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We use a well known problem in discrete and computational geometry (partitions of measures by $k$-fans) as a motivation and as a point of departure to illustrate many aspects, both theoretical and computational, of the problem of…

Algebraic Topology · Mathematics 2007-05-23 Pavle V. M. Blagojevic , Sinisa T. Vrecica , Rade T. Zivaljevic

Counterfactual explanations (CE) explain model decisions by identifying input modifications that lead to different predictions. Most existing methods operate at the instance level. Distributional Counterfactual Explanations (DCE) extend…

Machine Learning · Computer Science 2026-03-18 Yikai Gu , Lele Cao , Bo Zhao , Lei Lei , Lei You

Counterfactuals have been established as a popular explainability technique which leverages a set of minimal edits to alter the prediction of a classifier. When considering conceptual counterfactuals on images, the edits requested should…

Machine Learning · Computer Science 2024-05-06 Angeliki Dimitriou , Nikolaos Chaidos , Maria Lymperaiou , Giorgos Stamou

In recent years, there has been a surge of interests in interpretable graph reasoning methods. However, these models often suffer from limited performance when working on sparse and incomplete graphs, due to the lack of evidential paths…

Artificial Intelligence · Computer Science 2019-09-15 Cong Fu , Tong Chen , Meng Qu , Woojeong Jin , Xiang Ren

Explainable AI aims to render model behavior understandable by humans, which can be seen as an intermediate step in extracting causal relations from correlative patterns. Due to the high risk of possible fatal decisions in image-based…

Computer Vision and Pattern Recognition · Computer Science 2023-06-16 Lukas Klein , João B. S. Carvalho , Mennatallah El-Assady , Paolo Penna , Joachim M. Buhmann , Paul F. Jaeger

Counterfactual explanations have emerged as a powerful tool to unveil the opaque decision-making processes of graph neural networks (GNNs). However, existing techniques primarily focus on edge modifications, often overlooking the crucial…

Machine Learning · Computer Science 2025-02-17 Flavio Giorgi , Fabrizio Silvestri , Gabriele Tolomei

Machines are being increasingly used in decision-making processes, resulting in the realization that decisions need explanations. Unfortunately, an increasing number of these deployed models are of a 'black-box' nature where the reasoning…

Artificial Intelligence · Computer Science 2023-11-07 Sopam Dasgupta

Counterfactual explanations indicate the smallest change in input that can translate to a different outcome for a machine learning model. Counterfactuals have generated immense interest in high-stakes applications such as finance,…

Machine Learning · Computer Science 2025-03-12 Erfaun Noorani , Pasan Dissanayake , Faisal Hamman , Sanghamitra Dutta

There is a growing concern that the recent progress made in AI, especially regarding the predictive competence of deep learning models, will be undermined by a failure to properly explain their operation and outputs. In response to this…

Machine Learning · Computer Science 2020-09-15 Eoin M. Kenny , Mark T. Keane

Counterfactual inference is a powerful tool, capable of solving challenging problems in high-profile sectors. To perform counterfactual inference, one requires knowledge of the underlying causal mechanisms. However, causal mechanisms cannot…

Machine Learning · Computer Science 2023-01-23 Athanasios Vlontzos , Bernhard Kainz , Ciaran M. Gilligan-Lee

Understanding the predictions made by deep learning models remains a central challenge, especially in high-stakes applications. A promising approach is to equip models with the ability to answer counterfactual questions -- hypothetical…

Machine Learning · Computer Science 2025-10-28 Inwoo Hwang , Yushu Pan , Elias Bareinboim

Counterfactual inference is a useful tool for comparing outcomes of interventions on complex systems. It requires us to represent the system in form of a structural causal model, complete with a causal diagram, probabilistic assumptions on…

Recently, counterfactuals using "if-only" explanations have become very popular in eXplainable AI (XAI), as they describe which changes to feature-inputs of a black-box AI system result in changes to a (usually negative) decision-outcome.…

Artificial Intelligence · Computer Science 2024-06-28 Saugat Aryal , Mark T. Keane

Sophisticated machine models are increasingly used for high-stakes decisions in everyday life. There is an urgent need to develop effective explanation techniques for such automated decisions. Rule-Based Explanations have been proposed for…

Machine Learning · Computer Science 2022-11-01 Zixuan Geng , Maximilian Schleich , Dan Suciu

Physical experiments often involve multiple imaging representations, such as X-ray scans and microscopic images. Deep learning models have been widely used for supervised analysis in these experiments. Combining different image…

Computer Vision and Pattern Recognition · Computer Science 2024-07-30 Nadav Schneider , Muriel Tzdaka , Galit Sturm , Guy Lazovski , Galit Bar , Gilad Oren , Raz Gvishi , Gal Oren

Counterfactual inference aims to answer retrospective "what if" questions and thus belongs to the most fine-grained type of inference in Pearl's causality ladder. Existing methods for counterfactual inference with continuous outcomes aim at…

Machine Learning · Statistics 2024-01-12 Valentyn Melnychuk , Dennis Frauen , Stefan Feuerriegel

An important line of research attempts to explain CNN image classifier predictions and intermediate layer representations in terms of human-understandable concepts. Previous work supports that deep representations are linearly separable…

Computer Vision and Pattern Recognition · Computer Science 2025-09-23 Alexandros Doumanoglou , Stylianos Asteriadis , Dimitrios Zarpalas

As AI models grow more complex, explainability is essential for building trust, yet concept-based counterfactual methods still face a trade-off between expressivity and efficiency. Representing underlying concepts as atomic sets is fast but…

Artificial Intelligence · Computer Science 2026-05-22 Angeliki Dimitriou , Nikolaos Chaidos , Maria Lymperaiou , Giorgos Filandrianos , Giorgos Stamou

Evaluation of counterfactual queries (e.g., "If A were true, would C have been true?") is important to fault diagnosis, planning, determination of liability, and policy analysis. We present a method of revaluating counterfactuals when the…

Artificial Intelligence · Computer Science 2013-02-21 Alexander Balke , Judea Pearl

We consider the problem of estimating the counterfactual joint distribution of multiple quantities of interests (e.g., outcomes) in a multivariate causal model extended from the classical difference-in-difference design. Existing methods…

Machine Learning · Statistics 2023-11-03 Thong Pham , Shohei Shimizu , Hideitsu Hino , Tam Le