Compressive Kriging Using Multi-Dimensional Generalized Nested Sampling

Qiao, Heng; Hucumenoglu, Mehmet Can; Pal, Piya

doi:10.1109/acssc.2018.8645258

Cited by 2 publications

(2 citation statements)

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“…Remark 3. (Alternative framework) The spatial prediction problem has been investigated in a different statistical framework, much more restrictive regarding practical applications, assuming the observation of N ≥ 1 independent copies of X(s n ), in Qiao et al (2018), where a nonasymptotic analysis is carried out as N increases. We also point out that, instead of the classic in-fill setting considered in Section 3.2 (stipulating that the grid s n formed by the observed sites in S is denser and denser, while S is fixed), the out-fill framework can be considered alternatively (prediction accuracy is then analyzed as the spatial domain S becomes wider and wider) or combined with the in-fill model in a hybrid fashion, see e.g.…”

Section: Statistical Krigingmentioning

confidence: 99%

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A Statistical Learning View of Simple Kriging

Siviero¹,

Chautru²,

Clémençon³

2022

Preprint

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In the Big Data era, with the ubiquity of geolocation sensors in particular, massive datasets exhibiting a possibly complex spatial dependence structure are becoming increasingly available. In this context, the standard probabilistic theory of statistical learning does not apply directly and guarantees of the generalization capacity of predictive rules learned from such data are left to establish. We analyze here the simple Kriging task, the flagship problem in Geostatistics: the values of a square integrable random field X = {Xs}s∈S, S ⊂ R 2 , with unknown covariance structure are to be predicted with minimum quadratic risk, based upon observing a single realization of the spatial process at a finite number of locations s1, . . . , sn in S. Despite the connection of this minimization problem with kernel ridge regression, establishing the generalization capacity of empirical risk minimizers is far from straightforward, due to the non i.i.d. nature of the spatial data Xs 1 , . . . , Xs n involved. In this article, nonasymptotic bounds of order O P (1/n) are proved for the excess risk of a plug-in predictive rule mimicking the true minimizer in the case of isotropic stationary Gaussian processes observed at locations forming a regular grid. These theoretical results, as well as the role played by the technical conditions required to establish them, are illustrated by various numerical experiments and hopefully pave the way for further developments in statistical learning based on spatial data.

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Section: Statistical Krigingmentioning

confidence: 99%

“…Note that in (Qiao et al, 2018), nonasymptotic analysis has been carried out but in a much more restrictive statistical framework regarding practical assumptions: concentration analysis bounds have been derived when independent copies of the spatial process are assumed to be observed.…”

Section: B7 Proof Of Theoremmentioning

confidence: 99%