Structure Learning for Cyclic Linear Causal Models

Carlos Amendola, Philipp Dettling, Mathias Drton, Federica Onori, Jun Wu
Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI), PMLR 124:999-1008, 2020.

Abstract

We consider the problem of structure learning for linear causal models based on observational data. We treat models given by possibly cyclic mixed graphs, which allow for feedback loops and effects of latent confounders. Generalizing related work on bow-free acyclic graphs, we assume that the underlying graph is simple. This entails that any two observed variables can be related through at most one direct causal effect and that (confounding-induced) correlation between error terms in structural equations occurs only in absence of direct causal effects.We show that, despite new subtleties in the cyclic case, the considered simple cyclic models are of expected dimension and that a previously considered criterion for distributional equivalence of bow-free acyclic graphs has an analogue in the cyclic case. Our result on model dimension justifies in particular score-based methods for structure learning of linear Gaussian mixed graph models, which we implement via greedy search.

Cite this Paper

BibTeX
@InProceedings{pmlr-v124-amendola20a, title = {Structure Learning for Cyclic Linear Causal Models}, author = {Amendola, Carlos and Dettling, Philipp and Drton, Mathias and Onori, Federica and Wu, Jun}, booktitle = {Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI)}, pages = {999--1008}, year = {2020}, editor = {Peters, Jonas and Sontag, David}, volume = {124}, series = {Proceedings of Machine Learning Research}, month = {03--06 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v124/amendola20a/amendola20a.pdf}, url = {https://proceedings.mlr.press/v124/amendola20a.html}, abstract = {We consider the problem of structure learning for linear causal models based on observational data. We treat models given by possibly cyclic mixed graphs, which allow for feedback loops and effects of latent confounders. Generalizing related work on bow-free acyclic graphs, we assume that the underlying graph is simple. This entails that any two observed variables can be related through at most one direct causal effect and that (confounding-induced) correlation between error terms in structural equations occurs only in absence of direct causal effects.We show that, despite new subtleties in the cyclic case, the considered simple cyclic models are of expected dimension and that a previously considered criterion for distributional equivalence of bow-free acyclic graphs has an analogue in the cyclic case. Our result on model dimension justifies in particular score-based methods for structure learning of linear Gaussian mixed graph models, which we implement via greedy search.} }
Endnote
%0 Conference Paper %T Structure Learning for Cyclic Linear Causal Models %A Carlos Amendola %A Philipp Dettling %A Mathias Drton %A Federica Onori %A Jun Wu %B Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI) %C Proceedings of Machine Learning Research %D 2020 %E Jonas Peters %E David Sontag %F pmlr-v124-amendola20a %I PMLR %P 999--1008 %U https://proceedings.mlr.press/v124/amendola20a.html %V 124 %X We consider the problem of structure learning for linear causal models based on observational data. We treat models given by possibly cyclic mixed graphs, which allow for feedback loops and effects of latent confounders. Generalizing related work on bow-free acyclic graphs, we assume that the underlying graph is simple. This entails that any two observed variables can be related through at most one direct causal effect and that (confounding-induced) correlation between error terms in structural equations occurs only in absence of direct causal effects.We show that, despite new subtleties in the cyclic case, the considered simple cyclic models are of expected dimension and that a previously considered criterion for distributional equivalence of bow-free acyclic graphs has an analogue in the cyclic case. Our result on model dimension justifies in particular score-based methods for structure learning of linear Gaussian mixed graph models, which we implement via greedy search.
APA
Amendola, C., Dettling, P., Drton, M., Onori, F. & Wu, J.. (2020). Structure Learning for Cyclic Linear Causal Models. Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI), in Proceedings of Machine Learning Research 124:999-1008 Available from https://proceedings.mlr.press/v124/amendola20a.html.

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