Magíster en Ciencias de la Ingeniería, Mención Matemáticas Aplicadas. Ingeniero Civil Matemático / Multi-Output Gaussian Processes (MOGPs) are the multivariate extension of Gaussian processes (GPs \cite{Rasmussen:2006}), a Bayesian nonparametric method for univariate regression. MOGPs address the multi-channel regression problem by modeling the correlation in time and/or space (as scalar GPs do), but also across channels and thus revealing statistical dependencies among different sources of data. This is crucial in a number of real-world applications such as fault detection, data imputation and financial time-series analysis. Analogously to the univariate case, MOGPs are entirely determined by a multivariate covariance function, which in this case is matrix valued. The design of this matrix-valued covariance function is challenging, since we have to deal with the trade off between (i) choosing a broad class of cross-covariances and auto-covariances, while at the same time (ii) ensuring positive definiteness of the symmetric matrix containing these scalar-valued covariance functions. In the stationary univariate case, these difficulties can be bypassed by virtue of Bochner's theorem, that is, by building the covariance function in the spectral (Fourier) domain to then transform it to the time and/or space domain, thus yielding the (single-output) Spectral Mixture kernel \cite{Wilson:2013}. A classical approach to define multivariate covariance functions for MOGPs is through linear combinations of independent (latent) GPs; this is the case of the Linear Model of Coregionalization (LMC \cite{goo1997}) and the Convolution Model \cite{Alvarez:2008}. In these cases, the resulting multivariate covariance function is a function of both the latent-GP covariances and the linear operator considered, which usually results in symmetric cross-covariances that do not admit lags across channels. Due to their simplicity, these approaches fail to provide interpretability of the dependencies learnt and force the auto-covariances to have similar structure. The main purpose of this work is to extend the spectral mixture concept to MOGPs: We rely on Cram\'er's theorem \cite, the multivariate version of Bochner's theorem, to propose an expressive family of complex-valued square-exponential cross-spectral densities, which, through the Fourier transform yields the Multi-Output Spectral Mixture kernel (MOSM). The proposed MOSM model provides clear interpretation of all the parameters in spectral terms. Besides the theoretical presentation and interpretation of the proposed multi-output covariance kernel based on square-exponential spectral densities, we inquiry the plausibility of complex-valued t-Student cross-spectral densities. We validate our contribution experimentally through an illustrative example using a tri-variate synthetic signal, and then compare it against all the aforementioned methods on two real-world datasets.

[EN] To obtain the market value for urban properties, the following is necessary for the decision making in different scenarios: in case of dealing with financial institutions, the focus will be in acquiring knowledge of the value of the property to finance a mortgage. One of the different government orders are to collect property taxes, so this profit will serve as the foundation for proceedings before public and private organizations. For an accurate estimate of the price or value that will describe the market conditions, it is necessary to build models that will be capable of calculating such value. The synthetic methods that currently use a minor amount of information are the ones that are mostly used by appraisers, as well as the econometric models. Also, they are considered as the concept of multiple linear regression that utilize abundant observations. In reality the econometric models are a generalization of synthetic methods. On the other hand, artificial neural networks and in particular the multi-layer network, can be an alternative for a price estimate. Currently a comparison is being performed between the selected econometric model and the neural network, revealing that the networks give a better outcome for price estimates. This study has been achieved in Morelia, Michoacán, Mexico for several housing segments. / [ES] Obtener el valor de mercado para inmuebles urbanos es necesario para la toma de decisiones en diferentes escenarios: tratándose de instituciones financieras, su interés radica en conocer este valor para el financiamiento de préstamo con garantía hipotecaria, a los diferentes órdenes de gobierno para cobrar los impuestos catastrales, así este valor servirá de base para la realización de diferentes trámites ante entidades públicas o particulares. Para una buena estimación del precio o valor que explique las condiciones del mercado, es necesario construir modelos capaces de estimar dicho valor. Actualmente los métodos sintéticos que usan información escasa son los más utilizados por los tasadores, así como los modelos econométricos -también denominados con el concepto de regresión lineal múltiple- que usan muchas observaciones, en realidad los modelos econométricos son una generalización de los métodos sintéticos. Por otro lado, las redes neuronales artificiales, y en concreto la red multicapa, pueden ser una alternativa para la estimación del precio. En el presente se realiza una comparativa entre el modelo econométrico seleccionado y la red neuronal, demostrando que las redes obtienen mejores resultados en la estimación de precio. El estudio se ha realizado en la ciudad de Morelia, Michoacán, México, para varios segmentos de vivienda. / [CA] Obtindre el valor de mercat per a immobles urbans és necessari per a la presa de decisions en diferents escenaris: tractant-se d'institucions financeres, el seu interès està en conèixer aquest valor per al finançament de préstec amb garantia hipotecària, als diferents ordres de govern per cobrar els impostos cadastrals. Així aquest valor servirà de base per a la realització de diferents tràmits davant entitats públiques o particulars. Per a una bona estimació del preu o valor que expliqui les condicions del mercat, cal construir models capaços d'estimar aquest valor. Actualment els mètodes sintètics que fan servir informació escassa són els més utilitzats pels valuadors, així com els models economètrics -també denominats de regressió lineal múltiple, que fan servir moltes observacions. En realitat els models economètrics són una generalització dels mètodes sintètics. D'altra banda, les xarxes neuronals artificials, i en concret la xarxa multicapa, poden ser una alternativa per a l'estimació del preu. En el present treball es realitza una comparativa entre el model economètric seleccionat i la xarxa neuronal, demostrant que les xarxes obtenen millors resultats en l'estimació de preu. L'estudi s'ha realitzat a la ciutat de Morelia, Michoacán, Mèxic, per a diversos segments d'habitatge. / Preciado Carrillo, JC. (2016). Valoración de inmuebles urbanos comparativa modelo regresión multivariable versus redes neuronales artificiales para la ciudad de Morelia Michoacán, México [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/62202