Lightning-speed Structure Learning of Nonlinear Continuous Networks

Gal Elidan
Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, PMLR 22:355-363, 2012.

Abstract

Graphical models are widely used to reason about high-dimensional domains. Yet, learning the structure of the model from data remains a formidable challenge, particularly in complex continuous domains. We present a highly accelerated structure learning approach for continuous densities based on the recently introduced copula Bayesian network representation. For two common copula families, we prove that the expected likelihood of a building block edge in the model is monotonic in Spearman’s rank correlation measure. We also show numerically that the same relationship holds for many other copula families. This allows us to perform structure learning while bypassing costly parameter estimation as well as explicit computation of the log-likelihood function. We demonstrate the merit of our approach for structure learning in three varied real-life domains. Importantly, the computational benefits are such that they open the door for practical scaling-up of structure learning in complex nonlinear continuous domains.

Cite this Paper

BibTeX
@InProceedings{pmlr-v22-elidan12b, title = {Lightning-speed Structure Learning of Nonlinear Continuous Networks}, author = {Elidan, Gal}, booktitle = {Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics}, pages = {355--363}, year = {2012}, editor = {Lawrence, Neil D. and Girolami, Mark}, volume = {22}, series = {Proceedings of Machine Learning Research}, address = {La Palma, Canary Islands}, month = {21--23 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v22/elidan12b/elidan12b.pdf}, url = {https://proceedings.mlr.press/v22/elidan12b.html}, abstract = {Graphical models are widely used to reason about high-dimensional domains. Yet, learning the structure of the model from data remains a formidable challenge, particularly in complex continuous domains. We present a highly accelerated structure learning approach for continuous densities based on the recently introduced copula Bayesian network representation. For two common copula families, we prove that the expected likelihood of a building block edge in the model is monotonic in Spearman’s rank correlation measure. We also show numerically that the same relationship holds for many other copula families. This allows us to perform structure learning while bypassing costly parameter estimation as well as explicit computation of the log-likelihood function. We demonstrate the merit of our approach for structure learning in three varied real-life domains. Importantly, the computational benefits are such that they open the door for practical scaling-up of structure learning in complex nonlinear continuous domains.} }
Endnote
%0 Conference Paper %T Lightning-speed Structure Learning of Nonlinear Continuous Networks %A Gal Elidan %B Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2012 %E Neil D. Lawrence %E Mark Girolami %F pmlr-v22-elidan12b %I PMLR %P 355--363 %U https://proceedings.mlr.press/v22/elidan12b.html %V 22 %X Graphical models are widely used to reason about high-dimensional domains. Yet, learning the structure of the model from data remains a formidable challenge, particularly in complex continuous domains. We present a highly accelerated structure learning approach for continuous densities based on the recently introduced copula Bayesian network representation. For two common copula families, we prove that the expected likelihood of a building block edge in the model is monotonic in Spearman’s rank correlation measure. We also show numerically that the same relationship holds for many other copula families. This allows us to perform structure learning while bypassing costly parameter estimation as well as explicit computation of the log-likelihood function. We demonstrate the merit of our approach for structure learning in three varied real-life domains. Importantly, the computational benefits are such that they open the door for practical scaling-up of structure learning in complex nonlinear continuous domains.
RIS
TY - CPAPER TI - Lightning-speed Structure Learning of Nonlinear Continuous Networks AU - Gal Elidan BT - Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics DA - 2012/03/21 ED - Neil D. Lawrence ED - Mark Girolami ID - pmlr-v22-elidan12b PB - PMLR DP - Proceedings of Machine Learning Research VL - 22 SP - 355 EP - 363 L1 - http://proceedings.mlr.press/v22/elidan12b/elidan12b.pdf UR - https://proceedings.mlr.press/v22/elidan12b.html AB - Graphical models are widely used to reason about high-dimensional domains. Yet, learning the structure of the model from data remains a formidable challenge, particularly in complex continuous domains. We present a highly accelerated structure learning approach for continuous densities based on the recently introduced copula Bayesian network representation. For two common copula families, we prove that the expected likelihood of a building block edge in the model is monotonic in Spearman’s rank correlation measure. We also show numerically that the same relationship holds for many other copula families. This allows us to perform structure learning while bypassing costly parameter estimation as well as explicit computation of the log-likelihood function. We demonstrate the merit of our approach for structure learning in three varied real-life domains. Importantly, the computational benefits are such that they open the door for practical scaling-up of structure learning in complex nonlinear continuous domains. ER -
APA
Elidan, G.. (2012). Lightning-speed Structure Learning of Nonlinear Continuous Networks. Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 22:355-363 Available from https://proceedings.mlr.press/v22/elidan12b.html.

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