Level sets of conditional Gaussian fields
Gaussian processes are extensively used for regression and optimization tasks. This thesis aims to understand the behavior of the level sets of three-dimensional conditional Gaussian processes. Given a random sample of one of these processes, we can infer information about the geometrical structure...
| Autor: | |
|---|---|
| Formato: | tesis de maestría |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2020 |
| País: | México |
| Recursos: | Centro de Investigación en Matemáticas |
| Repositorio: | Repositorio Institucional CIMAT |
| OAI Identifier: | oai:cimat.repositorioinstitucional.mx:1008/1079 |
| Acesso em linha: | http://cimat.repositorioinstitucional.mx/jspui/handle/1008/1079 |
| Access Level: | acceso abierto |
| Palavra-chave: | info:eu-repo/classification/MSC/PROBABILIDAD Y ESTADÍSTICA info:eu-repo/classification/cti/1 info:eu-repo/classification/cti/12 info:eu-repo/classification/cti/1299 info:eu-repo/classification/cti/129999 |
| Resumo: | Gaussian processes are extensively used for regression and optimization tasks. This thesis aims to understand the behavior of the level sets of three-dimensional conditional Gaussian processes. Given a random sample of one of these processes, we can infer information about the geometrical structure of the process that generates it. With this knowledge, we can improve our predictions or avoid local minima in the optimization case. For our empirical analysis, we simplify the problem by conditioning a Gaussian process over a known smooth boundary that is contained inside a given square. We model the level sets topology of this conditioned Gaussian process via Vietoris-Rips complexes, for which we can use fast computer algorithms to calculate the rank of their corresponding homology groups. |
|---|