Graphical continuous Lyapunov models

Gherardo Varando; Niels Richard Hansen

UAI 2020poster23 citations

Graphical continuous Lyapunov models

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.

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 = 	 {Peters, Jonas and Sontag, David},
  volume = 	 {124},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {03--06 Aug},
  publisher =    {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v124/varando20a/varando20a.pdf},
  url = 	 {https://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.}
}