Information-Theoretic Bounds on the Moments of the Generalization Error of Learning Algorithms

Generalization error bounds are critical to understanding the performance of\nmachine learning models. In this work, building upon a new bound of the\nexpected value of an arbitrary function of the population and empirical risk of\na learning algorithm, we offer a more refined analysis of the generalization\nbehaviour of a machine learning models based on a characterization of (bounds)\nto their generalization error moments. We discuss how the proposed bounds --\nwhich also encompass new bounds to the expected generalization error -- relate\nto existing bounds in the literature. We also discuss how the proposed\ngeneralization error moment bounds can be used to construct new generalization\nerror high-probability bounds.\n