  In this paper, we introduce Partial Information Decomposition of Features
(PIDF), a new paradigm for simultaneous data interpretability and feature
selection. Contrary to traditional methods that assign a single importance
value, our approach is based on three metrics per feature: the mutual
information shared with the target variable, the feature's contribution to
synergistic information, and the amount of this information that is redundant.
In particular, we develop a novel procedure based on these three metrics, which
reveals not only how features are correlated with the target but also the
additional and overlapping information provided by considering them in
combination with other features. We extensively evaluate PIDF using both
synthetic and real-world data, demonstrating its potential applications and
effectiveness, by considering case studies from genetics and neuroscience.
