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 Gaus- sian 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 graph- ical object that can contain more edge orien- tations. We show that this object can be re- covered from observational data under a type of strong faithfulness assumption. We present a new algorithm for this purpose, called ag- gregated greedy equivalence search (AGES), that aggregates the solution path of the greedy equivalence search (GES) algorithm for vary- ing values of the penalty parameter. We prove consistency of AGES and demonstrate its per- formance in a simulation study and on single cell data from Sachs et al. (2005). The algo- rithm 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 Gaus- sian 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 graph- ical object that can contain more edge orien- tations. We show that this object can be re- covered from observational data under a type of strong faithfulness assumption. We present a new algorithm for this purpose, called ag- gregated greedy equivalence search (AGES), that aggregates the solution path of the greedy equivalence search (GES) algorithm for vary- ing values of the penalty parameter. We prove consistency of AGES and demonstrate its per- formance in a simulation study and on single cell data from Sachs et al. (2005). The algo- rithm 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 Gaus- sian 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 graph- ical object that can contain more edge orien- tations. We show that this object can be re- covered from observational data under a type of strong faithfulness assumption. We present a new algorithm for this purpose, called ag- gregated greedy equivalence search (AGES), that aggregates the solution path of the greedy equivalence search (GES) algorithm for vary- ing values of the penalty parameter. We prove consistency of AGES and demonstrate its per- formance in a simulation study and on single cell data from Sachs et al. (2005). The algo- rithm 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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