  Identifying the causal structure of systems with multiple dynamic elements is
critical to several scientific disciplines. The conventional approach is to
conduct statistical tests of causality, for example with Granger Causality,
between observed signals that are selected a priori. Here it is posited that,
in many systems, the causal relations are embedded in a latent space that is
expressed in the observed data as a linear mixture. A technique for blindly
identifying the latent sources is presented: the observations are projected
into pairs of components -- driving and driven -- to maximize the strength of
causality between the pairs. This leads to an optimization problem with closed
form expressions for the objective function and gradient that can be solved
with off-the-shelf techniques. After demonstrating proof-of-concept on
synthetic data with known latent structure, the technique is applied to
recordings from the human brain and historical cryptocurrency prices. In both
cases, the approach recovers multiple strong causal relationships that are not
evident in the observed data. The proposed technique is unsupervised and can be
readily applied to any multiple time series to shed light on the causal
relationships underlying the data.
