Detecting the Direction of causal Time Series
Patrik Hoyer, Domnik Janzing, Joris Mooij, Jonas Peters, Bernhard Schoelkopf
(Max Plank Institute for Biological Cybernetics, Germany)
The discovery of causal relationships between a set of observed
variables is a fundamental problem in science.
For continuous-valued data *linear* acyclic causal models with additive noise are
often used because these models are well understood and there are
well-known methods to fit them to data. In reality, of course, many
causal relationships are more or less *nonlinear*, raising some
doubts as to the applicability and usefulness of purely linear
methods. In this contribution we show that in fact the basic linear
framework can be generalized to nonlinear models. In this extended framework, nonlinearities in the
data-generating process are in fact a blessing rather than a curse,
as they typically provide information on the underlying causal
system and allow more aspects of the true data-generating mechanisms
to be identified. In addition to theoretical results we show
simulations and some simple real data experiments illustrating the
identification power provided by nonlinearities.