KRMM-package: Kernel Ridge Mixed Model

In KRMM: Kernel Ridge Mixed Model

Description

Solves kernel ridge regression, within the the mixed model framework, for the linear, polynomial, Gaussian, Laplacian and ANOVA kernels. The model components (i.e. fixed and random effects) and variance parameters are estimated using the expectation-maximization (EM) algorithm. All the estimated components and parameters, e.g. BLUP of dual variables and BLUP of random predictor effects for the linear kernel (also known as RR-BLUP), are available. The kernel ridge mixed model (KRMM) is described in Jacquin L, Cao T-V and Ahmadi N (2016) A Unified and Comprehensible View of Parametric and Kernel Methods for Genomic Prediction with Application to Rice. Front. Genet. 7:145.

Details

This package solves kernel ridge regression for various kernels within the following mixed model framework: Y =X*Beta + Z*U + E, where X and Z correspond to the design matrices of predictors with fixed and random effects respectively. The functions provided with this package are Kernel_Ridge_MM, Tune_kernel_Ridge_MM, Predict_kernel_Ridge_MM and EM_REML_MM.

Author(s)

Laval Jacquin Maintainer: Laval Jacquin <[e-mail]>

References

Jacquin et al. (2016). A unified and comprehensible view of parametric and kernel methods for genomic prediction with application to rice (in peer review).

Robinson, G. K. (1991). That blup is a good thing: the estimation of random effects. Statistical science, 534 15-32

Foulley, J.-L. (2002). Algorithme em: théorie et application au modèle mixte. Journal de la Société française de Statistique 143, 57-109

Examples

## Not run: 

library(KRMM)

### SIMULATE DATA 
set.seed(123)
p=200
N=100

beta=rnorm(p, mean=0, sd=1.0)
X=matrix(runif(p*N, min=0, max=1), ncol=p, byrow=TRUE)  #X: covariates (i.e. predictors)

f=X%*%beta                    #f: data generating process (i.e. DGP)
E=rnorm(N, mean=0, sd=0.5)

Y=f+E                           #Y: observed response data

hist(f)
hist(beta)
Nb_train=floor((2/3)*N)

###======================================================================###
### CREATE TRAINING AND TARGET SETS FOR RESPONSE AND PREDICTOR VARIABLES ###
###======================================================================###

Index_train=sample(1:N, size=Nb_train, replace=FALSE)

### Covariates (i.e. predictors) for training and target sets

Predictors_train=X[Index_train, ]
Response_train=Y[Index_train]

Predictors_target=X[-Index_train, ]
True_value_target=f[-Index_train]    #True value (generated by DGP) we want to predict

###=================================================================================###
### PREDICTION WITH KERNEL RIDGE REGRESSION SOLVED WITHIN THE MIXED MODEL FRAMEWORK ### 
###=================================================================================###

#Linear kernel

Linear_KRR_model_train = Kernel_Ridge_MM(Y_train=Response_train, 
 Matrix_covariates_train=Predictors_train, method="RR-BLUP")

f_hat_target_Linear_KRR = Predict_kernel_Ridge_MM( Linear_KRR_model_train,
 Matrix_covariates_target=Predictors_target )

#Gaussian kernel

Gaussian_KRR_model_train = Kernel_Ridge_MM( Y_train=Response_train, 
 Matrix_covariates_train=Predictors_train, method="RKHS", rate_decay_kernel=5.0)

f_hat_target_Gaussian_KRR = Predict_kernel_Ridge_MM( Gaussian_KRR_model_train, 
 Matrix_covariates_target=Predictors_target )


#Graphics for RR-BLUP

dev.new(width=30, height=20)
par(mfrow=c(3,1))	
plot(f_hat_target_Linear_KRR, True_value_target)
plot(Linear_KRR_model_train$Gamma_hat, xlab="Feature (i.e. covariate) number", 
ylab="Feature effect (i.e. Gamma_hat)", main="BLUP of covariate effects based on training data")
hist(Linear_KRR_model_train$Gamma_hat, main="Distribution of BLUP of 
covariate effects based on training data" )


# Compare prediction based on linear (i.e. RR-BLUP) and Gaussian kernel

dev.new(width=30, height=20)
par(mfrow=c(1,2))
plot(f_hat_target_Linear_KRR, True_value_target)
plot(f_hat_target_Gaussian_KRR, True_value_target)

mean((f_hat_target_Linear_KRR - True_value_target)^2)
mean((f_hat_target_Gaussian_KRR - True_value_target)^2)


## End(Not run)

KRMM documentation built on May 2, 2019, 2:50 p.m.