uma.predict: Prediction for Universal Adaptive Regression by Mixing

In zhzhao07/UMA: Universal Model Averaging

Prediction for Universal Adaptive Regression by Mixing

Description

The predictions based on different MA methods, including SAIC (SAICp), SBIC (SBICp), SFIC, ARM, L1-ARM, UARM, L1-UARM, MMA, JMA, PMA, BMA and MCV.

Usage

uma.predict(x,y,factorID=NULL,newdata,candi_models,weight,method,dim)

Arguments

x	Matrix of predictors.
y	Response variable.
factorID	Indication on whether there are categorical variables among the predictors.

If factorID= NULL, the predictors are all continuous or have the identifiable categorical variables; If factorID='colnames' or the location numbers of categorical variables, the name or location of variables provided by the user are treated as categorical variables in the linear model. The default factorID is NULL.

candi_models	The candidate models under specific method, you can be calculated by gma, gma_h, uarm, and uarm_h functions, as shown in the examples.
newdata	An optional data frame in which to look for variables with which to predict. If omitted, the fitted values are used.
weight	The weights of candidate models under specific methods, you can be calculated by gma, gma_h, uarm, and uarm_h functions, as shown in the examples
method	The method= 'UARM' is the Universal Adaptive Regression by Mixing method; the method= 'L1-UARM' is the L1 Universal Adaptive Regression by Mixing method; the method= 'SAIC' is the Smooth-AIC method; the method= 'SBIC' is the Smooth-BIC method; the method= 'SAICp' is the Smooth-AIC method with the penalty term; the method= 'SBICp' is the Smooth-BIC method with the penalty term; the method= 'SFIC' is the Smooth-FIC method; the method= 'ARM' is the Adaptive Regression by Mixing method; the method= 'L1-ARM' is the L1 Adaptive Regression by Mixing method; the method= 'MMA' is the Mallows Model Averaging (MMA); the method= 'JMA' is the Jackknife Model Averaging (JMA); the method= 'UARM.rf' is the Universal Adaptive Regression by Mixing method using the random forest to estimate the standard deviation of random error for candidate models; the method= 'L1-UARM.rf' is the L1 Universal Adaptive Regression by Mixing method using the random forest to estimate the standard deviation of random error for candidate models; the method= 'PMA' is the Parsimonious Model Averaging; the method= 'MCV' is the Cross-validation for Model Averaging (MCV).
dim	High-dimensional or low-dimensional methods are used for prediction. If dim ='H', high-dimensional methods are used; otherwise, low-dimensional methods are used.

Details

See the paper provided in Reference section.

Value

A 'uma.predict' object is retured. The components is:

pre_out

The prediction by given method.

Examples

### low dimension

# generate simulation data
n<-50
p<-8
beta<-c(3,1.5,0,0,2,0,0,0)
b0<-1
x<-matrix(rnorm(n*p,0,1),nrow=n,ncol=p)
e<-rnorm(n,0,3)
y<-x%*%beta+b0+e

# user supplied candidate models
candi_models<-rbind(c(0,0,0,0,0,0,0,1),
                    c(0,1,0,0,0,0,0,1),
                    c(0,1,1,1,0,0,0,1),
                    c(0,1,1,0,0,0,0,1),
                    c(1,1,0,1,1,0,0,0),
                    c(1,1,0,0,1,0,0,0))

# compute weight for candidate models using L1-UARM
weightL<-uarm(x,y,factorID=NULL,candi_models=candi_models,n_train=ceiling(n/2),
         no_rep=50,psi=1,method='L1-UARM',prior=TRUE,p0=0.5)$weight

# compute the prediction by method L1-UARM
luma.predict<-uma.predict(x,y,factorID=NULL,newdata=x,candi_models=candi_models,
              weight=weightL,method='L1-UARM',dim='L')$pre_out

# early COVID-19 data in China
data(covid19)
y<-covid19[,1]
x<-covid19[,-1]
n<-length(y)

# compute the predicts for L1-UARM, MMA and SFIC
# user supplied all subsets candidate models
Cl1uarmw<-uarm(x,y,factorID=NULL,candi_models=2,n_train=ceiling(n/2),no_rep=50,
          psi=1,method='L1-UARM',prior=TRUE,p0=0.5)$weight
Cmmaw<-gma(x,y,factorID=NULL,method='MMA',candi_models=2)$weight
Csficw<-gma(x,y,factorID=NULL,method='SFIC',candi_models=2)$weight

# compute the prediction by methods L1-UARM, MMA, SFIC and BMA
cl1uarm.predict<-uma.predict(x,y,factorID=NULL,newdata=x,candi_models=2,
                             weight=Cl1uarmw,method='L1-UARM',dim='L')$pre_out
cmma.predict<-uma.predict(x,y,factorID=NULL,newdata=x,candi_models=2,
                          weight=Cmmaw,method='MMA',dim='L')$pre_out
csfic.predict<-uma.predict(x,y,factorID=NULL,newdata=x,candi_models=2,
                           weight=Cmmaw,method='SFIC',dim='L')$pre_out

#The BMA prediction does not depend on candidate models
cbma.predict<-uma.predict(x,y,factorID=NULL,newdata=x,candi_models=2,
                          method='BMA',dim='L')$pre_out



###high dimension
library(mvtnorm) 
n1=100;n2=1000
p=200
sigma0=1
######
b=rep(0,len=p) #1*p,beta
for(j in 1:12){
  b[j]=2/j
}
# cov setting
Sig = matrix(0,p,p)
rho = 0.5
for(i in 1:p)
{
  for(j in 1:p)
  {
    Sig[i,j] = rho^abs(i-j)
  }
}
# new data
X=matrix(rmvnorm(n1,matrix(0,ncol=1,nrow=p),Sig),nrow=n1)
X_test=matrix(rmvnorm(n2,matrix(0,ncol=1,nrow=p),Sig),nrow=n2)
mu0=X%*%b
mu_test=X_test%*%b
y=mu0+rnorm(n1,0,sigma0)##normal distribution
##########the prediction on each methods
g1=gma_h(x=X,y,factorID=NULL,candidate='H4',method='SBICp',psi=1, prior=TRUE)
pre_out1=uma.predict(x=X,y,factorID=NULL,newdata=X_test,method='SBICp',weight=g1$weight,
                    candi_models=g1$candi_models,dim='H')$pre_out

g2=gma_h(x=X,y,factorID=NULL,candidate='H4',method='PMA',lambda=log(n1))
pre_out2=uma.predict(x=X,y,factorID=NULL,newdata=X_test,method='PMA',weight=g2$weight,
                     candi_models=g2$candi_models,dim='H')$pre_out

g3=gma_h(x=X,y,factorID=NULL,method='MCV',alpha = 0.05)
pre_out3=uma.predict(x=X,y,factorID=NULL,newdata=X_test,method='MCV',weight=g3$weight,
                     candi_models=g3$candi_models,dim='H')$pre_out

g4=gma_h(x=X, y, factorID=NULL,candidate='H4',method='ARM',n_train=n1/2, no_rep=50, psi=1) 
pre_out4=uma.predict(x=X,y,factorID=NULL,newdata=X_test,method='ARM',weight=g4$weight,
                     candi_models=g4$candi_models,dim='H')$pre_out

g5=gma_h(x=X, y, factorID=NULL,candidate='H4',method='L1-ARM',n_train=n1/2, no_rep=50, psi=1)
pre_out5=uma.predict(x=X,y,factorID=NULL,newdata=X_test,method='L1-ARM',weight=g5$weight,
                     candi_models=g5$candi_models,dim='H')$pre_out

g6=uarm_h(x=X,y,factorID=NULL,candidate='H4',n_train=n1/2,method='UARM',
            no_rep=50,p0=0.5,psi=1, prior = TRUE)
pre_out6=uma.predict(x=X,y,factorID=NULL,newdata=X_test,method='UARM',weight=g6$weight,
                candi_models=g6$candi_models,dim='H')$pre_out

g7=uarm_h(x=X,y,factorID=NULL,candidate='H4',n_train=n1/2,method='L1-UARM',
          no_rep=50,p0=0.5,psi=1, prior = TRUE) 
pre_out7=uma.predict(x=X,y,factorID=NULL,newdata=X_test,method='L1-UARM',weight=g7$weight,
                candi_models=g7$candi_models,dim='H')$pre_out

####the performance of different methods
pre_out=cbind(pre_out1,pre_out2,pre_out3,pre_out4,pre_out5,pre_out6,pre_out7)
se=(pre_out-matrix(mu_test,n2,1)%*%rep(1,7))^2
colnames(se)=c('SBICp','PMA','MCV','ARM','L1-ARM','UARM','L1-UARM')
Pre=apply(se,2,mean)
Pre_se=apply(se,2,se)

zhzhao07/UMA documentation built on Sept. 1, 2022, 2:49 p.m.