  We derive a well-defined renormalized version of mutual information that
allows to estimate the dependence between continuous random variables in the
important case when one is deterministically dependent on the other. This is
the situation relevant for feature extraction, where the goal is to produce a
low-dimensional effective description of a high-dimensional system. Our
approach enables the discovery of collective variables in physical systems,
thus adding to the toolbox of artificial scientific discovery, while also
aiding the analysis of information flow in artificial neural networks.
