Identification in Tree-shaped Linear Structural Causal Models

Benito Van Der Zander, Marcel Wienöbst, Markus Bläser, Maciej Liskiewicz
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:6770-6792, 2022.

Abstract

Linear structural equation models represent direct causal effects as directed edges and confounding factors as bidirected edges. An open problem is to identify the causal parameters from correlations between the nodes. We investigate models, whose directed component forms a tree, and show that there, besides classical instrumental variables, missing cycles of bidirected edges can be used to identify the model. They can yield systems of quadratic equations that we explicitly solve to obtain one or two solutions for the causal parameters of adjacent directed edges. We show how multiple missing cycles can be combined to obtain a unique solution. This results in an algorithm that can identify instances that previously required approaches based on Gröbner bases, which have doubly-exponential time complexity in the number of structural parameters.

Cite this Paper

BibTeX
@InProceedings{pmlr-v151-van-der-zander22a, title = { Identification in Tree-shaped Linear Structural Causal Models }, author = {Van Der Zander, Benito and Wien\"obst, Marcel and Bl\"aser, Markus and Liskiewicz, Maciej}, booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics}, pages = {6770--6792}, year = {2022}, editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel}, volume = {151}, series = {Proceedings of Machine Learning Research}, month = {28--30 Mar}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v151/van-der-zander22a/van-der-zander22a.pdf}, url = {https://proceedings.mlr.press/v151/van-der-zander22a.html}, abstract = { Linear structural equation models represent direct causal effects as directed edges and confounding factors as bidirected edges. An open problem is to identify the causal parameters from correlations between the nodes. We investigate models, whose directed component forms a tree, and show that there, besides classical instrumental variables, missing cycles of bidirected edges can be used to identify the model. They can yield systems of quadratic equations that we explicitly solve to obtain one or two solutions for the causal parameters of adjacent directed edges. We show how multiple missing cycles can be combined to obtain a unique solution. This results in an algorithm that can identify instances that previously required approaches based on Gröbner bases, which have doubly-exponential time complexity in the number of structural parameters. } }
Endnote
%0 Conference Paper %T Identification in Tree-shaped Linear Structural Causal Models %A Benito Van Der Zander %A Marcel Wienöbst %A Markus Bläser %A Maciej Liskiewicz %B Proceedings of The 25th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2022 %E Gustau Camps-Valls %E Francisco J. R. Ruiz %E Isabel Valera %F pmlr-v151-van-der-zander22a %I PMLR %P 6770--6792 %U https://proceedings.mlr.press/v151/van-der-zander22a.html %V 151 %X Linear structural equation models represent direct causal effects as directed edges and confounding factors as bidirected edges. An open problem is to identify the causal parameters from correlations between the nodes. We investigate models, whose directed component forms a tree, and show that there, besides classical instrumental variables, missing cycles of bidirected edges can be used to identify the model. They can yield systems of quadratic equations that we explicitly solve to obtain one or two solutions for the causal parameters of adjacent directed edges. We show how multiple missing cycles can be combined to obtain a unique solution. This results in an algorithm that can identify instances that previously required approaches based on Gröbner bases, which have doubly-exponential time complexity in the number of structural parameters.
APA
Van Der Zander, B., Wienöbst, M., Bläser, M. & Liskiewicz, M.. (2022). Identification in Tree-shaped Linear Structural Causal Models . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:6770-6792 Available from https://proceedings.mlr.press/v151/van-der-zander22a.html.

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