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In observational studies, treatment may be adapted to covariates at several times without a fixed protocol, in continuous time. Treatment influences covariates, which influence treatment, which influences covariates, and so on. Then even…

Statistics Theory · Mathematics 2015-09-02 Judith J. Lok

Causal inference from observational data following the restricted structural causal models (SCM) framework hinges largely on the asymmetry between cause and effect from the data generating mechanisms, such as non-Gaussianity or…

Machine Learning · Computer Science 2024-05-30 Kang Du , Yu Xiang

We consider the problem of causal inference based on observational data (or the related missing data problem) with a binary or discrete treatment variable. In that context, we study inference for the counterfactual density functions and…

Methodology · Statistics 2024-12-13 Daeyoung Ham , Ted Westling , Charles R. Doss

Counterfactual thinking is a crucial yet challenging topic for artificial intelligence to learn knowledge from data and ultimately improve performance for new scenarios. Many research works, including the Potential Outcome Model (POM) and…

Artificial Intelligence · Computer Science 2026-02-24 Mingyu Kang , Duxin Chen , Ziyuan Pu , Jianxi Gao , Wenwu Yu

Parametric causal modelling techniques rarely provide functionality for counterfactual estimation, often at the expense of modelling complexity. Since causal estimations depend on the family of functions used to model the data, simplistic…

Machine Learning · Statistics 2020-06-16 Álvaro Parafita , Jordi Vitrià

Developing reliable and generalizable deep learning systems for medical imaging faces significant obstacles due to spurious correlations, data imbalances, and limited text annotations in datasets. Addressing these challenges requires…

Computer Vision and Pattern Recognition · Computer Science 2025-07-23 Amar Kumar , Anita Kriz , Mohammad Havaei , Tal Arbel

Comparing counterfactual distributions can provide more nuanced and valuable measures for causal effects, going beyond typical summary statistics such as averages. In this work, we consider characterizing causal effects via distributional…

Machine Learning · Statistics 2024-11-05 Kwangho Kim , Jisu Kim , Edward H. Kennedy

An important problem in econometrics and marketing is to infer the causal impact that a designed market intervention has exerted on an outcome metric over time. This paper proposes to infer causal impact on the basis of a…

Applications · Statistics 2015-06-02 Kay H. Brodersen , Fabian Gallusser , Jim Koehler , Nicolas Remy , Steven L. Scott

A structural causal model is made of endogenous (manifest) and exogenous (latent) variables. We show that endogenous observations induce linear constraints on the probabilities of the exogenous variables. This allows to exactly map a causal…

Artificial Intelligence · Computer Science 2020-08-04 Marco Zaffalon , Alessandro Antonucci , Rafael Cabañas

Judea Pearl's vision of Structural Causal Models (SCMs) as engines for counterfactual reasoning hinges on faithful abduction: the precise inference of latent exogenous noise. For decades, operationalizing this step for complex, non-linear…

Machine Learning · Computer Science 2025-11-10 Rui Wu , Lizheng Wang , Yongjun Li

Most counterfactual inference frameworks traditionally assume acyclic structural causal models (SCMs), i.e. directed acyclic graphs (DAGs). However, many real-world systems (e.g. biological systems) contain feedback loops or cyclic…

Artificial Intelligence · Computer Science 2026-01-21 Saptarshi Saha , Dhruv Vansraj Rathore , Utpal Garain

The notion of causality assumes a paramount position within the realm of human cognition. Over the past few decades, there has been significant advancement in the domain of causal effect estimation across various disciplines, including but…

Machine Learning · Statistics 2024-05-24 Zongyu Li , Xiaobo Guo , Siwei Qiang

The number of samples in structural brain MRI studies is often too small to properly train deep learning models. Generative models show promise in addressing this issue by effectively learning the data distribution and generating…

Computer Vision and Pattern Recognition · Computer Science 2026-03-20 Wei Peng , Tian Xia , Fabio De Sousa Ribeiro , Tomas Bosschieter , Ehsan Adeli , Qingyu Zhao , Ben Glocker , Kilian M. Pohl

Counterfactual explanations utilize feature perturbations to analyze the outcome of an original decision and recommend an actionable recourse. We argue that it is beneficial to provide several alternative explanations rather than a single…

Machine Learning · Computer Science 2023-01-24 Natraj Raman , Daniele Magazzeni , Sameena Shah

Diffusion models offer stable training and state-of-the-art performance for deep generative modeling tasks. Here, we consider their use in the context of multivariate subsurface modeling and probabilistic inversion. We first demonstrate…

Computer Vision and Pattern Recognition · Computer Science 2026-01-28 Roberto Miele , Niklas Linde

We address the problem of integrating data from multiple, possibly biased, observational and interventional studies, to eventually compute counterfactuals in structural causal models. We start from the case of a single observational dataset…

Methodology · Statistics 2023-08-01 Marco Zaffalon , Alessandro Antonucci , Rafael Cabañas , David Huber

Counterfactual image editing is an important task in generative AI, which asks how an image would look if certain features were different. The current literature on the topic focuses primarily on changing individual features while remaining…

Computer Vision and Pattern Recognition · Computer Science 2024-03-18 Yushu Pan , Elias Bareinboim

Shortcut learning is when a model -- e.g. a cardiac disease classifier -- exploits correlations between the target label and a spurious shortcut feature, e.g. a pacemaker, to predict the target label based on the shortcut rather than real…

Computer Vision and Pattern Recognition · Computer Science 2024-07-18 Nina Weng , Paraskevas Pegios , Eike Petersen , Aasa Feragen , Siavash Bigdeli

We present a conditional diffusion model - ConDiSim, for simulation-based inference of complex systems with intractable likelihoods. ConDiSim leverages denoising diffusion probabilistic models to approximate posterior distributions,…

Machine Learning · Computer Science 2025-10-17 Mayank Nautiyal , Andreas Hellander , Prashant Singh

The discovery of patient-specific imaging markers that are predictive of future disease outcomes can help us better understand individual-level heterogeneity of disease evolution. In fact, deep learning models that can provide data-driven…

Computer Vision and Pattern Recognition · Computer Science 2022-08-05 Amar Kumar , Anjun Hu , Brennan Nichyporuk , Jean-Pierre R. Falet , Douglas L. Arnold , Sotirios Tsaftaris , Tal Arbel