Reproducing kernel Hilbert spaces regression: a general framework for genetic evaluation.

Reproducing kernel Hilbert spaces (RKHS) methods are widely used for statistical learning in many areas of endeavor. Recently, these methods have been suggested as a way of incorporating dense markers into genetic models. This note argues that RKHS regression provides a general framework for genetic evaluation that can be used either for pedigree- or marker-based regressions and under any genetic model, infinitesimal or not, and additive or not. Most of the standard models for genetic evaluation, such as infinitesimal animal or sire models, and marker-assisted selection models appear as special cases of RKHS methods.

[1]  Daniel Gianola,et al.  Inferring genetic values for quantitative traits non-parametrically. , 2008, Genetics research.

[2]  Peter Craven,et al.  Smoothing noisy data with spline functions , 1978 .

[3]  C. Cockerham,et al.  An Extension of the Concept of Partitioning Hereditary Variance for Analysis of Covariances among Relatives When Epistasis Is Present. , 1954, Genetics.

[4]  C. R. Henderson,et al.  Best linear unbiased estimation and prediction under a selection model. , 1975, Biometrics.

[5]  M Grossman,et al.  Marker assisted selection using best linear unbiased prediction , 1989, Genetics Selection Evolution.

[6]  Jean-Philippe Vert,et al.  Graph-Driven Feature Extraction From Microarray Data Using Diffusion Kernels and Kernel CCA , 2002, NIPS.

[7]  Nello Cristianini,et al.  Kernel Methods for Pattern Analysis , 2003, ICTAI.

[8]  G. Wahba,et al.  A Correspondence Between Bayesian Estimation on Stochastic Processes and Smoothing by Splines , 1970 .

[9]  Christopher K. I. Williams,et al.  Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning) , 2005 .

[10]  R. L. Quaas,et al.  Mixed Model Methodology for Farm and Ranch Beef Cattle Testing Programs , 1980 .

[11]  G. Robinson.  That BLUP is a Good Thing: The Estimation of Random Effects , 1991 .

[12]  D. Gianola,et al.  Reproducing Kernel Hilbert Spaces Regression Methods for Genomic Assisted Prediction of Quantitative Traits , 2008, Genetics.

[13]  L. Penrose,et al.  THE CORRELATION BETWEEN RELATIVES ON THE SUPPOSITION OF MENDELIAN INHERITANCE , 2022 .

[14]  G. Wahba.  Spline models for observational data , 1990 .

[15]  H. Piepho,et al.  BLUP for phenotypic selection in plant breeding and variety testing , 2008, Euphytica.

[16]  S. Wright,et al.  Systems of Mating. I. the Biometric Relations between Parent and Offspring. , 1921, Genetics.

[17]  R. Fisher.  XV.—The Correlation between Relatives on the Supposition of Mendelian Inheritance. , 1919, Transactions of the Royal Society of Edinburgh.

[18]  Vladimir Vapnik,et al.  Statistical learning theory , 1998 .

[19]  David A. Harville,et al.  [That BLUP is a Good Thing: The Estimation of Random Effects]: Comment , 1991 .

[20]  R. L. Quaas,et al.  Multiple Trait Evaluation Using Relatives' Records , 1976 .

[21]  Kent A Weigel,et al.  Nonparametric Methods for Incorporating Genomic Information Into Genetic Evaluations: An Application to Mortality in Broilers , 2008, Genetics.

[22]  O. Kempthorne,et al.  The correlation between relatives in a random mating population , 1954, Proceedings of the Royal Society of London. Series B - Biological Sciences.

[23]  R. Fernando,et al.  Genomic-Assisted Prediction of Genetic Value With Semiparametric Procedures , 2006, Genetics.