Graphical continuous Lyapunov models
This work addresses the problem of network structure learning for researchers in statistics and computational biology, offering a novel graphical model approach with potential applications in biological data analysis.
The authors tackled the problem of learning graphical models from covariance matrices by introducing a new model class based on the linear Lyapunov equation, and demonstrated that their method outperforms alternative algorithms in simulations, achieving improved structure learning for applications like protein phosphorylation network reconstruction.
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.