Estimation Rates for Sparse Linear Cyclic Causal Models

Jan-Christian Huetter, Philippe Rigollet
Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI), PMLR 124:1169-1178, 2020.

Abstract

Causal models are fundamental tools to understand complex systems and predict the effect of interventions on such systems. However, despite an extensive literature in the population (or infinite-sample) case, where distributions are assumed to be known, little is known about the statistical rates of convergence of various methods, even for the simplest models. In this work, allowing for cycles, we study linear structural equations models with homoscedastic Gaussian noise and in the presence of interventions that make the model identifiable. More specifically, we present statistical rates of estimation for both the LLC estimator introduced by Hyttinen, Eberhardt and Hoyer and a novel two-step penalized maximum likelihood estimator. We establish asymptotic near minimax optimality for the maximum likelihood estimator over a class of sparse causal graphs in the case of near-optimally chosen interventions. Moreover, we find evidence for practical advantages of this estimator compared to LLC in synthetic numerical experiments.

Cite this Paper

BibTeX
@InProceedings{pmlr-v124-huetter20a, title = {Estimation Rates for Sparse Linear Cyclic Causal Models}, author = {Huetter, Jan-Christian and Rigollet, Philippe}, booktitle = {Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI)}, pages = {1169--1178}, 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/huetter20a/huetter20a.pdf}, url = {https://proceedings.mlr.press/v124/huetter20a.html}, abstract = {Causal models are fundamental tools to understand complex systems and predict the effect of interventions on such systems. However, despite an extensive literature in the population (or infinite-sample) case, where distributions are assumed to be known, little is known about the statistical rates of convergence of various methods, even for the simplest models. In this work, allowing for cycles, we study linear structural equations models with homoscedastic Gaussian noise and in the presence of interventions that make the model identifiable. More specifically, we present statistical rates of estimation for both the LLC estimator introduced by Hyttinen, Eberhardt and Hoyer and a novel two-step penalized maximum likelihood estimator. We establish asymptotic near minimax optimality for the maximum likelihood estimator over a class of sparse causal graphs in the case of near-optimally chosen interventions. Moreover, we find evidence for practical advantages of this estimator compared to LLC in synthetic numerical experiments.} }
Endnote
%0 Conference Paper %T Estimation Rates for Sparse Linear Cyclic Causal Models %A Jan-Christian Huetter %A Philippe Rigollet %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-huetter20a %I PMLR %P 1169--1178 %U https://proceedings.mlr.press/v124/huetter20a.html %V 124 %X Causal models are fundamental tools to understand complex systems and predict the effect of interventions on such systems. However, despite an extensive literature in the population (or infinite-sample) case, where distributions are assumed to be known, little is known about the statistical rates of convergence of various methods, even for the simplest models. In this work, allowing for cycles, we study linear structural equations models with homoscedastic Gaussian noise and in the presence of interventions that make the model identifiable. More specifically, we present statistical rates of estimation for both the LLC estimator introduced by Hyttinen, Eberhardt and Hoyer and a novel two-step penalized maximum likelihood estimator. We establish asymptotic near minimax optimality for the maximum likelihood estimator over a class of sparse causal graphs in the case of near-optimally chosen interventions. Moreover, we find evidence for practical advantages of this estimator compared to LLC in synthetic numerical experiments.
APA
Huetter, J. & Rigollet, P.. (2020). Estimation Rates for Sparse Linear Cyclic Causal Models. Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI), in Proceedings of Machine Learning Research 124:1169-1178 Available from https://proceedings.mlr.press/v124/huetter20a.html.

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