### Abstract

assumes the outputs (responses) are more correlated, the closer the inputs (ex-

planatory or independent variables) are. A GP has unknown (hyper)parameters

that must be estimated; the standard estimation method uses the "maximum

likelihood" criterion. However, big data make it hard to compute the estimates

of these GP parameters, and the resulting Kriging predictor and the variance

of this predictor. To solve this problem, some authors select a relatively small

subset from the big set of previously observed "old" data; their method is se-

quential and depends on the variance of the Kriging predictor. The resulting

designs turn out to be "local"; i.e., most design points are concentrated around

the point to be predicted. We develop three alternative one-shot methods that

do not depend on GP parameters: (i) select a small subset such that this sub-

set still covers the original input space–albeit coarser; (ii) select a subset with

relatively many— but not all— combinations close to the new combination that

is to be predicted, and (iii) select a subset with the nearest neighbors (NNs)

of this new combination. To evaluate these designs, we compare their squared

prediction errors in several numerical (Monte Carlo) experiments. These experi-

ments show that our NN design is a viable alternative for the more sophisticated

sequential designs.

Language | English |
---|---|

Place of Publication | Tilburg |

Publisher | CentER, Center for Economic Research |

Number of pages | 43 |

Volume | 2018-022 |

State | Published - 9 Jul 2018 |

### Publication series

Name | CentER Discussion Paper |
---|---|

Volume | 2018-022 |

### Fingerprint

### Keywords

- kriging
- Gaussian process
- big data
- experimental design
- nearest neighbor

### Cite this

*Prediction for Big Data through Kriging: Small Sequential and One-Shot Designs*. (CentER Discussion Paper; Vol. 2018-022). Tilburg: CentER, Center for Economic Research.

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**Prediction for Big Data through Kriging : Small Sequential and One-Shot Designs.** / Kleijnen, J.P.C.; van Beers, W.C.M.

Research output: Working paper › Discussion paper › Other research output

TY - UNPB

T1 - Prediction for Big Data through Kriging

T2 - Small Sequential and One-Shot Designs

AU - Kleijnen,J.P.C.

AU - van Beers,W.C.M.

N1 - CentER Discussion Paper Nr. 2018-022

PY - 2018/7/9

Y1 - 2018/7/9

N2 - Kriging or Gaussian process (GP) modeling is an interpolation method thatassumes the outputs (responses) are more correlated, the closer the inputs (ex-planatory or independent variables) are. A GP has unknown (hyper)parametersthat must be estimated; the standard estimation method uses the "maximumlikelihood" criterion. However, big data make it hard to compute the estimatesof these GP parameters, and the resulting Kriging predictor and the varianceof this predictor. To solve this problem, some authors select a relatively smallsubset from the big set of previously observed "old" data; their method is se-quential and depends on the variance of the Kriging predictor. The resultingdesigns turn out to be "local"; i.e., most design points are concentrated aroundthe point to be predicted. We develop three alternative one-shot methods thatdo not depend on GP parameters: (i) select a small subset such that this sub-set still covers the original input space–albeit coarser; (ii) select a subset withrelatively many— but not all— combinations close to the new combination thatis to be predicted, and (iii) select a subset with the nearest neighbors (NNs)of this new combination. To evaluate these designs, we compare their squaredprediction errors in several numerical (Monte Carlo) experiments. These experi-ments show that our NN design is a viable alternative for the more sophisticatedsequential designs.

AB - Kriging or Gaussian process (GP) modeling is an interpolation method thatassumes the outputs (responses) are more correlated, the closer the inputs (ex-planatory or independent variables) are. A GP has unknown (hyper)parametersthat must be estimated; the standard estimation method uses the "maximumlikelihood" criterion. However, big data make it hard to compute the estimatesof these GP parameters, and the resulting Kriging predictor and the varianceof this predictor. To solve this problem, some authors select a relatively smallsubset from the big set of previously observed "old" data; their method is se-quential and depends on the variance of the Kriging predictor. The resultingdesigns turn out to be "local"; i.e., most design points are concentrated aroundthe point to be predicted. We develop three alternative one-shot methods thatdo not depend on GP parameters: (i) select a small subset such that this sub-set still covers the original input space–albeit coarser; (ii) select a subset withrelatively many— but not all— combinations close to the new combination thatis to be predicted, and (iii) select a subset with the nearest neighbors (NNs)of this new combination. To evaluate these designs, we compare their squaredprediction errors in several numerical (Monte Carlo) experiments. These experi-ments show that our NN design is a viable alternative for the more sophisticatedsequential designs.

KW - kriging

KW - Gaussian process

KW - big data

KW - experimental design

KW - nearest neighbor

M3 - Discussion paper

VL - 2018-022

T3 - CentER Discussion Paper

BT - Prediction for Big Data through Kriging

PB - CentER, Center for Economic Research

CY - Tilburg

ER -