Projected sequential Gaussian processes: flexible interpolation for large data sets

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Abstract

Recently within the machine learning and spatial statistics communities many papers have explored the potential of reduced rank representations of the covariance matrix, often referred to as projected or fixed rank approaches. In such methods the covariance function of the posterior process is represented by a reduced rank approximation which is chosen such that there is minimal information loss. In this paper a sequential framework for inference in such projected processes is presented, where the observations are considered one at a time. We introduce a C++ library for carrying out such projected, sequential estimation which adds several novel features. In particular we have incorporated the ability to use a generic observation operator, or sensor model, to permit data fusion. We can also cope with a range of observation error characteristics, including non-Gaussian observation errors. Inference for the variogram parameters is based on maximum likelihood estimation. We illustrate the projected sequential method in application to synthetic and real data sets. We discuss the software implementation and suggest possible future extensions.

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Original languageEnglish
StatePublished - Jun 2009
EventStatGIS 2009 - Milos (GR)

Conference

ConferenceStatGIS 2009
CityMilos (GR)
Period16/06/0918/06/09

    Keywords

  • reduced rank representations, covariance matrix, projected rank approaches, fixed rank approaches, covariance function, posterior process, reduced rank approximation, sequential framework for inference, C++ library, sequential estimation, generic observation operator, sensor model, data fusion, non-Gaussian observation errors, inference for the variogram parameters, maximum likelihood estimation

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