Partial differential equation regularization for supervised machine\n learning

2019/10/03 by Adam M. Oberman, Oberman, Adam M
Computer Science · Physics and Astronomy · #49M99 #65C50 #Analysis of PDEs (math.AP) #FOS: Computer and information sciences #FOS: Mathematics #Image and Signal Denoising Methods #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Model Reduction and Neural Networks #Neural Networks and Applications #Primary 65N99 #Secondary 35A15

paper · pdf · doi:10.48550/arxiv.1910.01612

openalex publication_date 2019/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This article is an overview of supervised machine learning problems for\nregression and classification. Topics include: kernel methods, training by\nstochastic gradient descent, deep learning architecture, losses for\nclassification, statistical learning theory, and dimension independent\ngeneralization bounds. Implicit regularization in deep learning examples are\npresented, including data augmentation, adversarial training, and additive\nnoise. These methods are reframed as explicit gradient regularization.\n

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