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Due to the increasing use of machine learning in practice it becomes more and more important to be able to explain the prediction and behavior of machine learning models. An instance of explanations are counterfactual explanations which…

Machine Learning · Computer Science 2019-11-19 André Artelt , Barbara Hammer

Trust in counterfactual explanations depends critically on whether their recommended changes are truly minimal: suboptimal explanations may vastly overshoot the actual changes needed to alter a decision, and heuristic errors can affect…

Machine Learning · Computer Science 2026-05-08 Awa Khouna , Youssouf Emine , Julien Ferry , Thibaut Vidal

This paper proposes an iterative inference algorithm for multi-hop explanation regeneration, that retrieves relevant factual evidence in the form of text snippets, given a natural language question and its answer. Combining multiple sources…

Information Retrieval · Computer Science 2020-12-22 Ruben Cartuyvels , Graham Spinks , Marie-Francine Moens

In the field of Explainable Artificial Intelligence (XAI), counterfactual examples explain to a user the predictions of a trained decision model by indicating the modifications to be made to the instance so as to change its associated…

Artificial Intelligence · Computer Science 2023-05-11 Thibault Laugel , Adulam Jeyasothy , Marie-Jeanne Lesot , Christophe Marsala , Marcin Detyniecki

Counterfactual explanations (CEs) offer a human-understandable way to explain decisions by identifying specific changes to the input parameters of a base or present model that would lead to a desired change in the outcome. For optimization…

Optimization and Control · Mathematics 2026-01-06 Felix Engelhardt , Jannis Kurtz , Ş. İlker Birbil , Ted Ralphs

In eXplainable Artificial Intelligence (XAI), several counterfactual explainers have been proposed, each focusing on some desirable properties of counterfactual instances: minimality, actionability, stability, diversity, plausibility,…

Artificial Intelligence · Computer Science 2023-08-30 Riccardo Guidotti , Salvatore Ruggieri

Counterfactual explanations are usually obtained by identifying the smallest change made to an input to change a prediction made by a fixed model (hereafter called sparse methods). Recent work, however, has revitalized an old insight: there…

Machine Learning · Computer Science 2020-06-24 Martin Pawelczyk , Klaus Broelemann , Gjergji Kasneci

Counterfactual explanations are one of the most popular methods to make predictions of black box machine learning models interpretable by providing explanations in the form of `what-if scenarios'. Most current approaches optimize a…

Machine Learning · Statistics 2020-10-16 Susanne Dandl , Christoph Molnar , Martin Binder , Bernd Bischl

Counterfactual explanations provide a potentially significant solution to the Explainable AI (XAI) problem, but good, native counterfactuals have been shown to rarely occur in most datasets. Hence, the most popular methods generate…

Artificial Intelligence · Computer Science 2021-01-25 Barry Smyth , Mark T Keane

Multi-objective integer or mixed-integer programming problems typically have disconnected feasible domains, making the task of constructing an approximation of the Pareto front challenging. The present paper shows that certain algorithms…

Optimization and Control · Mathematics 2021-05-25 Regina S. Burachik , C. Yalçın Kaya , M. Mustafa Rizvi

We prove that any mixed-integer linear extended formulation for the matching polytope of the complete graph on $n$ vertices, with a polynomial number of constraints, requires $\Omega(\sqrt{\sfrac{n}{\log n}})$ many integer variables. By…

Optimization and Control · Mathematics 2022-06-27 Robert Hildebrand , Robert Weismantel , Rico Zenklusen

This is a survey on the computational complexity of nonlinear mixed-integer optimization. It highlights a selection of important topics, ranging from incomputability results that arise from number theory and logic, to recently obtained…

Optimization and Control · Mathematics 2010-06-28 Matthias Köppe

Post-hoc explanations of machine learning models are crucial for people to understand and act on algorithmic predictions. An intriguing class of explanations is through counterfactuals, hypothetical examples that show people how to obtain a…

Machine Learning · Computer Science 2019-12-09 Ramaravind Kommiya Mothilal , Amit Sharma , Chenhao Tan

Following the recent push for trustworthy AI, there has been an increasing interest in developing contrastive explanation techniques for optimisation, especially concerning the solution of specific decision-making processes formalised as…

Artificial Intelligence · Computer Science 2025-07-18 Roger Xavier Lera-Leri , Filippo Bistaffa , Athina Georgara , Juan Antonio Rodriguez-Aguilar

In recent years, various machine and deep learning architectures have been successfully introduced to the field of predictive process analytics. Nevertheless, the inherent opacity of these algorithms poses a significant challenge for human…

Artificial Intelligence · Computer Science 2024-03-15 Alexander Stevens , Chun Ouyang , Johannes De Smedt , Catarina Moreira

Counterfactual explanations are emerging as an attractive option for providing recourse to individuals adversely impacted by algorithmic decisions. As they are deployed in critical applications (e.g. law enforcement, financial lending), it…

Machine Learning · Computer Science 2021-11-05 Dylan Slack , Sophie Hilgard , Himabindu Lakkaraju , Sameer Singh

Existing algorithms for generating Counterfactual Explanations (CXs) for Machine Learning (ML) typically assume fully specified inputs. However, real-world data often contains missing values, and the impact of these incomplete inputs on the…

Artificial Intelligence · Computer Science 2026-04-10 Francesco Leofante , Daniel Neider , Mustafa Yalçıner

Counterfactual explanations (CFXs) provide human-understandable justifications for model predictions, enabling actionable recourse and enhancing interpretability. To be reliable, CFXs must avoid regions of high predictive uncertainty, where…

Machine Learning · Computer Science 2025-10-24 Aman Bilkhoo , Mehran Hosseini , Milad Kazemi , Nicola Paoletti

Deep Learning systems excel in complex tasks but often lack transparency, limiting their use in critical applications. Counterfactual explanations, a core tool within eXplainable Artificial Intelligence (XAI), offer insights into model…

Neural and Evolutionary Computing · Computer Science 2025-06-11 Mario Refoyo , David Luengo

We consider the disjoint bilinear programming problem in which one of the disjoint subsets has the structure of an acute-angled polytope. An optimality criterion for such a problem is formulated and proved, and based on this, a polynomial…

Optimization and Control · Mathematics 2025-02-13 Dmitrii Lozovanu