### Abstract

Original language | English |
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Publication status | Published - Jun 2009 |

Event | StatGIS 2009 - Milos (GR) Duration: 16 Jun 2009 → 18 Jun 2009 |

### Conference

Conference | StatGIS 2009 |
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City | Milos (GR) |

Period | 16/06/09 → 18/06/09 |

### Fingerprint

### 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

*Projected sequential Gaussian processes: flexible interpolation for large data sets*. Paper presented at StatGIS 2009, Milos (GR), .

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

Research output: Contribution to conference › Paper

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

Y1 - 2009/6

N2 - 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.

AB - 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.

KW - reduced rank representations

KW - covariance matrix

KW - projected rank approaches

KW - fixed rank approaches

KW - covariance function

KW - posterior process

KW - reduced rank approximation

KW - sequential framework for inference

KW - C++ library

KW - sequential estimation

KW - generic observation operator

KW - sensor model

KW - data fusion

KW - non-Gaussian observation errors

KW - inference for the variogram parameters

KW - maximum likelihood estimation

M3 - Paper

ER -