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Easy Uncertainty Quantification (EasyUQ): Generating Predictive Distributions from Single-Valued Model Output

Walz, Eva-Maria 1; Henzi, Alexander; Ziegel, Johanna; Gneiting, Tilmann 1
1 Institut für Stochastik (STOCH), Karlsruher Institut für Technologie (KIT)

Abstract:

How can we quantify uncertainty if our favorite computational tool---be it a numerical, statistical, or machine learning approach, or just any computer model---provides singlevalued output only? In this article, we introduce the Easy Uncertainty Quantification (EasyUQ) technique, which transforms real-valued model output into calibrated statistical distributions, based solely on training data of model output--outcome pairs, without any need to access model input. In its basic form, EasyUQ is a special case of the recently introduced isotonic distributional regression (IDR) technique that leverages the pool-adjacent-violators algorithm for nonparametric isotonic regression. EasyUQ yields discrete predictive distributions that are calibrated and optimal in finite samples, subject to stochastic monotonicity. The workflow is fully automated, without any need for tuning. The Smooth EasyUQ approach supplements IDR with kernel smoothing, to yield continuous predictive distributions that preserve key properties of the basic form, including both stochastic monotonicity with respect to the original model output and asymptotic consis-
tency. For the selection of kernel parameters, we introduce multiple one-fit grid search, a computationally much less demanding approximation to leave-one-out cross-validation. ... mehr


Verlagsausgabe §
DOI: 10.5445/IR/1000171601
Veröffentlicht am 26.08.2024
Originalveröffentlichung
DOI: 10.1137/22M1541915
Scopus
Zitationen: 2
Web of Science
Zitationen: 1
Dimensions
Zitationen: 2
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Stochastik (STOCH)
Publikationstyp Zeitschriftenaufsatz
Publikationsmonat/-jahr 02.2024
Sprache Englisch
Identifikator ISSN: 0036-1445, 1095-7200
KITopen-ID: 1000171601
Erschienen in SIAM Review
Verlag Society for Industrial and Applied Mathematics (SIAM)
Band 66
Heft 1
Seiten 91–122
Vorab online veröffentlicht am 08.02.2024
Nachgewiesen in Web of Science
Scopus
Dimensions
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