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Random directed acyclic graphs (DAGs) based on imposing an order on Erd\H{o}s-R\'enyi and scale free random graphs are widely used for evaluating causal discovery algorithms. We show that in such DAGs, the set of nodes reachable via open…

Methodology · Statistics 2026-05-08 Alexander G. Reisach , Antoine Chambaz , Gilles Blanchard , Sebastian Weichwald

It is known that from purely observational data, a causal DAG is identifiable only up to its Markov equivalence class, and for many ground truth DAGs, the direction of a large portion of the edges will be remained unidentified. The golden…

Machine Learning · Computer Science 2019-10-15 AmirEmad Ghassami , Saber Salehkaleybar , Negar Kiyavash

Causal structure learning from observational data remains a non-trivial task due to various factors such as finite sampling, unobserved confounding factors, and measurement errors. Constraint-based and score-based methods tend to suffer…

Machine Learning · Computer Science 2022-11-09 Rezaur Rashid , Jawad Chowdhury , Gabriel Terejanu

We consider structural equation models in which variables can be written as a function of their parents and noise terms, which are assumed to be jointly independent. Corresponding to each structural equation model, there is a directed…

Machine Learning · Statistics 2014-06-03 Jonas Peters , Peter Bühlmann

Fair machine learning aims to avoid treating individuals or sub-populations unfavourably based on \textit{sensitive attributes}, such as gender and race. Those methods in fair machine learning that are built on causal inference ascertain…

Machine Learning · Computer Science 2023-01-18 Aoqi Zuo , Susan Wei , Tongliang Liu , Bo Han , Kun Zhang , Mingming Gong

Learning DAG structures from purely observational data remains a long-standing challenge across scientific domains. An emerging line of research leverages the score of the data distribution to initially identify a topological order of the…

Machine Learning · Computer Science 2026-01-27 Vy Vo , He Zhao , Trung Le , Edwin V. Bonilla , Dinh Phung

Causal discovery is a fundamental problem with applications spanning various areas in science and engineering. It is well understood that solely using observational data, one can only orient the causal graph up to its Markov equivalence…

Machine Learning · Computer Science 2024-10-29 Zihan Zhou , Muhammad Qasim Elahi , Murat Kocaoglu

We consider identifying a conditional causal effect when a graph is known up to a maximally oriented partially directed acyclic graph (MPDAG). An MPDAG represents an equivalence class of graphs that is restricted by background knowledge and…

Artificial Intelligence · Computer Science 2025-07-22 Sara LaPlante , Emilija Perković

We introduce a novel class of labeled directed acyclic graph (LDAG) models for finite sets of discrete variables. LDAGs generalize earlier proposals for allowing local structures in the conditional probability distribution of a node, such…

Machine Learning · Statistics 2014-11-12 Johan Pensar , Henrik Nyman , Timo Koski , Jukka Corander

Causal processes in biomedicine may contain cycles, evolve over time or differ between populations. However, many graphical models cannot accommodate these conditions. We propose to model causation using a mixture of directed cyclic graphs…

Machine Learning · Statistics 2020-09-08 Eric V. Strobl

Structural causal models postulate noisy functional relations among a set of interacting variables. The causal structure underlying each such model is naturally represented by a directed graph whose edges indicate for each variable which…

Statistics Theory · Mathematics 2022-03-15 David Strieder , Tobias Freidling , Stefan Haffner , Mathias Drton

Causal discovery from multivariate time series is challenging when causal effects may occur both across time and within the same sampling interval. This issue is especially important in applications such as neuroscience, where the sampling…

Methodology · Statistics 2026-05-22 SeyedSina Seyedi HasanAbadi , Fahimeh Arab , Erfan Nozari , AmirEmad Ghassami

Observational causal discovery is only identifiable up to the Markov equivalence class. While interventions can reduce this ambiguity, in practice interventions are often soft with multiple unknown targets. In many realistic scenarios, only…

Machine Learning · Statistics 2026-03-05 Mingxuan Zhang , Khushi Desai , Sopho Kevlishvili , Elham Azizi

Assessing the accuracy of the output of causal discovery algorithms is crucial in developing and comparing novel methods. Common evaluation metrics such as the structural Hamming distance are useful for assessing individual links of causal…

Methodology · Statistics 2025-04-07 Jonas Wahl , Jakob Runge

Graphical models based on Directed Acyclic Graphs (DAGs) are widely used to answer causal questions across a variety of scientific and social disciplines. However, observational data alone cannot distinguish in general between DAGs…

Methodology · Statistics 2022-06-03 Federico Castelletti , Guido Consonni

Graph-based causal discovery methods aim to capture conditional independencies consistent with the observed data and differentiate causal relationships from indirect or induced ones. Successful construction of graphical models of data…

Machine Learning · Statistics 2021-01-08 Boris Hayete , Fred Gruber , Anna Decker , Raymond Yan

Discovering the causal relationship via recovering the directed acyclic graph (DAG) structure from the observed data is a well-known challenging combinatorial problem. When there are latent variables, the problem becomes even more…

Machine Learning · Statistics 2023-11-02 Yunfeng Cai , Xu Li , Minging Sun , Ping Li

If $X,Y,Z$ denote sets of random variables, two different data sources may contain samples from $P_{X,Y}$ and $P_{Y,Z}$, respectively. We argue that causal discovery can help inferring properties of the `unobserved joint distributions'…

Machine Learning · Statistics 2023-05-12 Dominik Janzing , Philipp M. Faller , Leena Chennuru Vankadara

Directed graphical models provide a useful framework for modeling causal or directional relationships for multivariate data. Prior work has largely focused on identifiability and search algorithms for directed acyclic graphical (DAG)…

Machine Learning · Statistics 2016-07-07 Gunwoong Park , Garvesh Raskutti

Causal discovery from observational data is a challenging task that can only be solved up to a set of equivalent solutions, called an equivalence class. Such classes, which are often large in size, encode uncertainties about the orientation…

Machine Learning · Computer Science 2022-03-01 Philippe Brouillard , Perouz Taslakian , Alexandre Lacoste , Sebastien Lachapelle , Alexandre Drouin
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