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Most modern supervised statistical/machine learning (ML) methods are explicitly designed to solve prediction problems very well. Achieving this goal does not imply that these methods automatically deliver good estimators of causal…

Causal machine learning (ML) algorithms recover graphical structures that tell us something about cause-and-effect relationships. The causal representation praovided by these algorithms enables transparency and explainability, which is…

Data augmentation is essential when applying Machine Learning in small-data regimes. It generates new samples following the observed data distribution while increasing their diversity and variability to help researchers and practitioners…

Machine Learning · Computer Science 2023-04-10 Audrey Poinsot , Alessandro Leite

Causal machine learning (ML) recovers graphical structures that inform us about potential cause-and-effect relationships. Most progress has focused on cross-sectional data with no explicit time order, whereas recovering causal structures…

Machine Learning · Computer Science 2026-05-11 Bruno Petrungaro , Anthony C. Constantinou

This Element offers a practical guide to estimating conditional marginal effects-how treatment effects vary with a moderating variable-using modern statistical methods. Commonly used approaches, such as linear interaction models, often…

Methodology · Statistics 2026-05-21 Jiehan Liu , Ziyi Liu , Yiqing Xu

Distributional models provide a convenient way to model semantics using dense embedding spaces derived from unsupervised learning algorithms. However, the dimensions of dense embedding spaces are not designed to resemble human semantic…

Computation and Language · Computer Science 2018-11-15 Steven Derby , Paul Miller , Brian Murphy , Barry Devereux

Continuous treatments (e.g., doses) arise often in practice, but many available causal effect estimators are limited by either requiring parametric models for the effect curve, or by not allowing doubly robust covariate adjustment. We…

Methodology · Statistics 2017-04-21 Edward H. Kennedy , Zongming Ma , Matthew D. McHugh , Dylan S. Small

Causal graphs may inform covariate adjustment for estimating causal effects and improve estimation efficiency by exploiting the graphical structure. In many applications, however, the target causal parameter may not be point-identified due…

Causal inference from observational data is crucial for many disciplines such as medicine and economics. However, sharp bounds for causal effects under relaxations of the unconfoundedness assumption (causal sensitivity analysis) are subject…

Machine Learning · Computer Science 2023-10-17 Dennis Frauen , Valentyn Melnychuk , Stefan Feuerriegel

Causal machine learning (CML) has experienced increasing popularity in healthcare. Beyond the inherent capabilities of adding domain knowledge into learning systems, CML provides a complete toolset for investigating how a system would react…

Machine Learning · Computer Science 2022-06-01 Pedro Sanchez , Jeremy P. Voisey , Tian Xia , Hannah I. Watson , Alison Q. ONeil , Sotirios A. Tsaftaris

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

Massive data collection holds the promise of a better understanding of complex phenomena and, ultimately, better decisions. Representation learning has become a key driver of deep learning applications, as it allows learning latent spaces…

Machine Learning · Computer Science 2025-11-10 Caroline Uhler , Jiaqi Zhang

Existing semi-supervised medical segmentation co-learning frameworks have realized that model performance can be diminished by the biases in model recognition caused by low-quality pseudo-labels. Due to the averaging nature of their…

Image and Video Processing · Electrical Eng. & Systems 2025-05-20 Yuanpeng He , Yali Bi , Lijian Li , Chi-Man Pun , Wenpin Jiao , Zhi Jin

Predicting the effect of unseen interventions is a fundamental research question across the data sciences. It is well established that in general such questions cannot be answered definitively from observational data. This realization has…

Machine Learning · Statistics 2024-05-27 Alexis Bellot

This paper considers the evaluation of discretely distributed treatments when outcomes are only observed for a subpopulation due to sample selection or outcome attrition. For identification, we combine a selection-on-observables assumption…

Econometrics · Economics 2021-07-16 Michela Bia , Martin Huber , Lukáš Lafférs

Deep learning (DL) has recently drawn much attention in image analysis, natural language process, and high-dimensional medical data analysis. Under the causal direct acyclic graph (DAG) interpretation, the input variables without incoming…

Applications · Statistics 2022-03-22 Jong-Hyeon Jeong , Yichen Jia

Causal inference has received great attention across different fields from economics, statistics, education, medicine, to machine learning. Within this area, inferring causal effects at individual level in observational studies has become…

Methodology · Statistics 2017-02-16 Thai Pham

Medical image analysis is a vibrant research area that offers doctors and medical practitioners invaluable insight and the ability to accurately diagnose and monitor disease. Machine learning provides an additional boost for this area.…

Computer Vision and Pattern Recognition · Computer Science 2022-11-29 Athanasios Vlontzos , Daniel Rueckert , Bernhard Kainz

Graphical causal models are an important tool for knowledge discovery because they can represent both the causal relations between variables and the multivariate probability distributions over the data. Once learned, causal graphs can be…

Artificial Intelligence · Computer Science 2017-04-11 Andrew J Sedgewick , Joseph D. Ramsey , Peter Spirtes , Clark Glymour , Panayiotis V. Benos

In this paper we review important aspects of semiparametric theory and empirical processes that arise in causal inference problems. We begin with a brief introduction to the general problem of causal inference, and go on to discuss…

Statistics Theory · Mathematics 2016-07-25 Edward H. Kennedy