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Counterfactual explanations constitute among the most popular methods for analyzing black-box systems since they can recommend cost-efficient and actionable changes to the input of a system to obtain the desired system output. While most of…

Machine Learning · Computer Science 2024-05-22 André Artelt , Andreas Gregoriades

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

The need to explain decisions made by AI systems is driven by both recent regulation and user demand. The decisions are often explainable only post hoc. In counterfactual explanations, one may ask what constitutes the best counterfactual…

Artificial Intelligence · Computer Science 2025-06-12 Jiri Nemecek , Tomas Pevny , Jakub Marecek

Predictive models are being increasingly used to support consequential decision making at the individual level in contexts such as pretrial bail and loan approval. As a result, there is increasing social and legal pressure to provide…

Machine Learning · Computer Science 2020-03-02 Amir-Hossein Karimi , Gilles Barthe , Borja Balle , Isabel Valera

This paper proposes new search algorithms for counterfactual explanations based upon mixed integer programming. We are concerned with complex data in which variables may take any value from a contiguous range or an additional set of…

Machine Learning · Computer Science 2019-01-16 Chris Russell

Counterfactuals operationalised through algorithmic recourse have become a powerful tool to make artificial intelligence systems explainable. Conceptually, given an individual classified as y -- the factual -- we seek actions such that…

Counterfactual explanations are viewed as an effective way to explain machine learning predictions. This interest is reflected by a relatively young literature with already dozens of algorithms aiming to generate such explanations. These…

Machine Learning · Computer Science 2022-12-05 Raphael Mazzine , David Martens

We present a sublinear query algorithm for outputting a near-optimal low-rank approximation to any positive semidefinite Toeplitz matrix $T \in \mathbb{R}^{d \times d}$. In particular, for any integer rank $k \leq d$ and $\epsilon,\delta >…

Data Structures and Algorithms · Computer Science 2022-11-22 Michael Kapralov , Hannah Lawrence , Mikhail Makarov , Cameron Musco , Kshiteej Sheth

Counterfactual explanations (CFE) are methods that explain a machine learning model by giving an alternate class prediction of a data point with some minimal changes in its features. It helps the users to identify their data attributes that…

Artificial Intelligence · Computer Science 2023-12-01 Shashank Shekhar , Asif Salim , Adesh Bansode , Vivaswan Jinturkar , Anirudha Nayak

We consider counterfactual explanations, the problem of minimally adjusting features in a source input instance so that it is classified as a target class under a given classifier. This has become a topic of recent interest as a way to…

Machine Learning · Computer Science 2021-03-02 Miguel Á. Carreira-Perpiñán , Suryabhan Singh Hada

We study the query complexity of min-max optimization of a nonconvex-nonconcave function $f$ over $[0,1]^d \times [0,1]^d$. We show that, given oracle access to $f$ and to its gradient $\nabla f$, any algorithm that finds an…

Data Structures and Algorithms · Computer Science 2026-05-14 Martino Bernasconi , Matteo Castiglioni , Andrea Celli , Alexandros Hollender

Motivated by the need to efficiently identify multiple candidates in high trial-and-error cost tasks such as drug discovery, we propose a near-optimal algorithm to identify all {\epsilon}-best arms (i.e., those at most {\epsilon} worse than…

Machine Learning · Statistics 2025-10-02 Zhekai Li , Tianyi Ma , Cheng Hua , Ruihao Zhu

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

The problem of minimizing the maximum of $N$ convex, Lipschitz functions plays significant roles in optimization and machine learning. It has a series of results, with the most recent one requiring $O(N\epsilon^{-2/3} + \epsilon^{-8/3})$…

Quantum Physics · Physics 2024-02-21 Hao Wang , Chenyi Zhang , Tongyang Li

Consider a generalization of the classical binary search problem in linearly sorted data to the graph-theoretic setting. The goal is to design an adaptive query algorithm, called a strategy, that identifies an initially unknown target…

Data Structures and Algorithms · Computer Science 2020-05-04 Dariusz Dereniowski , Aleksander Łukasiewicz , Przemysław Uznański

Machine learning is increasingly applied in high-stakes decision making that directly affect people's lives, and this leads to an increased demand for systems to explain their decisions. Explanations often take the form of counterfactuals,…

Machine Learning · Computer Science 2021-05-20 Maximilian Schleich , Zixuan Geng , Yihong Zhang , Dan Suciu

This paper investigates the problem of bounding counterfactual queries from an arbitrary collection of observational and experimental distributions and qualitative knowledge about the underlying data-generating model represented in the form…

Artificial Intelligence · Computer Science 2021-10-13 Junzhe Zhang , Jin Tian , Elias Bareinboim

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

Whenever a clinician reflects on the efficacy of a sequence of treatment decisions for a patient, they may try to identify critical time steps where, had they made different decisions, the patient's health would have improved. While recent…

Machine Learning · Computer Science 2023-11-07 Stratis Tsirtsis , Manuel Gomez-Rodriguez

The extended L\"uroth's Theorem says that if the transcendence degree of $\KK(\mathsf{f}_1,\dots,\mathsf{f}_m)/\KK$ is 1 then there exists $f \in \KK(\underline{X})$ such that $\KK(\mathsf{f}_1,\dots,\mathsf{f}_m)$ is equal to $\KK(f)$. In…

Symbolic Computation · Computer Science 2011-11-08 Guillaume Chèze