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Partial differential equation regularization for supervised machine learning. (English) Zbl 1478.65141

Brenner, Susanne C. (ed.) et al., 75 years of mathematics of computation. Symposium celebrating 75 years of mathematics of computation, Institute for Computational and Experimental Research in Mathematics, ICERM, Providence, RI, USA, November 1–3, 2018. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 754, 177-195 (2020).
Summary: This article is an overview of supervised machine learning problems for regression and classification. Topics include: kernel methods, training by stochastic gradient descent, deep learning architecture, losses for classification, statistical learning theory, and dimension independent generalization bounds. Implicit regularization in deep learning examples are presented, including data augmentation, adversarial training, and additive noise. These methods are reframed as explicit gradient regularization.
For the entire collection see [Zbl 1461.11002].

MSC:

65N99 Numerical methods for partial differential equations, boundary value problems
35A15 Variational methods applied to PDEs
35B65 Smoothness and regularity of solutions to PDEs
65C20 Probabilistic models, generic numerical methods in probability and statistics
68T07 Artificial neural networks and deep learning
68Q32 Computational learning theory

Software:

mixup; PRMLT
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References:

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