Projected sequential Gaussian processes: flexible interpolation for large data sets

Ben Ingham, Dan Cornford, Remi Barillec

Research output: Contribution to conferencePaper

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.
Original languageEnglish
Publication statusPublished - Jun 2009
EventStatGIS 2009 - Milos (GR)
Duration: 16 Jun 200918 Jun 2009

Conference

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

Fingerprint

Interpolation
Maximum likelihood estimation
Data fusion
Covariance matrix
Learning systems
Statistics
Sensors

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

Cite this

Ingham, B., Cornford, D., & Barillec, R. (2009). Projected sequential Gaussian processes: flexible interpolation for large data sets. Paper presented at StatGIS 2009, Milos (GR), .
Ingham, Ben ; Cornford, Dan ; Barillec, Remi. / Projected sequential Gaussian processes: flexible interpolation for large data sets. Paper presented at StatGIS 2009, Milos (GR), .
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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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author = "Ben Ingham and Dan Cornford and Remi Barillec",
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month = "6",
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Ingham, B, Cornford, D & Barillec, R 2009, 'Projected sequential Gaussian processes: flexible interpolation for large data sets' Paper presented at StatGIS 2009, Milos (GR), 16/06/09 - 18/06/09, .

Projected sequential Gaussian processes: flexible interpolation for large data sets. / Ingham, Ben; Cornford, Dan; Barillec, Remi.

2009. Paper presented at StatGIS 2009, Milos (GR), .

Research output: Contribution to conferencePaper

TY - CONF

T1 - Projected sequential Gaussian processes: flexible interpolation for large data sets

AU - Ingham, Ben

AU - Cornford, Dan

AU - Barillec, Remi

PY - 2009/6

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Ingham B, Cornford D, Barillec R. Projected sequential Gaussian processes: flexible interpolation for large data sets. 2009. Paper presented at StatGIS 2009, Milos (GR), .