Perlenkolloquium: Prof. Mathias Drton (Technical University Munich)

Identification and Statistical Estimation of Graphical Continuous Lyapunov Models

The ultimate aim of many data analyses is to infer cause-effect relationships between random variables of interest. While much of the available methodology for addressing causal questions relies on structural causal models, these models are best suited for systems without feedback loops. Extensions to accommodate feedback have been proposed but often result in models that are challenging to interpret.

In this talk, we present an alternative approach to structural causal modeling: graphical continuous Lyapunov models. This framework offers a novel perspective on modeling causally interpretable dependence structures in multivariate data by treating each independent observation as a one-time cross-sectional snapshot of an underlying temporal process. Specifically, we focus on models based on multivariate Ornstein-Uhlenbeck processes in equilibrium, which yield Gaussian distributions where the continuous Lyapunov equation determines the covariance matrix. Within this framework, each graphical model assumes a sparse drift matrix whose support is encoded by a directed graph.

We will discuss initial results on the identifiability of sparse drift matrices and explore methods for their regularized estimation, highlighting the potential as well as challenges in developing graphical continuous Lyapunov models as an interpretable tool for causal analysis in systems with feedback loops.

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