On Gaussian Process multiple-fold cross-validation - MASCOT NUM 2021 meeting - Main results and consequences

Sep 11, 2026

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Gaussian Process multiple-fold cross-validation is presented as a principled way to validate GP models, estimate hyperparameters through criteria built on cross-validation outputs, and support sequential design strategies. The core mechanism splits available training data into folds, repeatedly leaving out one fold, predicting at the left-out inputs using the remaining data, and comparing predictions against held-out responses. Diagnostics and selection criteria are then computed from residual vectors and the associated GP model outcomes across multiple folds, with emphasis on fast CV-based range fitting illustrated on the Stromboli.

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Introduction

Main results and some first few consequences

Fast CV-based range fitting: towards fold design on the Stromboli

On Gaussian Process multiple-fold cross-validation David Ginsbourger Based on joint works with Ath´ena¨􀀑s Gautier, Cedric Sch¨arer, C´edric Travelletti. DG, AG and CT acknowledge support from the Swiss National Science Foundation project number 178858 . MASCOT NUM 2021 meeting April 27th 2021 [ginsbourger@stat.unibe.ch](ginsbourger@stat.unibe.ch) On GP multiple-fold cross-validation 1/36 Introduction Main results and some 􀀂rst few consequences Fast CV-based range 􀀂tting on the Stromboli 1 Introduction 2 Main results and some 􀀂rst few consequences 3 Fast CV-based range 􀀂tting: towards fold design on the Stromboli [ginsbourger@stat.unibe.ch](ginsbourger@stat.unibe.ch) On GP multiple-fold cross-validation 2/36 Introduction Main results and some 􀀂rst few consequences Fast CV-based range 􀀂tting on the Stromboli 1 Introduction 2 Main results and some 􀀂rst few consequences 3 Fast CV-based range 􀀂tting: towards fold design on the Stromboli [ginsbourger@stat.unibe.ch](ginsbourger@stat.unibe.ch) On GP multiple-fold cross-validation 3/36 Introduction Main results and some 􀀂rst few consequences Fast CV-based range 􀀂tting on the Stromboli In GP modelling, cross-validation (CV) has been used for validating models without requiring external/validation data, estimating hyperparameters (via criteria building on CV outputs), and also, for guiding sequential design strategies [ginsbourger@stat.unibe.ch](ginsbourger@stat.unibe.ch) On GP multiple-fold cross-validation 4/36 Introduction Main results and some 􀀂rst few consequences Fast CV-based range 􀀂tting on the Stromboli In GP modelling, cross-validation (CV) has been used for validating models without requiring external/validation data, estimating hyperparameters (via criteria building on CV outputs), and also, for guiding sequential design strategies The essence of CV is to leave part of the available data / training set away (a“fold”), perform predictions at the corresponding inputs based on the remaining data, and compare predicted versus left out responses. [ginsbourger@stat.unibe.ch](ginsbourger@stat.unibe.ch) On GP multiple-fold cross-validation 4/36 Introduction Main results and some 􀀂rst few consequences Fast CV-based range 􀀂tting on the Stromboli In GP modelling, cross-validation (CV) has been used for validating models without requiring external/validation data, estimating hyperparameters (via criteria building on CV outputs), and also, for guiding sequential design strategies The essence of CV is to leave part of the available data / training set away (a“fold”), perform predictions at the corresponding inputs based on the remaining data, and compare predicted versus left out responses. This operation is conducted multiple times in sequence, i.e. for multiple folds, and then diagnostics/criteria are calculated based on the corresponding set of residual vectors and related model outcomes. [ginsbourger@stat.unibe.ch](ginsbourger@stat.unibe.ch) On GP multiple-fold cross-validation 4/36 Introduction Main results and some 􀀂rst few consequences Fast CV-based range 􀀂tting on the Stromboli Basic versus LOO GP predictions 0.0 0.2 0.4 0.6 0.8 1.0 x | .Pred errors | vs GP s .d . 0.0 0.1 0.2 0.3 0.4 Absolute prediction errors vs GP standard deviation 0.0 0.2 0.4 0.6 0.8 1.0 [ginsbourger@stat.unibe.ch](ginsbourger@stat.unibe.ch) On GP multiple-fold cross-validation 5/36 Introduction Main results and some 􀀂rst few consequences Fast CV-based range 􀀂tting on the Stromboli | .Pred errors | vs GP s .d . 0.00 0.10 0.20 0.30 Absolute prediction errors vs GP standard deviation 0.0 0.2 0.4 0.6 0.8 1.0 x | .Pred errors | vs GP s .d . 0.00 0.10 0.20 0.30 Absolute prediction errors vs GP standard deviation 0.0 0.2 0.4 0.6 0.8 1.0 [ginsbourger@stat.unibe.ch](ginsbourger@stat.unibe.ch) On GP multiple-fold cross-validation 6/36 Introduction Main results and some 􀀂rst few cons

FAQs

What problem does multiple-fold cross-validation address in Gaussian Process modeling?

It provides a way to validate GP models without external validation data, estimate hyperparameters from CV outputs, and guide sequential design strategies.

How does the multiple-fold cross-validation procedure work in this context?

The data are split into folds; for each fold, predictions are made at the left-out inputs using the remaining data, then prediction errors are compared against held-out responses.

What is the focus of the later part of the talk regarding CV results?

It emphasizes main results and early consequences, including fast CV-based range fitting and how it connects to fold design on the Stromboli.

Sep 11, 2026

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