Partial information decomposition for discrete target and continuous source random variables

The framework of partial information decomposition (PID) unveils complex nonlinear interactions in network systems by dissecting the mutual information (MI) between a target variable and several source variables. PID measures have been formulated mostly for discrete variables, with only recent extensions to continuous systems. In the case of mixed variables where the target is discrete and the sources are continuous, the application of existing PID schemes requires the manipulation of the data generated by the analyzed system, thus altering their information content. To overcome this issue, we introduce a PID scheme whereby the MI between a specific state of the discrete target and (subsets of) the continuous sources is expressed as a Kullback-Leibler divergence and is estimated through a nearest-neighbor strategy. The effectiveness of this PID is demonstrated in simulated systems of mixed variables and on benchmark data. Our approach is relevant to many scientific problems, including sensory coding in neuroscience and feature selection in machine learning.