  We introduce an approach which allows detecting causal relationships between
variables for which the time evolution is available. Causality is assessed by a
variational scheme based on the Information Imbalance of distance ranks, a
statistical test capable of inferring the relative information content of
different distance measures. We test whether the predictability of a putative
driven system Y can be improved by incorporating information from a potential
driver system X, without explicitly modeling the underlying dynamics and
without the need to compute probability densities of the dynamic variables.
This framework makes causality detection possible even between high-dimensional
systems where only few of the variables are known or measured. Benchmark tests
on coupled chaotic dynamical systems demonstrate that our approach outperforms
other model-free causality detection methods, successfully handling both
unidirectional and bidirectional couplings. We also show that the method can be
used to robustly detect causality in human electroencephalography data.
