Graphical continuous Lyapunov models

Gherardo Varando, Niels Richard Hansen
Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI), PMLR 124:989-998, 2020.

Abstract

The linear Lyapunov equation of a covariance matrix parametrizes theequilibrium covariance matrix of a stochastic process. This parametrization canbe interpreted as a new graphical model class, and we show how the model classbehaves under marginalization and introduce a method for structure learning via$\ell_1$-penalized loss minimization. Our proposed method is demonstrated tooutperform alternative structure learning algorithms in a simulation study, andwe illustrate its application for protein phosphorylation network reconstruction.

Cite this Paper


BibTeX
@InProceedings{pmlr-v124-varando20a, title = {Graphical continuous Lyapunov models}, author = {Varando, Gherardo and Richard Hansen, Niels}, booktitle = {Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI)}, pages = {989--998}, year = {2020}, editor = {Jonas Peters and David Sontag}, volume = {124}, series = {Proceedings of Machine Learning Research}, month = {03--06 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v124/varando20a/varando20a.pdf}, url = { http://proceedings.mlr.press/v124/varando20a.html }, abstract = {The linear Lyapunov equation of a covariance matrix parametrizes theequilibrium covariance matrix of a stochastic process. This parametrization canbe interpreted as a new graphical model class, and we show how the model classbehaves under marginalization and introduce a method for structure learning via$\ell_1$-penalized loss minimization. Our proposed method is demonstrated tooutperform alternative structure learning algorithms in a simulation study, andwe illustrate its application for protein phosphorylation network reconstruction.} }
Endnote
%0 Conference Paper %T Graphical continuous Lyapunov models %A Gherardo Varando %A Niels Richard Hansen %B Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI) %C Proceedings of Machine Learning Research %D 2020 %E Jonas Peters %E David Sontag %F pmlr-v124-varando20a %I PMLR %P 989--998 %U http://proceedings.mlr.press/v124/varando20a.html %V 124 %X The linear Lyapunov equation of a covariance matrix parametrizes theequilibrium covariance matrix of a stochastic process. This parametrization canbe interpreted as a new graphical model class, and we show how the model classbehaves under marginalization and introduce a method for structure learning via$\ell_1$-penalized loss minimization. Our proposed method is demonstrated tooutperform alternative structure learning algorithms in a simulation study, andwe illustrate its application for protein phosphorylation network reconstruction.
APA
Varando, G. & Richard Hansen, N.. (2020). Graphical continuous Lyapunov models. Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI), in Proceedings of Machine Learning Research 124:989-998 Available from http://proceedings.mlr.press/v124/varando20a.html .

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