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# Graphical continuous Lyapunov models

*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.