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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| 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 |
| 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. |
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