# Counterfactual Explanations as Interventions in Latent Space

arXiv: https://arxiv.org/abs/2106.07754 · HTML: https://mlsanity.com/paper/2106.07754/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 70 references that are in the map.
- First posted on arXiv 14 Jun 2021.

## Builds on (most cited first, 28 of 28)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI](https://mlsanity.com/paper/1910.10045/) (2019)
- [Explanation in Artificial Intelligence: Insights from the Social Sciences](https://mlsanity.com/paper/1706.07269/) (2017)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [A Survey Of Methods For Explaining Black Box Models](https://mlsanity.com/paper/1802.01933/) (2018)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems](https://mlsanity.com/paper/1603.04467/) (2016)
- [Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations](https://mlsanity.com/paper/1905.07697/) (2019)
- [Actionable Recourse in Linear Classification](https://mlsanity.com/paper/1809.06514/) (2018)
- [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)
- [Visualizing the Effects of Predictor Variables in Black Box Supervised Learning Models](https://mlsanity.com/paper/1612.08468/) (2016)
- [Deep Structural Causal Models for Tractable Counterfactual Inference](https://mlsanity.com/paper/2006.06485/) (2020)
- [Model-Agnostic Counterfactual Explanations for Consequential Decisions](https://mlsanity.com/paper/1905.11190/) (2019)
- [Local Rule-Based Explanations of Black Box Decision Systems](https://mlsanity.com/paper/1805.10820/) (2018)
- [Preserving Causal Constraints in Counterfactual Explanations for Machine Learning Classifiers](https://mlsanity.com/paper/1912.03277/) (2019)
- [Algorithmic recourse under imperfect causal knowledge: a probabilistic approach](https://mlsanity.com/paper/2006.06831/) (2020)
- [Towards Realistic Individual Recourse and Actionable Explanations in Black-Box Decision Making Systems](https://mlsanity.com/paper/1907.09615/) (2019)
- [The Hidden Assumptions Behind Counterfactual Explanations and Principal Reasons](https://mlsanity.com/paper/1912.04930/) (2019)
- ['It's Reducing a Human Being to a Percentage'; Perceptions of Justice in Algorithmic Decisions](https://mlsanity.com/paper/1801.10408/) (2018)
- [CERTIFAI: Counterfactual Explanations for Robustness, Transparency, Interpretability, and Fairness of Artificial Intelligence models](https://mlsanity.com/paper/1905.07857/) (2019)
- [Explaining Data-Driven Decisions made by AI Systems: The Counterfactual Approach](https://mlsanity.com/paper/2001.07417/) (2020)
- [Scaling Guarantees for Nearest Counterfactual Explanations](https://mlsanity.com/paper/2010.04965/) (2020)
- [Directions for Explainable Knowledge-Enabled Systems](https://mlsanity.com/paper/2003.07523/) (2020)
- [BeFair: Addressing Fairness in the Banking Sector](https://mlsanity.com/paper/2102.02137/) (2021)

## Built on by (most cited first, 18 of 18)

- [Backtracking Counterfactuals](https://mlsanity.com/paper/2211.00472/) (2022)
- [Deep Backtracking Counterfactuals for Causally Compliant Explanations](https://mlsanity.com/paper/2310.07665/) (2023)
- [Time Can Invalidate Algorithmic Recourse](https://mlsanity.com/paper/2410.08007/) (2024)
- [Framing Algorithmic Recourse for Anomaly Detection](https://mlsanity.com/paper/2206.14384/) (2022)
- [Evaluative Item-Contrastive Explanations in Rankings](https://mlsanity.com/paper/2312.10094/) (2023)
- [FairLay-ML: Intuitive Remedies for Unfairness in Data-Driven Social-Critical Algorithms](https://mlsanity.com/paper/2307.05029/) (2023)
- [Mapping the Potential of Explainable AI for Fairness Along the AI Lifecycle](https://mlsanity.com/paper/2404.18736/) (2024)
- [Explanations Go Linear: Post-hoc Explainability for Tabular Data with Interpretable Meta-Encoding](https://mlsanity.com/paper/2504.20667/) (2025)
- [What's meant by explainable model: A Scoping Review](https://mlsanity.com/paper/2307.09673/) (2023)
- [DTOR: Decision Tree Outlier Regressor to explain anomalies](https://mlsanity.com/paper/2403.10903/) (2024)
- [RealAC: A Domain-Agnostic Framework for Realistic and Actionable Counterfactual Explanations](https://mlsanity.com/paper/2508.10455/) (2025)
- [The Impact of Machine Learning Uncertainty on the Robustness of Counterfactual Explanations](https://mlsanity.com/paper/2602.00063/) (2026)
- [Discovering Sparse Counterfactual Factors via Latent Adjustment for Survey-based Community Intervention](https://mlsanity.com/paper/2605.04460/) (2026)
- [MetaPlate: Counterfactual-Guided RAG-LLM Tool for Personalized Food Recommendation and Hyperglycemia Prevention](https://mlsanity.com/paper/2606.10120/) (2026)
- [Play Like Champions: Counterfactual Feedback Generation in Latent Space](https://mlsanity.com/paper/2607.00190/) (2026)
- [Class-Aware Reinforcement Learning for Counterfactual Explanation Generation](https://mlsanity.com/paper/2607.27905/) (2026)
- [FCx: An algorithm for finding Feasible Counterfactual Explanations](https://mlsanity.com/paper/2609.19383/) (2026)
- [CAFE: Counterfactual Prediction via Fast Posterior Estimation](https://mlsanity.com/paper/2609.32167/) (2026)

## Abstract (arXiv)

Explainable Artificial Intelligence (XAI) is a set of techniques that allows the understanding of both technical and non-technical aspects of Artificial Intelligence (AI) systems. XAI is crucial to help satisfying the increasingly important demand of trustworthy Artificial Intelligence, characterized by fundamental characteristics such as respect of human autonomy, prevention of harm, transparency, accountability, etc. Within XAI techniques, counterfactual explanations aim to provide to end users a set of features (and their corresponding values) that need to be changed in order to achieve a desired outcome. Current approaches rarely take into account the feasibility of actions needed to achieve the proposed explanations, and in particular they fall short of considering the causal impact of such actions. In this paper, we present Counterfactual Explanations as Interventions in Latent Space (CEILS), a methodology to generate counterfactual explanations capturing by design the underlying causal relations from the data, and at the same time to provide feasible recommendations to reach the proposed profile. Moreover, our methodology has the advantage that it can be set on top of existing counterfactuals generator algorithms, thus minimising the complexity of imposing additional causal constrains. We demonstrate the effectiveness of our approach with a set of different experiments using synthetic and real datasets (including a proprietary dataset of the financial domain).