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Characterizing and Learning Equivalence Classes of Causal DAGs under Interventions [article]

Karren D. Yang, Abigail Katcoff, Caroline Uhler
2019 arXiv   pre-print
We consider the problem of learning causal DAGs in the setting where both observational and interventional data is available.  ...  Hauser and B\"uhlmann (2012) previously characterized the identifiability of causal DAGs under perfect interventions, which eliminate dependencies between targeted variables and their direct causes.  ...  Caroline Uhler was partially supported by NSF (DMS-1651995), ONR (N00014-17-1-2147), and a Sloan Fellowship.  ... 
arXiv:1802.06310v3 fatcat:zdfhekfwo5aedm6kf2ueiqagoy

Causal Structure Learning: a Combinatorial Perspective [article]

Chandler Squires, Caroline Uhler
2022 arXiv   pre-print
Second, we discuss the structure of equivalence classes over causal graphs, i.e., sets of graphs which represent what can be learned from observational data alone, and how these equivalence classes can  ...  In particular, we focus on approaches for learning directed acyclic graphs (DAGs) and various generalizations which allow for some variables to be unobserved in the available data.  ...  Caroline Uhler was partially supported by NSF (DMS-1651995), ONR (N00014-17-1-2147 and N00014-22-1-2116), the MIT-IBM Watson AI Lab, MIT J-Clinic for Machine Learning and Health, the Eric and Wendy Schmidt  ... 
arXiv:2206.01152v1 fatcat:k7bha6htu5cwlmhh2haquuja7m

Perturbations and Causality in Gaussian Latent Variable Models [article]

Armeen Taeb, Juan L. Gamella, Christina Heinze-Deml, Peter Bühlmann
2022 arXiv   pre-print
Furthermore, under certain structural assumptions on the population model, we provide a simple graphical characterization of all the DAGs in the interventional equivalence class.  ...  Specifically, we propose a maximum-likelihood estimator in a structural equation model that exploits system-wide invariances to output an equivalence class of causal structures from perturbation data.  ...  Proposition 4 (Equivalence class characterization under incoherent latent effects).  ... 
arXiv:2101.06950v3 fatcat:oguoniey2zdwrkwregh3nusly4

Permutation-Based Causal Structure Learning with Unknown Intervention Targets [article]

Chandler Squires, Yuhao Wang, Caroline Uhler
2020 arXiv   pre-print
We characterize the interventional Markov equivalence class of DAGs that can be identified from interventional data with unknown intervention targets.  ...  We consider the problem of estimating causal DAG models from a mix of observational and interventional data, when the intervention targets are partially or completely unknown.  ...  We thank the reviewers of an early version of this paper for pointing out the connection of our algorithm to Joint Causal Inference , which we used to obtain simplified proofs of our results.  ... 
arXiv:1910.09007v2 fatcat:a3eta6lnu5gpxdla2x6p6eqho4

A Bayesian Active Learning Experimental Design for Inferring Signaling Networks

Robert O. Ness, Karen Sachs, Parag Mallick, Olga Vitek
2018 Journal of Computational Biology  
To learn the causal patterns of influence between proteins in a regulatory network, the methods require experiments that include targeted interventions.  ...  However, the interventions are costly, have varying availability and effectiveness, and add complexity and cost. We describe a Bayesian active learning strategy for selecting optimal interventions.  ...  This work was supported in part by the NSF CAREER award DBI-1054826, and by the Sy and Laurie Sternberg award to OV.  ... 
doi:10.1089/cmb.2017.0247 pmid:29927613 fatcat:humwqmytfbexze3weng2pejvxi

Structural learning and estimation of joint causal effects among network-dependent variables

Federico Castelletti, Alessandro Mascaro
2021 Statistical Methods & Applications  
We propose a Bayesian methodology which combines structural learning of Gaussian DAG models and inference of causal effects as arising from simultaneous interventions on any given set of variables in the  ...  In addition, when equipped with the notion of intervention, a causal DAG model can be adopted to quantify the causal effect on a response due to a hypothetical intervention on some variable.  ...  Accordingly, a frequentist approach would estimate first an equivalence class of DAGs using observational data and then a set of DAG-dependent causal effects within the class.  ... 
doi:10.1007/s10260-021-00579-1 fatcat:fnvjdtrnqjcx5iz56tcgixlbau

Two optimal strategies for active learning of causal models from interventional data

Alain Hauser, Peter Bühlmann
2014 International Journal of Approximate Reasoning  
From observational data alone, a causal DAG is only identifiable up to Markov equivalence.  ...  In a simulation study, we compare our two active learning approaches to random interventions and an existing approach, and analyze the influence of estimation errors on the overall performance of active  ...  Acknowledgements We thank Jonas Peters, Frederick Eberhardt and the anonymous reviewers for valuable comments on the manuscript.  ... 
doi:10.1016/j.ijar.2013.11.007 fatcat:lyj4pglrwbcf7imkr6h7dxsjse

Distributional Invariances and Interventional Markov Equivalence for Mixed Graph Models [article]

Liam Solus
2020 arXiv   pre-print
The invariance properties of interventional distributions relative to the observational distribution, and how these properties allow us to refine Markov equivalence classes (MECs) of DAGs, is central to  ...  causal DAG discovery algorithms that use both interventional and observational data.  ...  Katcoff, and C. Uhler. Characterizing and learning equivalence classes of causal dags under interventions. 27] H. Zhao, Z. Zheng, and B. Liu. On the markov equivalence of maximal ancestral graphs.  ... 
arXiv:1911.10114v2 fatcat:3uirbn7o75ds3dgdxhnsvforqy

Causal statistical inference in high dimensions

Peter Bühlmann
2013 Mathematical Methods of Operations Research  
Furthermore, we discuss open problems in optimization, non-linear estimation and for assigning statistical measures of uncertainty, and we illustrate the benefits and limitations of high-dimensional causal  ...  We present a short selective review of causal inference from observational data, with a particular emphasis on the high-dimensional scenario where the number of measured variables may be much larger than  ...  Acknowledgments I would like to thank Alain Hauser, Markus Kalisch and Caroline Uhler for many constructive comments.  ... 
doi:10.1007/s00186-012-0404-7 fatcat:a3ggqylkrvbsrpcyihgkp4qydi

Representation of Context-Specific Causal Models with Observational and Interventional Data [article]

Eliana Duarte, Liam Solus
2022 arXiv   pre-print
These results extend to the general interventional model setting, making CStrees the first family of context-specific models admitting a characterization of interventional model equivalence.  ...  , while affording DAG representations of context-specific causal information.  ...  Acknowledgements Eliana Duarte was supported by the Deutsche Forschungsgemeinschaft DFG under grant 314838170, GRK 2297 MathCoRe, by the FCT grant 2020.01933.CEECIND, and partially supported by CMUP under  ... 
arXiv:2101.09271v3 fatcat:erw2tv4cjrcl3fba3zpc23s5qy

Estimating the effect of joint interventions from observational data in sparse high-dimensional settings [article]

Preetam Nandy, Marloes H. Maathuis, Thomas S. Richardson
2016 arXiv   pre-print
In particular, we propose new methods to estimate the effect of multiple simultaneous interventions (e.g., multiple gene knockouts), under the assumption that the observational data come from an unknown  ...  We also propose a generalization of our methodology to the class of nonparanormal distributions.  ...  Conceptually, we can then list all DAGs in the Markov equivalence class. One of these DAGs is the true causal DAG, but we do not know which one.  ... 
arXiv:1407.2451v3 fatcat:zxf2kzjpwnhedoep6yynk7orqe

Bayesian sample size determination for causal discovery [article]

Federico Castelletti, Guido Consonni
2022 arXiv   pre-print
Starting from an equivalence class of DAGs, a few procedures have been devised to produce a collection of variables to be manipulated in order to identify a causal DAG.  ...  Interventional data, produced by exogenous manipulations of variables in the network, enhance the process of structure learning because they allow to distinguish among equivalent DAGs, thus sharpening  ...  On the other hand, if all we can learn is a Markov equivalence class, we will obtain a collection of causal effects for the same intervention on a variable (each DAG may potentially produce a distinct  ... 
arXiv:2206.00755v1 fatcat:4jqlvmtdkjbltfwkmhyhqrzxyi

Matching a Desired Causal State via Shift Interventions [article]

Jiaqi Zhang, Chandler Squires, Caroline Uhler
2021 arXiv   pre-print
We define the Markov equivalence class that is identifiable from shift interventions and propose two active learning strategies that are guaranteed to exactly match a desired mean.  ...  We then derive a worst-case lower bound for the number of interventions required and show that these strategies are optimal for certain classes of graphs.  ...  All authors were partially supported by NSF (DMS-1651995), ONR (N00014-17-1-2147 and N00014-18-1-2765), the MIT-IBM Watson AI Lab, and a Simons Investigator Award to C. Uhler.  ... 
arXiv:2107.01850v2 fatcat:gysfcfp6qvgljhvq6izd3lcf5y

Size of Interventional Markov Equivalence Classes in Random DAG Models [article]

Dmitriy Katz, Karthikeyan Shanmugam, Chandler Squires, Caroline Uhler
2019 arXiv   pre-print
From observational and interventional data, a DAG model can only be determined up to its interventional Markov equivalence class (I-MEC).  ...  Our results have important consequences for experimental design of interventions and the development of algorithms for causal inference.  ...  Uhler was partially supported by NSF (DMS-1651995), ONR (N00014-17-1-2147 and N00014-18-1-2765), IBM, and a Sloan Fellowship.  ... 
arXiv:1903.02054v1 fatcat:j26zfpdvwzeffkh6s2he5ub3uy

Characterization and Greedy Learning of Interventional Markov Equivalence Classes of Directed Acyclic Graphs [article]

Alain Hauser, Peter Bühlmann
2012 arXiv   pre-print
We give a graph theoretic criterion for two DAGs being Markov equivalent under interventions and show that each interventional Markov equivalence class can, analogously to the observational case, be uniquely  ...  ; many algorithms exist for model selection and structure learning in Markov equivalence classes.  ...  of partial identifiability under a limited number of interventions nor provide an algorithm for learning the causal structure from data.  ... 
arXiv:1104.2808v2 fatcat:uicko2he5bbrna3hc77nfcxzzu
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