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Title: Identifiability in continuous graphical Lyapunov models Authors:  Carlos Amendola - Technical University Berlin (Germany) [presenting]
Philipp Dettling - Technical University of Munich (Germany)
Mathias Drton - Technical University of Munich (Germany)
Niels Richard Hansen - University of Copenhagen (Denmark)
Roser Homs - Technical University of Munich (Germany)
Abstract: Lyapunov graphical models represent a new approach in graphical modeling where independent observations are taken to be one-time cross-sectional snapshots of the multivariate Ornstein-Uhlenbeck process in equilibrium. The non-zero pattern of the drift matrix allows for a causally interpretable dependence structure among the coordinates of the process which can be represented by a directed graph. We will introduce these models and focus on the fundamental question of identifiability, i.e. being able to recover the parameters knowing the true data generating distribution. Familiar algebraic tools such as matrix rank computations and the sum of squares decompositions help us study this identifiability problem for both directed acyclic and simple cyclic graphs.