Causal Structure Discovery from Distributions Arising from Mixtures of DAGs

Basil Saeed, Snigdha Panigrahi, Caroline Uhler
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:8336-8345, 2020.

Abstract

We consider distributions arising from a mixture of causal models, where each model is represented by a directed acyclic graph (DAG). We provide a graphical representation of such mixture distributions and prove that this representation encodes the conditional independence relations of the mixture distribution. We then consider the problem of structure learning based on samples from such distributions. Since the mixing variable is latent, we consider causal structure discovery algorithms such as FCI that can deal with latent variables. We show that such algorithms recover a “union” of the component DAGs and can identify variables whose conditional distribution across the component DAGs vary. We demonstrate our results on synthetic and real data showing that the inferred graph identifies nodes that vary between the different mixture components. As an immediate application, we demonstrate how retrieval of this causal information can be used to cluster samples according to each mixture component.

Cite this Paper

BibTeX
@InProceedings{pmlr-v119-saeed20a, title = {Causal Structure Discovery from Distributions Arising from Mixtures of {DAG}s}, author = {Saeed, Basil and Panigrahi, Snigdha and Uhler, Caroline}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {8336--8345}, year = {2020}, editor = {III, Hal Daumé and Singh, Aarti}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/saeed20a/saeed20a.pdf}, url = {https://proceedings.mlr.press/v119/saeed20a.html}, abstract = {We consider distributions arising from a mixture of causal models, where each model is represented by a directed acyclic graph (DAG). We provide a graphical representation of such mixture distributions and prove that this representation encodes the conditional independence relations of the mixture distribution. We then consider the problem of structure learning based on samples from such distributions. Since the mixing variable is latent, we consider causal structure discovery algorithms such as FCI that can deal with latent variables. We show that such algorithms recover a “union” of the component DAGs and can identify variables whose conditional distribution across the component DAGs vary. We demonstrate our results on synthetic and real data showing that the inferred graph identifies nodes that vary between the different mixture components. As an immediate application, we demonstrate how retrieval of this causal information can be used to cluster samples according to each mixture component.} }
Endnote
%0 Conference Paper %T Causal Structure Discovery from Distributions Arising from Mixtures of DAGs %A Basil Saeed %A Snigdha Panigrahi %A Caroline Uhler %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-saeed20a %I PMLR %P 8336--8345 %U https://proceedings.mlr.press/v119/saeed20a.html %V 119 %X We consider distributions arising from a mixture of causal models, where each model is represented by a directed acyclic graph (DAG). We provide a graphical representation of such mixture distributions and prove that this representation encodes the conditional independence relations of the mixture distribution. We then consider the problem of structure learning based on samples from such distributions. Since the mixing variable is latent, we consider causal structure discovery algorithms such as FCI that can deal with latent variables. We show that such algorithms recover a “union” of the component DAGs and can identify variables whose conditional distribution across the component DAGs vary. We demonstrate our results on synthetic and real data showing that the inferred graph identifies nodes that vary between the different mixture components. As an immediate application, we demonstrate how retrieval of this causal information can be used to cluster samples according to each mixture component.
APA
Saeed, B., Panigrahi, S. & Uhler, C.. (2020). Causal Structure Discovery from Distributions Arising from Mixtures of DAGs. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:8336-8345 Available from https://proceedings.mlr.press/v119/saeed20a.html.

Related Material