Group Kernels for Gaussian Process Metamodels with Categorical Inputs

Roustant, Olivier; Padonou, Espéran; Deville, Yves; Clement, A.; Perrin, Guillaume; Giorla, J.; Wynn, Henry P.

doi:10.1137/18m1209386

Cited by 46 publications

(87 citation statements)

References 13 publications

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“…To construct the fused , one approach is to take the product between a kernel for the Age–Year covariates and a kernel for the categorical ones (Qian et al ., 2008; Roustant et al ., 2018). Let: with Note that is symmetric in i and j .…”

Section: Mogp Modelsmentioning

confidence: 99%

Multi-output Gaussian processes for multi-population longevity modelling

Huynh

Ludkovski

2021

Ann. actuar. sci.

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We investigate joint modelling of longevity trends using the spatial statistical framework of Gaussian process (GP) regression. Our analysis is motivated by the Human Mortality Database (HMD) that provides unified raw mortality tables for nearly 40 countries. Yet few stochastic models exist for handling more than two populations at a time. To bridge this gap, we leverage a spatial covariance framework from machine learning that treats populations as distinct levels of a factor covariate, explicitly capturing the cross-population dependence. The proposed multi-output GP models straightforwardly scale up to a dozen populations and moreover intrinsically generate coherent joint longevity scenarios. In our numerous case studies, we investigate predictive gains from aggregating mortality experience across nations and genders, including by borrowing the most recently available “foreign” data. We show that in our approach, information fusion leads to more precise (and statistically more credible) forecasts. We implement our models in R, as well as a Bayesian version in Stan that provides further uncertainty quantification regarding the estimated mortality covariance structure. All examples utilise public HMD datasets.

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Section: Mogp Modelsmentioning

confidence: 99%

Multi-output Gaussian processes for multi-population longevity modelling

Huynh

Ludkovski

2021

Ann. actuar. sci.

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“…As recommended in Reference 15, d is typically set to 1 or 2, which renders ∑ j at most rank‐2 or rank‐3. Although low‐rank correlation matrices like (10) have been used in many statistical models in various contexts, its use for GP modeling appears to have been first considered in Reference 17, who compared it to the LV‐Car model.…”

Section: Two LV Representations Of Qualitative Factorsmentioning

confidence: 99%

“…Another parameter is the type of latent space and the associated correlation function. While it is straightforward to use Cartesian latent spaces with Gaussian correlation function as in Zhang et al, 15 another latent‐variable approach using hyperspherical latent spaces and dot‐product function also achieves remarkable performance 17 . We respectively refer to these as LVs in Cartesian (LV‐Car) and hyperspherical (LV‐sph).…”

Section: Introductionmentioning

confidence: 99%

Latent variable Gaussian process models: A rank‐based analysis and an alternative approach

Tao

Apley

Plumlee

et al. 2021

Numerical Meth Engineering

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Gaussian process (GP) models have been extended to emulate expensive computer simulations with both qualitative/categorical and quantitative/continuous variables. Latent variable (LV) GP models, which have been recently developed to map each qualitative variable to some underlying numerical LVs, have strong physics-based justification and have achieved promising performance.Two versions use LVs in Cartesian (LV-Car) space and hyperspherical (LV-sph) space, respectively. Despite their success, the effects of these different LV structures are still poorly understood. This article illuminates this issue with two contributions. First, we develop a theorem on the effect of the ranks of the qualitative factor correlation matrices of mixed-variable GP models, from which we conclude that the LV-sph model restricts the interactions between the input variables and thus restricts the types of response surface data with which the model can be consistent. Second, following a rank-based perspective like in the theorem, we propose a new alternative model named LV-mix that combines the LV-based correlation structures from both LV-Car and LV-sph models to achieve better model flexibility than them. Through extensive case studies, we show that LV-mix achieves higher average accuracy compared with the existing two.

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“…A thorough discussion on the choices of the correlation matrix R (·| θ ) in the GP model for QQ factors can be found in Roustant, Padonou, Deville, Clément, and Wynn () and Zhang and Notz ().…”

Section: Analysis Of Computer Experiments With Qq Inputsmentioning

confidence: 99%

“…A few other directions of analyzing computer experiments for QQ factors are also developed recently. Roustant et al () proposed “group kernels” for the GP model with QQ factors to accommodate a potentially large number of combination levels of qualitative factors. Zhang, Tao, Chen, and Apley () introduced an approach that maps each qualitative factor to an underlying quantitative latent variable, such that the GP model with QQ factors can be transformed to a standard GP model with only quantitative factors.…”

Section: Analysis Of Computer Experiments With Qq Inputsmentioning

confidence: 99%

Design and analysis of computer experiments with quantitative and qualitative inputs: A selective review

Kang

Deng

2020

WIREs Data Min & Knowl

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Computer experiment refers to the study of complex systems by using computer simulations to emulate the physical system. Design and analysis of computer experiments have attracted great attention in past decades. However, many computer experiments involve not only quantitative inputs, but also qualitative inputs, which make the design and analysis more challenging. The Latin hypercube design and its variants are widely used in computer experiments, but mainly for the quantitative inputs. Constructing desirable emulators for computer experiments with qualitative inputs also remains a challenging problem due to the discrete nature of qualitative inputs. In this review, we describe a set of statistical approaches for design and analysis of computer experiments with both quantitative and qualitative factors. This article is categorized under: Fundamental Concepts of Data and Knowledge > Key Design Issues in Data Mining Algorithmic Development > Statistics

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Group Kernels for Gaussian Process Metamodels with Categorical Inputs

Cited by 46 publications

References 13 publications

Multi-output Gaussian processes for multi-population longevity modelling

Multi-output Gaussian processes for multi-population longevity modelling

Latent variable Gaussian process models: A rank‐based analysis and an alternative approach

Design and analysis of computer experiments with quantitative and qualitative inputs: A selective review

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