  We introduce and test a general machine-learning-based technique for the
inference of short term causal dependence between state variables of an unknown
dynamical system from time series measurements of its state variables. Our
technique leverages the results of a machine learning process for short time
prediction to achieve our goal. The basic idea is to use the machine learning
to estimate the elements of the Jacobian matrix of the dynamical flow along an
orbit. The type of machine learning that we employ is reservoir computing. We
present numerical tests on link inference of a network of interacting dynamical
nodes. It is seen that dynamical noise can greatly enhance the effectiveness of
our technique, while observational noise degrades the effectiveness. We believe
that the competition between these two opposing types of noise will be the key
factor determining the success of causal inference in many of the most
important application situations.
