Leveraging Local Variation in Data: Sampling and Weighting Schemes for Supervised Deep Learning

In the context of supervised learning of a function by a neural network, we claim and empirically verify that the neural network yields better results when the distribution of the data set focuses on regions where the function to learn is steep. We first traduce this assumption in a mathematically w...

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Bibliographic Details
Published inarXiv.org
Main Authors Novello, Paul, Poëtte, Gaël, Lugato, David, Congedo, Pietro
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 27.09.2022
Subjects
Computer Science - Learning
Deep learning
Image classification
Mathematics - Statistics Theory
Multivariate analysis
Neural networks
Statistics - Machine Learning
Statistics - Theory
Taylor series
Weighting
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Summary:In the context of supervised learning of a function by a neural network, we claim and empirically verify that the neural network yields better results when the distribution of the data set focuses on regions where the function to learn is steep. We first traduce this assumption in a mathematically workable way using Taylor expansion and emphasize a new training distribution based on the derivatives of the function to learn. Then, theoretical derivations allow constructing a methodology that we call Variance Based Samples Weighting (VBSW). VBSW uses labels local variance to weight the training points. This methodology is general, scalable, cost-effective, and significantly increases the performances of a large class of neural networks for various classification and regression tasks on image, text, and multivariate data. We highlight its benefits with experiments involving neural networks from linear models to ResNet and Bert.
ISSN:2331-8422
DOI:10.48550/arxiv.2101.07561