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One well motivated explanation method for classifiers leverages counterfactuals which are hypothetical events identical to real observations in all aspects except for one feature. Constructing such counterfactual poses specific challenges…

Machine Learning · Computer Science 2024-09-12 Pirmin Lemberger , Antoine Saillenfest

In this paper, we introduce a variant of optimal transport adapted to the causal structure given by an underlying directed graph $G$. Different graph structures lead to different specifications of the optimal transport problem. For…

Statistics Theory · Mathematics 2024-07-08 Patrick Cheridito , Stephan Eckstein

Counterfactual explanations are widely used to interpret machine learning predictions by identifying minimal changes to input features that would alter a model's decision. However, most existing counterfactual methods have not been tested…

Machine Learning · Computer Science 2026-02-03 Leonidas Christodoulou , Chang Sun

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

Optimal transport has emerged as a fundamental methodology with applications spanning multiple research areas in recent years. However, the convergence rate of the empirical estimator to its population counterpart suffers from the curse of…

Statistics Theory · Mathematics 2025-10-06 Jiaping Yang , Yunxin Zhang

Natural language counterfactual generation aims to minimally modify a given text such that the modified text will be classified into a different class. The generated counterfactuals provide insight into the reasoning behind a model's…

Computation and Language · Computer Science 2024-10-08 Yongjie Wang , Xiaoqi Qiu , Yu Yue , Xu Guo , Zhiwei Zeng , Yuhong Feng , Zhiqi Shen

Nowadays, deep vision models are being widely deployed in safety-critical applications, e.g., autonomous driving, and explainability of such models is becoming a pressing concern. Among explanation methods, counterfactual explanations aim…

Computer Vision and Pattern Recognition · Computer Science 2023-03-27 Mehdi Zemni , Mickaël Chen , Éloi Zablocki , Hédi Ben-Younes , Patrick Pérez , Matthieu Cord

The need to reason about uncertainty in large, complex, and multi-modal datasets has become increasingly common across modern scientific environments. The ability to transform samples from one distribution $P$ to another distribution $Q$…

Machine Learning · Statistics 2018-11-30 Diego A. Mesa , Justin Tantiongloc , Marcela Mendoza , Todd P. Coleman

Classic optimal transport theory is formulated through minimizing the expected transport cost between two given distributions. We propose the framework of distorted optimal transport by minimizing a distorted expected cost, which is the…

Optimization and Control · Mathematics 2025-05-20 Haiyan Liu , Bin Wang , Ruodu Wang , Sheng Chao Zhuang

Natural language explanations of deep neural network decisions provide an intuitive way for a AI agent to articulate a reasoning process. Current textual explanations learn to discuss class discriminative features in an image. However, it…

Computer Vision and Pattern Recognition · Computer Science 2018-06-27 Lisa Anne Hendricks , Ronghang Hu , Trevor Darrell , Zeynep Akata

A novel algorithm is proposed to solve the sample-based optimal transport problem. An adversarial formulation of the push-forward condition uses a test function built as a convolution between an adaptive kernel and an evolving probability…

Machine Learning · Statistics 2020-06-11 Daeyoung Kim , Esteban G. Tabak

Optimal maps, solutions to the optimal transportation problems, are completely determined by the corresponding c-convex potential functions. In this paper, we give simple sufficient conditions for a smooth function to be c-convex when the…

Differential Geometry · Mathematics 2010-06-22 Paul W. Y. Lee

The inverse optimal transport problem is to find the underlying cost function from the knowledge of optimal transport plans. While this amounts to solving a linear inverse problem, in this work we will be concerned with the nonlinear…

Optimization and Control · Mathematics 2025-09-03 Alberto González-Sanz , Michel Groppe , Axel Munk

Being able to provide counterfactual interventions - sequences of actions we would have had to take for a desirable outcome to happen - is essential to explain how to change an unfavourable decision by a black-box machine learning model…

Machine Learning · Computer Science 2023-02-08 Giovanni De Toni , Bruno Lepri , Andrea Passerini

There is a broad consensus on the importance of deep learning models in tasks involving complex data. Often, an adequate understanding of these models is required when focusing on the transparency of decisions in human-critical…

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

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…

As machine learning (ML) models become more widely deployed in high-stakes applications, counterfactual explanations have emerged as key tools for providing actionable model explanations in practice. Despite the growing popularity of…

Machine Learning · Computer Science 2022-12-16 Martin Pawelczyk , Chirag Agarwal , Shalmali Joshi , Sohini Upadhyay , Himabindu Lakkaraju

When an image classifier outputs a wrong class label, it can be helpful to see what changes in the image would lead to a correct classification. This is the aim of algorithms generating counterfactual explanations. However, there is no…

Computer Vision and Pattern Recognition · Computer Science 2021-12-01 Benedikt Höltgen , Lisa Schut , Jan M. Brauner , Yarin Gal

We consider optimal route planning when the objective function is a general nonlinear and non-monotonic function. Such an objective models user behavior more accurately, for example, when a user is risk-averse, or the utility function needs…

Data Structures and Algorithms · Computer Science 2015-11-24 Ger Yang , Evdokia Nikolova