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Towards Understanding Generalization via Analytical Learning Theory

Author(s)
Kawaguchi, Kenji; Benigo, Yoshua; Verma, Vikas; Kaelbling, Leslie Pack
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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.
Date issued
2018-10-01
URI
http://hdl.handle.net/1721.1/118307
Series/Report no.
;MIT-CSAIL-TR-2018-019
Keywords
Machine Learning, Measure Theory, Regularization method, Neural Network

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