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Difference-in-differences (DID) is one of the most popular tools used to evaluate causal effects of policy interventions. This paper extends the DID methodology to accommodate interval outcomes, which are often encountered in empirical…

Econometrics · Economics 2025-12-10 Daisuke Kurisu , Yuta Okamoto , Taisuke Otsu

We develop a criterion to certify whether causal effects are identifiable in linear structural equation models with latent variables. Linear structural equation models correspond to directed graphs whose nodes represent the random variables…

Statistics Theory · Mathematics 2025-07-25 Nils Sturma , Mathias Drton

We consider linear structural equation models with explicitly modelled latent variables. In such models, observed and latent variables solve linear equations including stochastic noise terms. The goal of our work is to identify the direct…

Methodology · Statistics 2026-05-28 Tom Hochsprung , Nils Sturma , Jakob Runge , Mathias Drton , Andreas Gerhardus

Algorithms for constraint-based causal discovery select graphical causal models among a space of possible candidates (e.g., all directed acyclic graphs) by executing a sequence of conditional independence tests. These may be used to inform…

Methodology · Statistics 2025-09-19 Ting-Hsuan Chang , Zijian Guo , Daniel Malinsky

Causal discovery serves a pivotal role in mitigating model uncertainty through recovering the underlying causal mechanisms among variables. In many practical domains, such as healthcare, access to the data gathered by individual entities is…

Machine Learning · Computer Science 2024-02-13 Amin Abyaneh , Nino Scherrer , Patrick Schwab , Stefan Bauer , Bernhard Schölkopf , Arash Mehrjou

Understanding causal mechanisms across different populations is essential for designing effective public health interventions. Recently, difference graphs have been introduced as a tool to visually represent causal variations between two…

Artificial Intelligence · Computer Science 2025-02-18 Charles K. Assaad

This paper discusses the problem of causal query in observational data with hidden variables, with the aim of seeking the change of an outcome when "manipulating" a variable while given a set of plausible confounding variables which affect…

Artificial Intelligence · Computer Science 2020-11-25 Debo Cheng , Jiuyong Li , Lin Liu , Jixue Liu , Kui Yu , Thuc Duy Le

Differential privacy is a strong mathematical notion of privacy. Still, a prominent challenge when using differential privacy in real data collection is understanding and counteracting the accuracy loss that differential privacy imposes. As…

Cryptography and Security · Computer Science 2021-08-24 Boel Nelson

Unmeasured confounding, unethical exposure, and ill-defined interventions pose significant challenges to evaluating policy-relevant mediation estimands in medicine and public health. In observational studies involving harmful exposures, the…

Methodology · Statistics 2026-05-12 Yang Bai , Yifan Cui , Baoluo Sun

We consider the estimation of average and counterfactual treatment effects, under two settings: back-door adjustment and front-door adjustment. The goal in both cases is to recover the treatment effect without having an access to a hidden…

Machine Learning · Computer Science 2022-10-14 Liyuan Xu , Arthur Gretton

In modern scientific research, the objective is often to identify which variables are associated with an outcome among a large class of potential predictors. This goal can be achieved by selecting variables in a manner that controls the the…

Methodology · Statistics 2023-10-10 Yushu Shi , Michael Martens

Instrumental variable approaches have gained popularity for estimating causal effects in the presence of unmeasured confounders. However, the availability of instrumental variables in the primary dataset is often challenged due to stringent…

Methodology · Statistics 2026-03-31 Kang Shuai , Shanshan Luo , Wei Li , Yangbo He

One of the goals of causal inference is to generalize from past experiments and observational data to novel conditions. While it is in principle possible to eventually learn a mapping from a novel experimental condition to an outcome of…

Machine Learning · Statistics 2023-11-10 Gecia Bravo-Hermsdorff , David S. Watson , Jialin Yu , Jakob Zeitler , Ricardo Silva

Difference-in-differences is one of the most used identification strategies in empirical work in economics. This chapter reviews a number of important, recent developments related to difference-in-differences. First, this chapter reviews…

Econometrics · Economics 2022-08-02 Brantly Callaway

Estimates of heterogeneous treatment assignment effects can inform treatment decisions. Under the presence of non-adherence (e.g., patients do not adhere to their assigned treatment), both the standard backdoor adjustment (SBD) and the…

Machine Learning · Computer Science 2025-07-22 Winston Chen , Trenton Chang , Jenna Wiens

A common theme in causal inference is learning causal relationships between observed variables, also known as causal discovery. This is usually a daunting task, given the large number of candidate causal graphs and the combinatorial nature…

Machine Learning · Statistics 2022-10-11 Romain Lopez , Jan-Christian Hütter , Jonathan K. Pritchard , Aviv Regev

Identifying effects of actions (treatments) on outcome variables from observational data and causal assumptions is a fundamental problem in causal inference. This identification is made difficult by the presence of confounders which can be…

Methodology · Statistics 2012-03-19 Ilya Shpitser , Tyler VanderWeele , James M. Robins

Estimating causal effects from observational data is not always possible due to confounding. Identifying a set of appropriate covariates (adjustment set) and adjusting for their influence can remove confounding bias; however, such a set is…

Methodology · Statistics 2020-11-19 Sofia Triantafillou , Gregory Cooper

Quantifying cause and effect relationships is an important problem in many domains. The gold standard solution is to conduct a randomised controlled trial. However, in many situations such trials cannot be performed. In the absence of such…

Methodology · Statistics 2023-01-19 Jakob Zeitler , Athanasios Vlontzos , Ciaran M. Gilligan-Lee

Pearl's causal hierarchy has garnered sustained attention as a foundational lens for formulating and understanding causal questions, and has been extensively discussed within the framework of structural causal models. In this paper, we…

Other Statistics · Statistics 2026-01-29 Peng Wu , Linbo Wang