# Causal Generative Explainers using Counterfactual Inference: A Case Study on the Morpho-MNIST Dataset

arXiv: https://arxiv.org/abs/2401.11394 · HTML: https://mlsanity.com/paper/2401.11394/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 32 references that are in the map.
- First posted on arXiv 21 Jan 2024.

## Builds on (most cited first, 20 of 20)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Adversarial Feature Learning](https://mlsanity.com/paper/1605.09782/) (2016)
- [Explanations based on the Missing: Towards Contrastive Explanations with Pertinent Negatives](https://mlsanity.com/paper/1802.07623/) (2018)
- [Interpretable Counterfactual Explanations Guided by Prototypes](https://mlsanity.com/paper/1907.02584/) (2019)
- [Adversarially Learned Inference](https://mlsanity.com/paper/1606.00704/) (2016)
- [Deep Structural Causal Models for Tractable Counterfactual Inference](https://mlsanity.com/paper/2006.06485/) (2020)
- [CausalGAN: Learning Causal Implicit Generative Models with Adversarial Training](https://mlsanity.com/paper/1709.02023/) (2017)
- [Preserving Causal Constraints in Counterfactual Explanations for Machine Learning Classifiers](https://mlsanity.com/paper/1912.03277/) (2019)
- [Morpho-MNIST: Quantitative Assessment and Diagnostics for Representation Learning](https://mlsanity.com/paper/1809.10780/) (2018)
- [Evaluating and Mitigating Bias in Image Classifiers: A Causal Perspective Using Counterfactuals](https://mlsanity.com/paper/2009.08270/) (2020)
- [Generative causal explanations of black-box classifiers](https://mlsanity.com/paper/2006.13913/) (2020)
- [Generating Interpretable Counterfactual Explanations By Implicit Minimisation of Epistemic and Aleatoric Uncertainties](https://mlsanity.com/paper/2103.08951/) (2021)
- [Conditional Generative Models for Counterfactual Explanations](https://mlsanity.com/paper/2101.10123/) (2021)
- [ECINN: Efficient Counterfactuals from Invertible Neural Networks](https://mlsanity.com/paper/2103.13701/) (2021)
- [Explaining Visual Models by Causal Attribution](https://mlsanity.com/paper/1909.08891/) (2019)
- [Model-Based Counterfactual Synthesizer for Interpretation](https://mlsanity.com/paper/2106.08971/) (2021)
- [On Quantitative Evaluations of Counterfactuals](https://mlsanity.com/paper/2111.00177/) (2021)

## Built on by (most cited first, 4 of 4)

- [Benchmarking Counterfactual Image Generation](https://mlsanity.com/paper/2403.20287/) (2024)
- [Diffusion Counterfactual Generation with Semantic Abduction](https://mlsanity.com/paper/2506.07883/) (2025)
- [A Review of Global Sensitivity Analysis Methods and a comparative case study on Digit Classification](https://mlsanity.com/paper/2406.16975/) (2024)
- [Ranking Counterfactual Explanations](https://mlsanity.com/paper/2503.15817/) (2025)

## Abstract (arXiv)

In this paper, we propose leveraging causal generative learning as an interpretable tool for explaining image classifiers. Specifically, we present a generative counterfactual inference approach to study the influence of visual features (i.e., pixels) as well as causal factors through generative learning. To this end, we first uncover the most influential pixels on a classifier's decision by varying the value of a causal attribute via counterfactual inference and computing both Shapely and contrastive explanations for counterfactual images with these different attribute values. We then establish a Monte-Carlo mechanism using the generator of a causal generative model in order to adapt Shapley explainers to produce feature importances for the human-interpretable attributes of a causal dataset in the case where a classifier has been trained exclusively on the images of the dataset. Finally, we present optimization methods for creating counterfactual explanations of classifiers by means of counterfactual inference, proposing straightforward approaches for both differentiable and arbitrary classifiers. We exploit the Morpho-MNIST causal dataset as a case study for exploring our proposed methods for generating counterfacutl explantions. We employ visual explanation methods from OmnixAI open source toolkit to compare them with our proposed methods. By employing quantitative metrics to measure the interpretability of counterfactual explanations, we find that our proposed methods of counterfactual explanation offer more interpretable explanations compared to those generated from OmnixAI. This finding suggests that our methods are well-suited for generating highly interpretable counterfactual explanations on causal datasets.