Graphical continuous Lyapunov models

Abstract

The linear Lyapunov equation of a covariance matrix parametrizes the equilibrium covariance matrix of a stochastic process. This parametrization can be interpreted as a new graphical model class, and we show how the model class behaves under marginalization and introduce a method for structure learning via ${\ell }_1$-penalized loss minimization. Our proposed method is demonstrated to outperform alternative structure learning algorithms in a simulation study, and we illustrate its application for protein phosphorylation network reconstruction.

10 pages, 5 figures

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