Generalization in Machine Learning via Analytical Learning Theory
Abstract
This paper introduces a novel measure-theoretic theory for machine learning that does not require statistical assumptions. Based on this theory, a new regularization method in deep learning is derived and shown to outperform previous methods in CIFAR-10, CIFAR-100, and SVHN. Moreover, the proposed theory provides a theoretical basis for a family of practically successful regularization methods in deep learning. We discuss several consequences of our results on one-shot learning, representation learning, deep learning, and curriculum learning. Unlike statistical learning theory, the proposed learning theory analyzes each problem instance individually via measure theory, rather than a set of problem instances via statistics. As a result, it provides different types of results and insights when compared to statistical learning theory.
Cite
@article{arxiv.1802.07426,
title = {Generalization in Machine Learning via Analytical Learning Theory},
author = {Kenji Kawaguchi and Yoshua Bengio and Vikas Verma and Leslie Pack Kaelbling},
journal= {arXiv preprint arXiv:1802.07426},
year = {2019}
}