Learning linear non-Gaussian polytree models

Daniele Tramontano, Anthea Monod, Mathias Drton
Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence, PMLR 180:1960-1969, 2022.

Abstract

In the context of graphical causal discovery, we adapt the versatile framework of linear non-Gaussian acyclic models (LiNGAMs) to propose new algorithms to efficiently learn graphs that are polytrees. Our approach combines the Chow–Liu algorithm, which first learns the undirected tree structure, with novel schemes to orient the edges. The orientation schemes assess algebraic relations among moments of the data-generating distribution and are computationally inexpensive. We establish high-dimensional consistency results for our approach and compare different algorithmic versions in numerical experiments.

Cite this Paper

BibTeX
@InProceedings{pmlr-v180-tramontano22a, title = {Learning linear non-{G}aussian polytree models}, author = {Tramontano, Daniele and Monod, Anthea and Drton, Mathias}, booktitle = {Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence}, pages = {1960--1969}, year = {2022}, editor = {Cussens, James and Zhang, Kun}, volume = {180}, series = {Proceedings of Machine Learning Research}, month = {01--05 Aug}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v180/tramontano22a/tramontano22a.pdf}, url = {https://proceedings.mlr.press/v180/tramontano22a.html}, abstract = { In the context of graphical causal discovery, we adapt the versatile framework of linear non-Gaussian acyclic models (LiNGAMs) to propose new algorithms to efficiently learn graphs that are polytrees. Our approach combines the Chow–Liu algorithm, which first learns the undirected tree structure, with novel schemes to orient the edges. The orientation schemes assess algebraic relations among moments of the data-generating distribution and are computationally inexpensive. We establish high-dimensional consistency results for our approach and compare different algorithmic versions in numerical experiments.} }
Endnote
%0 Conference Paper %T Learning linear non-Gaussian polytree models %A Daniele Tramontano %A Anthea Monod %A Mathias Drton %B Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2022 %E James Cussens %E Kun Zhang %F pmlr-v180-tramontano22a %I PMLR %P 1960--1969 %U https://proceedings.mlr.press/v180/tramontano22a.html %V 180 %X In the context of graphical causal discovery, we adapt the versatile framework of linear non-Gaussian acyclic models (LiNGAMs) to propose new algorithms to efficiently learn graphs that are polytrees. Our approach combines the Chow–Liu algorithm, which first learns the undirected tree structure, with novel schemes to orient the edges. The orientation schemes assess algebraic relations among moments of the data-generating distribution and are computationally inexpensive. We establish high-dimensional consistency results for our approach and compare different algorithmic versions in numerical experiments.
APA
Tramontano, D., Monod, A. & Drton, M.. (2022). Learning linear non-Gaussian polytree models. Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 180:1960-1969 Available from https://proceedings.mlr.press/v180/tramontano22a.html.

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