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Abstract:
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Cross-sectional correlations among variables that evolve according to a dynamical system are not in general compatible with a sparse graphical model in the classical sense. The Graphical Continuous Lyapunov Model (GCLM) is a better alternative. It is a model class of covariance matrices that describe a stationary state of the dynamical system in terms of the solution to a continuous Lyapunov equation. In the talk I will outline the motivation behind GCLMs and the Markov semantics of their graphs for a fully observed dynamical system. However, for cross-sectionally observed variables there may be no non-trivial Markov properties. It is, nevertheless, possible to learn the parameters of the dynamical system from the cross-sectional correlations if the graph is suitably sparse. I will present recent results on parameter identification for GCLMs.
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