A warped kernel improving robustness in Bayesian optimization via random embeddings

David Ginsbourger ((M\'ethodes d'Analyse Stochastique des Codes et Traitements Num\'eriques); DEMO-ENSMSE); IMSV); Micka\"el Binois (DEMO-ENSMSE); Olivier Roustant ((M\'ethodes d'Analyse Stochastique des Codes et Traitements Num\'eriques)

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A warped kernel improving robustness in Bayesian optimization via random embeddings

Mickaël Binois (DEMO-ENSMSE), David Ginsbourger ((Méthodes d'Analyse Stochastique des Codes et Traitements Numériques), IMSV), Olivier Roustant ((Méthodes d'Analyse Stochastique des Codes et Traitements Numériques), DEMO-ENSMSE)

Optimization and Control · Submitted 13 Nov 2014

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim It also alleviates constraints on bound selection for the embedded domain, thus improving the robustness, as illustrated with a test case with 25 variables and intrinsic dimension 6.

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arXiv ID1411.3685 (version 3)

Pith IDOU3QDPKU, Pith's permanent record of this paper and its review

CitationDavid Ginsbourger ((M\'ethodes d'Analyse Stochastique des Codes et Traitements Num\'eriques), DEMO-ENSMSE), IMSV), Micka\"el Binois (DEMO-ENSMSE), Olivier Roustant ((M\'ethodes d'Analyse Stochastique des Codes et Traitements Num\'eriques). "A warped kernel improving robustness in Bayesian optimization via random embeddings." arXiv:1411.3685 (2014). https://pith.science/paper/OU3QDPKU

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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,971 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.14 · human participants 0.02 · controlled comparison 0.12 · randomized assignment 0.02 · states quantitative result 0.68 · compares with prior results 0.25 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

This works extends the Random Embedding Bayesian Optimization approach by integrating a warping of the high dimensional subspace within the covariance kernel. The proposed warping, that relies on elementary geometric considerations, allows mitigating the drawbacks of the high extrinsic dimensionality while avoiding the algorithm to evaluate points giving redundant information. It also alleviates constraints on bound selection for the embedded domain, thus improving the robustness, as illustrated with a test case with 25 variables and intrinsic dimension 6.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	This works extends the Random Embedding Bayesian Optimization approach by integrating a warping of the high dimensional subspace within the covariance kernel.	contribution 0.98	0.85	0.13	asserted 1.00
s1	The proposed warping, that relies on elementary geometric considerations, allows mitigating the drawbacks of the high extrinsic dimensionality while avoiding the algorithm to evaluate points giving redundant information.	method 0.64	0.78	0.28	asserted 0.96
s2	It also alleviates constraints on bound selection for the embedded domain, thus improving the robustness, as illustrated with a test case with 25 variables and intrinsic dimension 6.	result 0.84	0.88	0.46	asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.89.

What was examined, and what was not

sources read

arXiv listing abstract v3

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

This works extends the Random Embedding Bayesian Optimization approach by integrating a warping of the high dimensional subspace within the covariance kernel. The proposed warping, that relies on elementary geometric considerations, allows mitigating the drawbacks of the high extrinsic dimensionality while avoiding the algorithm to evaluate points giving redundant information. It also alleviates constraints on bound selection for the embedded domain, thus improving the robustness, as illustrated with a test case with 25 variables and intrinsic dimension 6.

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2 arXiv papers cite this in 5 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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Cites it as background 1 paper

Alternating learning and optimization steps has also been proposed [ref] , as well as bypassing learning and directly optimizing in randomly-chosen low-dimensional subspaces (provided an estimate of the effective dimension is known) [ref] .

A dimensionality reduction technique for unconstrained global optimization of functions with low effective dimensionality · Introduction · 0.93

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