The doctoral dissertations of the former Helsinki University of Technology (TKK) and Aalto University Schools of Technology (CHEM, ELEC, ENG, SCI) published in electronic format are available in the electronic publications archive of Aalto University - Aaltodoc.
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Doctoral dissertation for the degree of Doctor of Science in Technology to be presented with due permission of the Faculty of Information and Natural Sciences for public examination and debate in Auditorium E at the Aalto University School of Science and Technology (Espoo, Finland) on the 19th of October 2010 at 12 noon.
Overview in PDF format (ISBN 978-952-60-3381-5) [580 KB]
Errata (in PDF format)
Dissertation is also available in print (ISBN 978-952-60-3380-8)
In this dissertation Gaussian processes are used to define prior distributions over latent functions in hierarchical Bayesian models. Gaussian process is a non-parametric model with which one does not need to fix the functional form of the latent function, but its properties can be defined implicitly. These implicit statements are encoded in the mean and covariance function, which determine, for example, the smoothness and variability of the function. This non-parametric nature of the Gaussian process gives rise to a flexible and diverse class of probabilistic models.
There are two main challenges with using Gaussian processes. Their main complication is the computational time which increases rapidly as a function of a number of data points. Other challenge is the analytically intractable inference, which exacerbates the slow computational time. This dissertation considers methods to alleviate these problems.
The inference problem is attacked with approximative methods. The Laplace approximation and expectation propagation algorithm are utilized to give Gaussian approximation to the conditional posterior distribution of the latent function given the hyperparameters. The integration over hyperparameters is performed using a Monte Carlo, a grid based, or a central composite design integration. Markov chain Monte Carlo methods over all unknown parameters are used as a golden standard to which the other methods are compared. The rapidly increasing computational time is cured with sparse approximations to Gaussian process and compactly supported covariance functions. These are both analyzed in detail and tested in experiments. Practical details on their implementation with the approximative inference techniques are discussed.
The techniques for speeding up the inference are tested in three modeling problems. The problems considered are disease mapping, regression and classification. The disease mapping and regression problems are tackled with standard and robust observation models. The results show that the techniques presented speed up the inference considerably without compromising the accuracy severely.
This thesis consists of an overview and of the following 6 publications:
Keywords: sparse Gaussian process, approximate inference, compactly supported covariance function
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© 2010 Aalto University School of Science and Technology