- [Formalising the Robustness of Counterfactual Explanations for Neural Networks](https://mlsanity.com/paper/2208.14878/) (2022)
- [Counterfactual Shapley Additive Explanations](https://mlsanity.com/paper/2110.14270/) (2021)
- [GREASE: Generate Factual and Counterfactual Explanations for GNN-based Recommendations](https://mlsanity.com/paper/2208.04222/) (2022)
- [Attribution-based Explanations that Provide Recourse Cannot be Robust](https://mlsanity.com/paper/2205.15834/) (2022)

## Abstract (arXiv)

Predictive models are being increasingly used to support consequential decision making at the individual level in contexts such as pretrial bail and loan approval. As a result, there is increasing social and legal pressure to provide explanations that help the affected individuals not only to understand why a prediction was output, but also how to act to obtain a desired outcome. To this end, several works have proposed optimization-based methods to generate nearest counterfactual explanations. However, these methods are often restricted to a particular subset of models (e.g., decision trees or linear models) and differentiable distance functions. In contrast, we build on standard theory and tools from formal verification and propose a novel algorithm that solves a sequence of satisfiability problems, where both the distance function (objective) and predictive model (constraints) are represented as logic formulae. As shown by our experiments on real-world data, our algorithm is: i) model-agnostic (non-linear, non-differentiable, non-convex); ii) data-type-agnostic (heterogeneous features); iii) distance-agnostic (ℓ0, ℓ1, ℓ_∞, and combinations thereof); iv) able to generate plausible and diverse counterfactuals for any sample (i.e., 100% coverage); and v) at provably optimal distances.