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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

The capacity to address counterfactual "what if" inquiries is crucial for understanding and making use of causal influences. Traditional counterfactual inference, under Pearls' counterfactual framework, typically depends on having access to…

Machine Learning · Computer Science 2024-02-29 Shaoan Xie , Biwei Huang , Bin Gu , Tongliang Liu , Kun Zhang

Counterfactual explanations have been a popular method of post-hoc explainability for a variety of settings in Machine Learning. Such methods focus on explaining classifiers by generating new data points that are similar to a given…

Machine Learning · Computer Science 2024-10-21 Joshua Nathaniel Williams , Anurag Katakkar , Hoda Heidari , J. Zico Kolter

One of the main concerns while deploying machine learning models in real-world applications is fairness. Counterfactual fairness has emerged as an intuitive and natural definition of fairness. However, existing methodologies for enforcing…

Machine Learning · Computer Science 2025-09-08 Krishn Vishwas Kher , Saksham Mittal , Aditya Varun , Shantanu Das , SakethaNath Jagarlapudi

Estimating the kernel mean in a reproducing kernel Hilbert space is a critical component in many kernel learning algorithms. Given a finite sample, the standard estimate of the target kernel mean is the empirical average. Previous works…

Machine Learning · Computer Science 2021-07-13 Xiaobo Xia , Shuo Shan , Mingming Gong , Nannan Wang , Fei Gao , Haikun Wei , Tongliang Liu

While methods for measuring and correcting differential performance in risk prediction models have proliferated in recent years, most existing techniques can only be used to assess fairness across relatively large subgroups. The purpose of…

Methodology · Statistics 2024-01-30 Solvejg Wastvedt , Jared D Huling , Julian Wolfson

Counterfactual explanations have been successfully applied to create human interpretable explanations for various black-box models. They are handy for tasks in the image domain, where the quality of the explanations benefits from recent…

Machine Learning · Computer Science 2025-03-27 Trung Duc Ha , Sidney Bender

A Hilbert space embedding for probability measures has recently been proposed, with applications including dimensionality reduction, homogeneity testing, and independence testing. This embedding represents any probability measure as a mean…

We introduce new inference procedures for counterfactual and synthetic control methods for policy evaluation. We recast the causal inference problem as a counterfactual prediction and a structural breaks testing problem. This allows us to…

Econometrics · Economics 2022-01-26 Victor Chernozhukov , Kaspar Wüthrich , Yinchu Zhu

Answering counterfactual queries has important applications such as explainability, robustness, and fairness but is challenging when the causal variables are unobserved and the observations are non-linear mixtures of these latent variables,…

Machine Learning · Computer Science 2024-04-16 Zeyu Zhou , Ruqi Bai , Sean Kulinski , Murat Kocaoglu , David I. Inouye

Machine learning models that operate on graph-structured data, such as molecular graphs or social networks, often make accurate predictions but offer little insight into why certain predictions are made. Counterfactual explanations address…

Machine Learning · Computer Science 2025-11-21 David Bechtoldt , Sidney Bender

Representing, comparing, and measuring the distance between probability distributions is a key task in computational statistics and machine learning. The choice of representation and the associated distance determine properties of the…

Machine Learning · Statistics 2026-02-26 Masha Naslidnyk

The development of causal prediction models is challenged by the fact that the outcome is only observable for the applied (factual) intervention and not for its alternatives (the so-called counterfactuals); in medicine we only know…

Machine Learning · Computer Science 2023-11-29 Stefan Schrod , Fabian Sinz , Michael Altenbuchinger

Counterfactual explanations (CFE) are being widely used to explain algorithmic decisions, especially in consequential decision-making contexts (e.g., loan approval or pretrial bail). In this context, CFEs aim to provide individuals affected…

Machine Learning · Computer Science 2021-02-09 Kiarash Mohammadi , Amir-Hossein Karimi , Gilles Barthe , Isabel Valera

The linear conditional expectation (LCE) provides a best linear (or rather, affine) estimate of the conditional expectation and hence plays an important r\^ole in approximate Bayesian inference, especially the Bayes linear approach. This…

Statistics Theory · Mathematics 2021-08-26 Ilja Klebanov , Björn Sprungk , T. J. Sullivan

Linear Mixed Effects (LME) models have been widely applied in clustered data analysis in many areas including marketing research, clinical trials, and biomedical studies. Inference can be conducted using maximum likelihood approach if…

Methodology · Statistics 2022-11-10 Hao Chen , Lanshan Han , Alvin Lim

This study proposes median consensus embedding (MCE) to address variability in low-dimensional embeddings caused by random initialization in nonlinear dimensionality reduction techniques such as $t$-distributed stochastic neighbor…

Machine Learning · Statistics 2025-12-10 Yui Tomo , Daisuke Yoneoka

We study the problem of model selection in causal inference, specifically for conditional average treatment effect (CATE) estimation. Unlike machine learning, there is no perfect analogue of cross-validation for model selection as we do not…

Machine Learning · Computer Science 2024-04-30 Divyat Mahajan , Ioannis Mitliagkas , Brady Neal , Vasilis Syrgkanis

Adaptive experiments improve efficiency by adjusting treatment assignments based on past outcomes, but this adaptivity breaks the i.i.d.\ assumptions that underpin classical asymptotics. At the same time, many questions of interest are…

Machine Learning · Statistics 2026-05-05 Houssam Zenati , Bariscan Bozkurt , Arthur Gretton

We mathematically axiomatise the stochastics of counterfactuals, by introducing two related frameworks, called counterfactual probability spaces and counterfactual causal spaces, which we collectively term counterfactual spaces. They are,…

Statistics Theory · Mathematics 2026-01-05 Junhyung Park , Fanny Yang , Thomas Icard