On the composition of neural and kernel layers for machine learning

Deep Learning architectures in which neural layers alternate with mappings to infinitedimensional feature spaces have been proposed in recent years, showing improvements on the results obtained when using either technique separately. However, these new algorithms have been presented without delving...

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Detalles Bibliográficos
Autor: Martorell Locascio, Alex
Tipo de recurso: tesis de maestría
Fecha de publicación:2023
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/394525
Acceso en línea:https://hdl.handle.net/2117/394525
Access Level:acceso abierto
Palabra clave:Machine learning
Neural networks (Computer science)
Deep learning (Machine learning)
Kernel functions
Hilbert, Espaces de
aprenentatge automàtic
xarxes neuronals
aprenentatge profund
mètodes kernel
optimització
teorema de representació
espais de Hilbert
regularització
machine learning
neural networks
deep learning
kernel methods
optimitzation
representer theorem
Hilbert spaces
regularization
Aprenentatge automàtic
Xarxes neuronals (Informàtica)
Aprenentatge profund
Kernel, Funcions de
Hilbert, Espais de
Àrees temàtiques de la UPC::Informàtica::Intel·ligència artificial::Aprenentatge automàtic
Descripción
Sumario:Deep Learning architectures in which neural layers alternate with mappings to infinitedimensional feature spaces have been proposed in recent years, showing improvements on the results obtained when using either technique separately. However, these new algorithms have been presented without delving into the rich mathematical structure that sustains kernel methods. The main focus of this thesis is not only to review these advances in the field of Deep Learning, but to extend and generalize them by defining a broader family of models that operate under the mathematical framework defined by the composition of a neural layerwith a kernel mapping, all of which operate in reproducing kernel Hilbert spaces thatare then concatenated. Each of these spaces has a specific reproducing kernel that we can characterize. Together all of this defines a regularization-based learning optimization problem, for which we prove that minimizers exist. This strong mathematical background is complemented by the presentation of a new a model, the Kernel Network, which manages to produce successful results on many classification problems.