Graphs in State-Space Models for Granger Causality in Climate Science
Víctor Elvira Émilie Chouzenoux Jordi Cerdà Gustau Camps-Valls
Granger causality (GC) is often considered not an actual form of causality.
Still, it is arguably the most widely used method to assess the predictability
of a time series from another one. Granger causality has been widely used in
many applied disciplines, from neuroscience and econometrics to Earth sciences.
We revisit GC under a graphical perspective of state-space models. For that, we
use GraphEM, a recently presented expectation-maximisation algorithm for
estimating the linear matrix operator in the state equation of a
linear-Gaussian state-space model. Lasso regularisation is included in the
M-step, which is solved using a proximal splitting Douglas-Rachford algorithm.
Experiments in toy examples and challenging climate problems illustrate the
benefits of the proposed model and inference technique over standard Granger
causality methods.