# Bayesian Hierarchical Models for Counterfactual Estimation

arXiv: https://arxiv.org/abs/2301.08833 · HTML: https://mlsanity.com/paper/2301.08833/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 45 references that are in the map.
- First posted on arXiv 21 Jan 2023.

## Builds on (most cited first, 30 of 30)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations](https://mlsanity.com/paper/1905.07697/) (2019)
- [Explanations based on the Missing: Towards Contrastive Explanations with Pertinent Negatives](https://mlsanity.com/paper/1802.07623/) (2018)
- [Algorithmic Recourse: from Counterfactual Explanations to Interventions](https://mlsanity.com/paper/2002.06278/) (2020)
- [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)
- [Fairness in Machine Learning](https://mlsanity.com/paper/2012.15816/) (2020)
- [Multi-Objective Counterfactual Explanations](https://mlsanity.com/paper/2004.11165/) (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)
- [Reliable Post hoc Explanations: Modeling Uncertainty in Explainability](https://mlsanity.com/paper/2008.05030/) (2020)
- [Counterfactual Explanations Can Be Manipulated](https://mlsanity.com/paper/2106.02666/) (2021)
- [Efficient Search for Diverse Coherent Explanations](https://mlsanity.com/paper/1901.04909/) (2019)
- [Rank-normalization, folding, and localization: An improved widehatR for assessing convergence of MCMC](https://mlsanity.com/paper/1903.08008/) (2019)
- [On the Fairness of Causal Algorithmic Recourse](https://mlsanity.com/paper/2010.06529/) (2020)
- [Counterfactual Risk Assessments, Evaluation, and Fairness](https://mlsanity.com/paper/1909.00066/) (2019)
- [Beyond Trivial Counterfactual Explanations with Diverse Valuable Explanations](https://mlsanity.com/paper/2103.10226/) (2021)
- [On the Adversarial Robustness of Causal Algorithmic Recourse](https://mlsanity.com/paper/2112.11313/) (2021)
- [Hamiltonian Monte Carlo for Hierarchical Models](https://mlsanity.com/paper/1312.0906/) (2013)
- [The Use and Misuse of Counterfactuals in Ethical Machine Learning](https://mlsanity.com/paper/2102.05085/) (2021)
- [Robust Counterfactual Explanations for Tree-Based Ensembles](https://mlsanity.com/paper/2207.02739/) (2022)
- [BRPO: Batch Residual Policy Optimization](https://mlsanity.com/paper/2002.05522/) (2020)
- [Counterfactual Shapley Additive Explanations](https://mlsanity.com/paper/2110.14270/) (2021)
- [A Few Good Counterfactuals: Generating Interpretable, Plausible and Diverse Counterfactual Explanations](https://mlsanity.com/paper/2101.09056/) (2021)
- [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)
- [Rational Shapley Values](https://mlsanity.com/paper/2106.10191/) (2021)
- [Robust Bayesian Recourse](https://mlsanity.com/paper/2206.10833/) (2022)
- [Explaining Groups of Points in Low-Dimensional Representations](https://mlsanity.com/paper/2003.01640/) (2020)

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

- [Robust Counterfactual Explanations for Neural Networks With Probabilistic Guarantees](https://mlsanity.com/paper/2305.11997/) (2023)
- [Robust Counterfactual Explanations in Machine Learning: A Survey](https://mlsanity.com/paper/2402.01928/) (2024)
- [Enhancing Counterfactual Explanation Search with Diffusion Distance and Directional Coherence](https://mlsanity.com/paper/2404.12810/) (2024)
- [CE-QArg: Counterfactual Explanations for Quantitative Bipolar Argumentation Frameworks (Technical Report)](https://mlsanity.com/paper/2407.08497/) (2024)
- [Perfect Counterfactuals in Imperfect Worlds: Modelling Noisy Implementation of Actions in Sequential Algorithmic Recourse](https://mlsanity.com/paper/2410.02273/) (2024)
- [A Generalized-Bayes Perspective on Counterfactual Explanations: Posterior-Based Decision-Making and Evaluation](https://mlsanity.com/paper/2607.29077/) (2026)

## Abstract (arXiv)

Counterfactual explanations utilize feature perturbations to analyze the outcome of an original decision and recommend an actionable recourse. We argue that it is beneficial to provide several alternative explanations rather than a single point solution and propose a probabilistic paradigm to estimate a diverse set of counterfactuals. Specifically, we treat the perturbations as random variables endowed with prior distribution functions. This allows sampling multiple counterfactuals from the posterior density, with the added benefit of incorporating inductive biases, preserving domain specific constraints and quantifying uncertainty in estimates. More importantly, we leverage Bayesian hierarchical modeling to share information across different subgroups of a population, which can both improve robustness and measure fairness. A gradient based sampler with superior convergence characteristics efficiently computes the posterior samples. Experiments across several datasets demonstrate that the counterfactuals estimated using our approach are valid, sparse, diverse and feasible.