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About this paper
Gherardo Varando, Niels Richard Hansen
Graphical Continuous Lyapunov Models (GCLMs) are introduced, leveraging the continuous Lyapunov equation to represent equilibrium covariance structures of continuous-time stochastic processes, including those with feedback loops. A new -penalized algorithm is proposed, demonstrating superior performance in recovering directed graph structures from cross-sectional data and successfully reconstructing protein phosphorylation networks.
Key insights
- GCLMs provide a rigorous theoretical framework that directly links equilibrium covariances of stable Ornstein-Uhlenbeck processes to graphical structures, naturally accommodating feedback loops.
- Generalized trek rules are established, showing that the -th entry of the covariance matrix is zero if no trek exists between nodes and in the mixed graph, explaining how graphical structure encodes dependencies.
- Marginalizing a GCLM results in an 'extended' GCLM for the projected subgraph, where new bidirected edges can emerge to account for unobserved variables, offering insights into latent confounding.
Summary by alphaXiv.
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