A Unified and Comprehensible View of Parametric and Kernel Methods for Genomic Prediction with Application to Rice

Abstract

One objective of this study was to provide readers with a clear and unified understanding of parametric statistical and kernel methods, used for genomic prediction, and to compare some of these in the context of rice breeding for quantitative traits. Furthermore, another objective was to provide a simple and user-friendly R package, named , which allows users to perform RKHS regression with several kernels. After introducing the concept of regularized empirical risk minimization, the connections between well-known parametric and kernel methods such as Ridge regression [i.e., genomic best linear unbiased predictor (GBLUP)] and reproducing kernel Hilbert space (RKHS) regression were reviewed. Ridge regression was then reformulated so as to show and emphasize the advantage of the kernel “trick” concept, exploited by kernel methods in the context of epistatic genetic architectures, over parametric frameworks used by conventional methods. Some parametric and kernel methods; least absolute shrinkage and selection operator (LASSO), GBLUP, support vector machine regression (SVR) and RKHS regression were thereupon compared for their genomic predictive ability in the context of rice breeding using three real data sets. Among the compared methods, RKHS regression and SVR were often the most accurate methods for prediction followed by GBLUP and LASSO. An R function which allows users to perform RR-BLUP of marker effects, GBLUP and RKHS regression, with a Gaussian, Laplacian, polynomial or ANOVA kernel, in a reasonable computation time has been developed. Moreover, a modified version of this function, which allows users to tune kernels for RKHS regression, has also been developed and parallelized for HPC Linux clusters. The corresponding package and all scripts have been made publicly available.

Selection of trait-specific markers and multi-environment models improve genomic predictive ability in rice

“…The implementation procedures of the two models is detailed in [42]. Briefly the GBLUP method that hypothesizes a strictly additive determinism of the genetic effects [54] was implemented using the genomic matrix G = M*M’ (M being the genotypic matrix) and the Expectation-Maximization convergence algorithm with the R package KRMM [55]. The RKHS method that captures more complex genetic determinism [56] was also implemented using the KRMM .…”

Rice diversity panel provides accurate genomic predictions for complex traits in the progenies of biparental crosses involving members of the panel

“…The R package kernlab (Karatzoglou et al 2004 ) was used to compute the kernel matrix. Both GBLUP and RKHS methods were implemented using the KRMM package ( https://cran.r-project.org/web/packages/KRMM/index.html ) described by Jacquin et al ( 2016 ). For BayesB, the model that specified two component mixtures prior with a point of mass at zero and a scaled- t slab for marker effect (Meuwissen et al 2001 ) was implemented using the BGLR statistical package (Pérez and de los Campos 2014 ).…”

Genomic Prediction of Breeding Values Using a Subset of SNPs Identified by Three Machine Learning Methods

“…Since Meuwissen et al ( 2001 ) pioneered the genome wide selection method using high-density SNP markers in breeding value prediction, there have been a number of studies that examined the influence of parametric and nonparametric methods on the predictability of phenotypic values (e.g., de los Campos et al, 2013 ; Howard et al, 2014 ; Okser et al, 2014 ; Jacquin et al, 2016 ; Waldmann, 2016 ). Using simulated SNP data with additive or two-way epistatic interactions, Howard et al ( 2014 ) evaluated the prediction accuracy and mean squared error (MSE) of phenotypic values of 10 parametric and four nonparametric methods.…”