Extended Linear Models with Gaussian Priors

Joaquin Quiñonero-Candela

AbstractIn extended linear models the input space is projected onto a feature space by
means of an arbitrary non-linear transformation. A linear model is then applied to
the feature space to construct the model output. The dimension of the feature
space can be very large, or even infinite, giving the model a very big flexibility.
Support Vector Machines (SVM's) and Gaussian processes are two examples of
such models. In this technical report I present a model in which the dimension of
the feature space remains finite, and where a Bayesian approach is used to train
the model with Gaussian priors on the parameters. The Relevance Vector
Machine, introduced by Tipping, is a particular case of such a model. I give the
detailed derivations of the expectation-maximisation (EM) algorithm used in the
training. These derivations are not found in the literature, and might be helpful for
Keywordslinear models, bayes, Gaussian processes, Relevance Vector Machine, Expectation-Maximization algorithm
TypeTechnical report
PublisherInformatics and Mathematical Modelling, Technical University of Denmark
AddressRichard Petersens Plads, Building 321, DK-2800 Kongens Lyngby, Denmark
Electronic version(s)[ps]
BibTeX data [bibtex]
IMM Group(s)Intelligent Signal Processing

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