Causal Structure Learning for Dynamical Systems with Theoretical Score Analysis

Nicholas Tagliapietra, Katharina Ensinger, Christoph Zimmer, Osman Mian

Abstract:

Real world systems evolve in continuous-time according to
their underlying causal relationships, yet their dynamics are
often unknown. Existing approaches to learning such dynam
ics typically either discretize time —leading to poor per
formance on irregularly sampled data— or ignore the un
derlying causality. We propose CADYT , a novel method
for causal discovery on dynamical systems addressing both
these challenges. In contrast to state-of-the-art causal dis
covery methods that model the problem using discrete-time
Dynamic Bayesian networks, our formulation is grounded
in Difference-based causal models, which allow milder as
sumptions for modeling the continuous nature of the system.
CADYTleverages exact Gaussian Process inference for mod
eling the continuous-time dynamics which is more aligned
with the underlying dynamical process. We propose a prac
tical instantiation that identifies the causal structure via a
greedy search guided by the Algorithmic Markov Condi
tion and Minimum Description Length principle. Our exper
iments show that CADYT outperforms state-of-the-art meth
ods on both regularly and irregularly-sampled data, discover
ing causal networks closer to the true underlying dynamics.