Gaussian process classification: singly versus doubly stochastic models, and new computational schemes |
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| Authors: | Jens R?der Raimon Tolosana-Delgado Fred A Hamprecht |
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| Institution: | (1) Corporate Sector Research and Advance Engineering Multimedia, Telematic and Surround Sensing Systems (CR/AEM), Robert Bosch GmbH, Hildesheim, Germany;(2) Maritime Engineering Laboratory (LIM), Universitat Polit?cnica de Catalunya (UPC), Barcelona, Spain;(3) Heidelberg Collaboratory for Image Processing (HCI), University of Heidelberg, Heidelberg, Germany;; |
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| Abstract: | The aim of this paper is to compare four different methods for binary classification with an underlying Gaussian process with
respect to theoretical consistency and practical performance. Two of the inference schemes, namely classical indicator kriging
and simplicial indicator kriging, are analytically tractable and fast. However, these methods rely on simplifying assumptions
which are inappropriate for categorical class labels. A consistent and previously described model extension involves a doubly
stochastic process. There, the unknown posterior class probability f(·) is considered a realization of a spatially correlated Gaussian process that has been squashed to the unit interval, and
a label at position x is considered an independent Bernoulli realization with success parameter f(x). Unfortunately, inference for this model is not known to be analytically tractable. In this paper, we propose two new computational
schemes for the inference in this doubly stochastic model, namely the “Aitchison Maximum Posterior” and the “Doubly Stochastic
Gaussian Quadrature”. Both methods are analytical up to a final step where optimization or integration must be carried out
numerically. For the comparison of practical performance, the methods are applied to storm forecasts for the Spanish coast
based on wave heights in the Mediterranean Sea. While the error rate of the doubly stochastic models is slightly lower, their
computational cost is much higher. |
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