  The ultimate goal of a supervised learning algorithm is to produce models
constructed on the training data that can generalize well to new examples. In
classification, functional margin maximization -- correctly classifying as many
training examples as possible with maximal confidence --has been known to
construct models with good generalization guarantees. This work gives an
information-theoretic interpretation of a margin maximizing model on a
noiseless training dataset as one that achieves lossless maximal compression of
said dataset -- i.e. extracts from the features all the useful information for
predicting the label and no more. The connection offers new insights on
generalization in supervised machine learning, showing margin maximization as a
special case (that of classification) of a more general principle and explains
the success and potential limitations of popular learning algorithms like
gradient boosting. We support our observations with theoretical arguments and
empirical evidence and identify interesting directions for future work.
