Ordering-Based Causal Structure Learning in the Presence of Latent Variables

Daniel Bernstein, Basil Saeed, Chandler Squires, Caroline Uhler
Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:4098-4108, 2020.

Abstract

We consider the task of learning a causal graph in the presence of latent confounders given i.i.d.samples from the model. While current algorithms for causal structure discovery in the presence of latent confounders are constraint-based, we here propose a hybrid approach. We prove that under assumptions weaker than faithfulness, any sparsest independence map (IMAP) of the distribution belongs to the Markov equivalence class of the true model. This motivates the Sparsest Poset formulation - that posets can be mapped to minimal IMAPs of the true model such that the sparsest of these IMAPs is Markov equivalent to the true model. Motivated by this result, we propose a greedy algorithm over the space of posets for causal structure discovery in the presence of latent confounders and compare its performance to the current state-of-the-art algorithms FCI and FCI+ on synthetic data.

Cite this Paper

BibTeX
@InProceedings{pmlr-v108-bernstein20a, title = {Ordering-Based Causal Structure Learning in the Presence of Latent Variables}, author = {Bernstein, Daniel and Saeed, Basil and Squires, Chandler and Uhler, Caroline}, booktitle = {Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics}, pages = {4098--4108}, year = {2020}, editor = {Chiappa, Silvia and Calandra, Roberto}, volume = {108}, series = {Proceedings of Machine Learning Research}, month = {26--28 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v108/bernstein20a/bernstein20a.pdf}, url = {https://proceedings.mlr.press/v108/bernstein20a.html}, abstract = {We consider the task of learning a causal graph in the presence of latent confounders given i.i.d.samples from the model. While current algorithms for causal structure discovery in the presence of latent confounders are constraint-based, we here propose a hybrid approach. We prove that under assumptions weaker than faithfulness, any sparsest independence map (IMAP) of the distribution belongs to the Markov equivalence class of the true model. This motivates the Sparsest Poset formulation - that posets can be mapped to minimal IMAPs of the true model such that the sparsest of these IMAPs is Markov equivalent to the true model. Motivated by this result, we propose a greedy algorithm over the space of posets for causal structure discovery in the presence of latent confounders and compare its performance to the current state-of-the-art algorithms FCI and FCI+ on synthetic data.} }
Endnote
%0 Conference Paper %T Ordering-Based Causal Structure Learning in the Presence of Latent Variables %A Daniel Bernstein %A Basil Saeed %A Chandler Squires %A Caroline Uhler %B Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2020 %E Silvia Chiappa %E Roberto Calandra %F pmlr-v108-bernstein20a %I PMLR %P 4098--4108 %U https://proceedings.mlr.press/v108/bernstein20a.html %V 108 %X We consider the task of learning a causal graph in the presence of latent confounders given i.i.d.samples from the model. While current algorithms for causal structure discovery in the presence of latent confounders are constraint-based, we here propose a hybrid approach. We prove that under assumptions weaker than faithfulness, any sparsest independence map (IMAP) of the distribution belongs to the Markov equivalence class of the true model. This motivates the Sparsest Poset formulation - that posets can be mapped to minimal IMAPs of the true model such that the sparsest of these IMAPs is Markov equivalent to the true model. Motivated by this result, we propose a greedy algorithm over the space of posets for causal structure discovery in the presence of latent confounders and compare its performance to the current state-of-the-art algorithms FCI and FCI+ on synthetic data.
APA
Bernstein, D., Saeed, B., Squires, C. & Uhler, C.. (2020). Ordering-Based Causal Structure Learning in the Presence of Latent Variables. Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 108:4098-4108 Available from https://proceedings.mlr.press/v108/bernstein20a.html.

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