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Counterfactual Explanations (CEs) are an important tool in Algorithmic Recourse for addressing two questions: 1. What are the crucial factors that led to an automated prediction/decision? 2. How can these factors be changed to achieve a…

Machine Learning · Computer Science 2023-11-23 Xuan Zhao , Klaus Broelemann , Gjergji Kasneci

Explainable artificial intelligence (XAI) has become increasingly important in decision-critical domains such as healthcare, finance, and law. Counterfactual (CF) explanations, a key approach in XAI, provide users with actionable insights…

Artificial Intelligence · Computer Science 2025-07-22 Volkan Bakir , Polat Goktas , Sureyya Akyuz

We present a new method for counterfactual explanations (CFEs) based on Bayesian optimisation that applies to both classification and regression models. Our method is a globally convergent search algorithm with support for arbitrary…

Machine Learning · Computer Science 2021-06-30 Thomas Spooner , Danial Dervovic , Jason Long , Jon Shepard , Jiahao Chen , Daniele Magazzeni

Counterfactual explanations play an important role in detecting bias and improving the explainability of data-driven classification models. A counterfactual explanation (CE) is a minimal perturbed data point for which the decision of the…

Machine Learning · Computer Science 2023-10-27 Donato Maragno , Jannis Kurtz , Tabea E. Röber , Rob Goedhart , Ş. Ilker Birbil , Dick den Hertog

Counterfactual explanations (CEs) are advocated as being ideally suited to providing algorithmic recourse for subjects affected by the predictions of machine learning models. While CEs can be beneficial to affected individuals, recent work…

Machine Learning · Computer Science 2024-02-06 Junqi Jiang , Francesco Leofante , Antonio Rago , Francesca Toni

Counterfactual explanations describe how to modify a feature vector in order to flip the outcome of a trained classifier. Obtaining robust counterfactual explanations is essential to provide valid algorithmic recourse and meaningful…

Machine Learning · Computer Science 2024-03-22 Alexandre Forel , Axel Parmentier , Thibaut Vidal

Counterfactual explanation is an important Explainable AI technique to explain machine learning predictions. Despite being studied actively, existing optimization-based methods often assume that the underlying machine-learning model is…

Artificial Intelligence · Computer Science 2022-06-01 Wenzhuo Yang , Jia Li , Caiming Xiong , Steven C. H. Hoi

Counterfactual explanations (CEs) provide recourse recommendations for individuals affected by algorithmic decisions. A key challenge is generating CEs that are robust against various perturbation types (e.g. input and model perturbations)…

Machine Learning · Computer Science 2026-03-02 Junqi Jiang , Francesco Leofante , Antonio Rago , Francesca Toni

Counterfactual explanations (CEs) are a powerful means for understanding how decisions made by algorithms can be changed. Researchers have proposed a number of desiderata that CEs should meet to be practically useful, such as requiring…

Machine Learning · Computer Science 2022-09-26 Marco Virgolin , Saverio Fracaros

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

Deep learning has led to tremendous success in computer vision, largely due to Convolutional Neural Networks (CNNs). However, CNNs have been shown to be vulnerable to crafted adversarial perturbations. This vulnerability of adversarial…

Machine Learning · Computer Science 2026-01-21 Hichem Debbi

The concept of counterfactual explanations (CE) has emerged as one of the important concepts to understand the inner workings of complex AI systems. In this paper, we translate the idea of CEs to linear optimization and propose, motivate,…

Optimization and Control · Mathematics 2024-05-27 Jannis Kurtz , Ş. İlker Birbil , Dick den Hertog

Counterfactual explanations offer an intuitive way to interpret graph neural networks (GNNs) by identifying minimal changes that alter a model's prediction, thereby answering "what must differ for a different outcome?". In this work, we…

Machine Learning · Computer Science 2026-02-09 Yu Zhang , Sean Bin Yang , Arijit Khan , Cuneyt Gurcan Akcora

Counterfactual explanations (CEs) offer interpretable insights into machine learning predictions by answering ``what if?" questions. However, in real-world settings where models are frequently updated, existing counterfactual explanations…

Machine Learning · Computer Science 2026-02-12 Jamie Duell , Xiuyi Fan

Counterfactual explanations (CFEs) are essential for interpreting black-box models, yet they often become invalid when models are slightly changed. Existing methods for generating robust CFEs are often limited to specific types of models,…

Machine Learning · Computer Science 2026-04-21 Marcin Kostrzewa , Maciej Zięba , Jerzy Stefanowski

Counterfactual Explanation (CE) techniques have garnered attention as a means to provide insights to the users engaging with AI systems. While extensively researched in domains such as medical imaging and autonomous vehicles, Graph…

Machine Learning · Computer Science 2024-01-12 Mario Alfonso Prado-Romero , Bardh Prenkaj , Giovanni Stilo

Recent work on counterfactual visual explanations has contributed to making artificial intelligence models more explainable by providing visual perturbation to flip the prediction. However, these approaches neglect the causal relationships…

Computer Vision and Pattern Recognition · Computer Science 2025-09-30 Yiran Qiao , Disheng Liu , Yiren Lu , Yu Yin , Mengnan Du , Jing Ma

Gaussian graphical models provide a powerful framework to reveal the conditional dependency structure between multivariate variables. The process of uncovering the conditional dependency network is known as structure learning. Bayesian…

Methodology · Statistics 2024-07-30 Lucas Vogels , Reza Mohammadi , Marit Schoonhoven , S. Ilker Birbil

Visual counterfactual explanation (CF) methods modify image concepts, e.g, shape, to change a prediction to a predefined outcome while closely resembling the original query image. Unlike self-explainable models (SEMs) and heatmap…

Computer Vision and Pattern Recognition · Computer Science 2024-09-20 Anselm Haselhoff , Kevin Trelenberg , Fabian Küppers , Jonas Schneider

Counterfactual explanations have emerged as a prominent method in Explainable Artificial Intelligence (XAI), providing intuitive and actionable insights into Machine Learning model decisions. In contrast to other traditional feature…

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