Structure Learning of Linear Gaussian Structural Equation Models with Weak Edges

Marco Eigenmann, Preetam Nandy, Marloes Maathuis
Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence, PMLR R15:760-769, 2017.

Abstract

We consider structure learning of linear Gaussian structural equation models with weak edges. Since the presence of weak edges can lead to a loss of edge orientations in the true underlying CPDAG, we define a new graphical object that can contain more edge orientations. We show that this object can be recovered from observational data under a type of strong faithfulness assumption. We present a new algorithm for this purpose, called aggregated greedy equivalence search (AGES), that aggregates the solution path of the greedy equivalence search (GES) algorithm for varying values of the penalty parameter. We prove consistency of AGES and demonstrate its performance in a simulation study and on single cell data from Sachs et al. (2005). The algorithm will be made available in the R-package pcalg.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR15-eigenmann17a, title = {Structure Learning of Linear {G}aussian Structural Equation Models with Weak Edges}, author = {Eigenmann, Marco and Nandy, Preetam and Maathuis, Marloes}, booktitle = {Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence}, pages = {760--769}, year = {2017}, editor = {Elidan, Gal and Kersting, Kristian}, volume = {R15}, series = {Proceedings of Machine Learning Research}, month = {11--15 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r15/main/assets/eigenmann17a/eigenmann17a.pdf}, url = {https://proceedings.mlr.press/r15/eigenmann17a.html}, abstract = {We consider structure learning of linear Gaussian structural equation models with weak edges. Since the presence of weak edges can lead to a loss of edge orientations in the true underlying CPDAG, we define a new graphical object that can contain more edge orientations. We show that this object can be recovered from observational data under a type of strong faithfulness assumption. We present a new algorithm for this purpose, called aggregated greedy equivalence search (AGES), that aggregates the solution path of the greedy equivalence search (GES) algorithm for varying values of the penalty parameter. We prove consistency of AGES and demonstrate its performance in a simulation study and on single cell data from Sachs et al. (2005). The algorithm will be made available in the R-package pcalg.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Structure Learning of Linear Gaussian Structural Equation Models with Weak Edges %A Marco Eigenmann %A Preetam Nandy %A Marloes Maathuis %B Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2017 %E Gal Elidan %E Kristian Kersting %F pmlr-vR15-eigenmann17a %I PMLR %P 760--769 %U https://proceedings.mlr.press/r15/eigenmann17a.html %V R15 %X We consider structure learning of linear Gaussian structural equation models with weak edges. Since the presence of weak edges can lead to a loss of edge orientations in the true underlying CPDAG, we define a new graphical object that can contain more edge orientations. We show that this object can be recovered from observational data under a type of strong faithfulness assumption. We present a new algorithm for this purpose, called aggregated greedy equivalence search (AGES), that aggregates the solution path of the greedy equivalence search (GES) algorithm for varying values of the penalty parameter. We prove consistency of AGES and demonstrate its performance in a simulation study and on single cell data from Sachs et al. (2005). The algorithm will be made available in the R-package pcalg. %Z Reissued by PMLR on 04 October 2026.
APA
Eigenmann, M., Nandy, P. & Maathuis, M.. (2017). Structure Learning of Linear Gaussian Structural Equation Models with Weak Edges. Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R15:760-769 Available from https://proceedings.mlr.press/r15/eigenmann17a.html. Reissued by PMLR on 04 October 2026.

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