coef.FAMILY: coef.FAMILY
In FAMILY: A Convex Formulation for Modeling Interactions with Strong Heredity
Description
Usage
Arguments
Value
Author(s)
References
See Also
Examples
Description
Similar to R's generic coef function which extracts the coefficients from the model for each value of alpha and lambda.
Usage
1
2
Arguments
object
The fitted object from the output of the main function FAMILY.
XequalZ
A logical variable indicating if X = Z.
Bias.corr
A logical variable indicating if we wish to re-fit the selected variables using glm or lm.
...
Extra arguments for the generic S3 coef function
Value
The function returns a list of dimensions length(alphas)*length(lambdas) where each element is a list with the following components:
Intercept
The estimated coefficient for the intercept of the model.
mains, mainsX, mainsZ
A matrix with two columns which show the selected non-zero coefficients in the model and the estimated coefficient. When XequalsZ == TRUE the function only returns the matrix mains and it returns mainsX and mainsZ otherwise.
interacts
The matrix showing the estimated non-zero interaction terms with corresponding coefficient estimates.
alpha
The alpha value used for the particular fitted model
lambda
The lambda value used for the particular fitted model
Author(s)
Asad Haris
References
Haris, Witten and Simon (2014). Convex Modeling of Interactions with Strong Heredity. Available on ArXiv at http://arxiv.org/abs/1410.3517
See Also
Examples
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library(FAMILY)
library(pROC)
library(pheatmap)
#####################################################################################
#####################################################################################
############################# EXAMPLE - CONTINUOUS RESPONSE #########################
#####################################################################################
#####################################################################################
############################## GENERATE DATA ########################################
#Generate training set of covariates X and Z
set.seed(1)
X.tr<- matrix(rnorm(10*100),ncol = 10, nrow = 100)
Z.tr<- matrix(rnorm(15*100),ncol = 15, nrow = 100)
#Generate test set of covariates X and Z
X.te<- matrix(rnorm(10*100),ncol = 10, nrow = 100)
Z.te<- matrix(rnorm(15*100),ncol = 15, nrow = 100)
#Scale appropiately
meanX<- apply(X.tr,2,mean)
meanY<- apply(Z.tr,2,mean)
X.tr<- scale(X.tr, scale = FALSE)
Z.tr<- scale(Z.tr, scale = FALSE)
X.te<- scale(X.te,center = meanX,scale = FALSE)
Z.te<- scale(Z.te,center = meanY,scale = FALSE)
#Generate full matrix of Covariates
w.tr<- c()
w.te<- c()
X1<- cbind(1,X.tr)
Z1<- cbind(1,Z.tr)
X2<- cbind(1,X.te)
Z2<- cbind(1,Z.te)
for(i in 1:16){
for(j in 1:11){
w.tr<- cbind(w.tr,X1[,j]*Z1[,i])
w.te<- cbind(w.te, X2[,j]*Z2[,i])
}
}
#Generate response variables with signal from
#First 5 X features and 5 Z features.
#We construct the coefficient matrix B.
#B[1,1] contains the intercept
#B[-1,1] contains the main effects for X.
# For instance, B[2,1] is the main effect for the first feature in X.
#B[1,-1] contains the main effects for Z.
# For instance, B[1,10] is the coefficient for the 10th feature in Z.
#B[i+1,j+1] is the coefficient of X_i Z_j
B<- matrix(0,ncol = 16,nrow = 11)
rownames(B)<- c("inter" , paste("X",1:(nrow(B)-1),sep = ""))
colnames(B)<- c("inter" , paste("Z",1:(ncol(B)-1),sep = ""))
# First, we simulate data as follows:
# The first five features in X, and the first five features in Z, are non-zero.
# And given the non-zero main effects, all possible interactions are involved.
# We call this "high strong heredity"
B_high_SH<- B
B_high_SH[1:6,1:6]<- 1
#View true coefficient matrix
pheatmap(as.matrix(B_high_SH), scale="none",
cluster_rows=FALSE, cluster_cols=FALSE)
Y_high_SH <- as.vector(w.tr%*%as.vector(B_high_SH))+rnorm(100,sd = 2)
Y_high_SH.te <- as.vector(w.te%*%as.vector(B_high_SH))+rnorm(100,sd = 2)
# Now a new setting:
# Again, the first five features in X, and the first five features in Z, are involved.
# But this time, only a subset of the possible interactions are involved.
# Strong heredity is still maintained.
# We call this "low strong heredity"
B_low_SH<- B_high_SH
B_low_SH[2:6,2:6]<-0
B_low_SH[3:4,3:5]<- 1
#View true coefficient matrix
pheatmap(as.matrix(B_low_SH), scale="none",
cluster_rows=FALSE, cluster_cols=FALSE)
Y_low_SH <- as.vector(w.tr%*%as.vector(B_low_SH))+rnorm(100,sd = 1.5)
Y_low_SH.te <- as.vector(w.te%*%as.vector(B_low_SH))+rnorm(100,sd = 1.5)
############################## FIT SOME MODELS ########################################
#Define alphas and lambdas
#Define 3 different alpha values
#Low alpha values penalize groups more
#High alpha values penalize individual Interactions more
alphas<- c(0.01,0.5,0.99)
lambdas<- seq(0.1,1,length = 50)
#high Strong heredity with l2 norm
fit_high_SH<- FAMILY(X.tr, Z.tr, Y_high_SH, lambdas ,
alphas, quad = TRUE,iter=500, verbose = TRUE )
yhat_hSH<- predict(fit_high_SH, X.te, Z.te)
mse_hSH <-apply(yhat_hSH,c(2,3), "-" ,Y_high_SH.te)
mse_hSH<- apply(mse_hSH^2,c(2,3),sum)
#Find optimal model and plot matrix
im<- which(mse_hSH==min(mse_hSH),TRUE)
plot(fit_high_SH$Estimate[[im[2] ]][[im[1]]])
#Plot some matrices for different alpha values
#Low alpha, higher penalty on groups
plot(fit_high_SH$Estimate[[ 1 ]][[ 25 ]])
#Medium alpha, equal penalty on groups and individual interactions
plot(fit_high_SH$Estimate[[ 2 ]][[ 25 ]])
#High alpha, more penalty on individual interactions
plot(fit_high_SH$Estimate[[ 3 ]][[ 40 ]])
#View Coefficients
coef(fit_high_SH)[[im[2]]][[im[1]]]
############################## Uncomment code for EXAMPLE ###########################
# #high Strong heredity with l_infinity norm norm
# fit_high_SH<- FAMILY(X.tr, Z.tr, Y_high_SH, lambdas ,
# alphas, quad = TRUE,iter=500, verbose = TRUE,
# norm = "l_inf")
# yhat_hSH<- predict(fit_high_SH, X.te, Z.te)
# mse_hSH <-apply(yhat_hSH,c(2,3), "-" ,Y_high_SH.te)
# mse_hSH<- apply(mse_hSH^2,c(2,3),sum)
#
# #Find optimal model and plot matrix
# im<- which(mse_hSH==min(mse_hSH),TRUE)
# plot(fit_high_SH$Estimate[[im[2] ]][[im[1]]])
#
#
# #Plot some matrices for different alpha values
# #Low alpha, higher penalty on groups
# plot(fit_high_SH$Estimate[[ 1 ]][[ 30 ]])
# #Medium alpha, equal penalty on groups and individual interactions
# plot(fit_high_SH$Estimate[[ 2 ]][[ 10 ]])
# #High alpha, more penalty on individual interactions
# plot(fit_high_SH$Estimate[[ 3 ]][[ 20 ]])
#
#
# #View Coefficients
# coef(fit_high_SH)[[im[2]]][[im[1]]]
############################## Uncomment code for EXAMPLE ###########################
# #Redefine lambdas
# lambdas<- seq(0.1,0.5,length = 50)
#
# #low Strong heredity with l_2 norm
# fit_low_SH<- FAMILY(X.tr, Z.tr, Y_low_SH, lambdas ,
# alphas, quad = TRUE,iter=500, verbose = TRUE )
# yhat_lSH<- predict(fit_low_SH, X.te, Z.te)
# mse_lSH <-apply(yhat_lSH,c(2,3), "-" ,Y_low_SH.te)
# mse_lSH<- apply(mse_lSH^2,c(2,3),sum)
#
# #Find optimal model and plot matrix
# im<- which(mse_lSH==min(mse_lSH),TRUE)
# plot(fit_low_SH$Estimate[[im[2] ]][[im[1]]])
#
#
# #Plot some matrices for different alpha values
# #Low alpha, higher penalty on groups
# plot(fit_low_SH$Estimate[[ 1 ]][[ 25 ]])
# #Medium alpha, equal penalty on groups and individual interactions
# plot(fit_low_SH$Estimate[[ 2 ]][[ 10 ]])
# #High alpha, more penalty on individual interactions
# plot(fit_low_SH$Estimate[[ 3 ]][[ 10 ]])
#
#
# #View Coefficients
# coef(fit_low_SH)[[im[2]]][[im[1]]]
#####################################################################################
#####################################################################################
############################### EXAMPLE - BINARY RESPONSE ###########################
#####################################################################################
#####################################################################################
############################## GENERATE DATA ########################################
#Generate data for logistic regression
Yp_high_SH<- as.vector((w.tr)%*%as.vector(B_high_SH))
Yp_high_SH.te<- as.vector((w.te)%*%as.vector(B_high_SH))
Yprobs_high_SH<- 1/(1+exp(-Yp_high_SH))
Yprobs_high_SH.te<- 1/(1+exp(-Yp_high_SH.te))
Yp_high_SH<- rbinom(100, size = 1, prob = Yprobs_high_SH)
Yp_high_SH.te<- rbinom(100, size = 1, prob = Yprobs_high_SH.te)
lambdas<- seq(0.01,0.15,length = 50)
############################## FIT SOME MODELS ########################################
#Fit glm via l_2 norm
fit_high_SH<- FAMILY(X.tr, Z.tr, Yp_high_SH, lambdas ,
alphas, quad = TRUE,iter=500, verbose = TRUE,
family = "binomial")
yhp_hSH<- predict(fit_high_SH, X.te, Z.te)
mse_high_SH <-apply(yhp_hSH,c(2,3), "-" ,Yp_high_SH.te)
mse_hSH<- apply(mse_high_SH^2,c(2,3),sum)
im<- which(mse_hSH==min(mse_hSH),TRUE)
plot(fit_high_SH$Estimate[[im[2] ]][[im[1]]])
roc( Yp_high_SH.te,yhp_hSH[,im[1],im[2]],plot = TRUE)
#View Coefficients
coef(fit_high_SH)[[im[2]]][[im[1]]]
############################## Uncomment code for EXAMPLE ###########################
# #Fit glm via l_infinity norm
# fit_high_SH<- FAMILY(X.tr, Z.tr, Yp_high_SH, lambdas , norm = "l_inf",
# alphas, quad = TRUE,iter=500, verbose = TRUE,
# family = "binomial")
# yhp_hSH<- predict(fit_high_SH, X.te, Z.te)
# mse_high_SH <-apply(yhp_hSH,c(2,3), "-" ,Yp_high_SH.te)
# mse_hSH<- apply(mse_high_SH^2,c(2,3),sum)
# im<- which(mse_hSH==min(mse_hSH),TRUE)
# plot(fit_high_SH$Estimate[[im[2] ]][[im[1]]])
# roc( Yp_high_SH.te,yhp_hSH[,im[1],im[2]],plot = TRUE)
#
# #View Coefficients
# coef(fit_high_SH)[[im[2]]][[im[1]]]
#####################################################################################
#####################################################################################
############################## EXAMPLE WHERE X=Z ####################################
######################## Uncomment Code for EXAMPLE #################################
#####################################################################################
############################## GENERATE DATA ########################################
# #Redefine Lambdas
# lambdas<- seq(0.01,0.3,length = 50)
#
#
# #We consider the case X=Z now
# w.tr<- c()
# w.te<- c()
# X1<- cbind(1,X.tr)
# X2<- cbind(1,X.te)
#
# for(i in 1:11){
# for(j in 1:11){
# w.tr<- cbind(w.tr,X1[,j]*X1[,i])
# w.te<- cbind(w.te, X2[,j]*X2[,i])
# }
# }
#
# B<- matrix(0,ncol = 11,nrow = 11)
# rownames(B)<- c("inter" , paste("X",1:(nrow(B)-1),sep = ""))
# colnames(B)<- c("inter" , paste("X",1:(ncol(B)-1),sep = ""))
#
#
# B_high_SH<- B
# B_high_SH[1:6,1:6]<- 1
# #We exclude quadratic terms in this example
# diag(B_high_SH)[-1]<-0
# #View true coefficient matrix
# pheatmap(as.matrix(B_high_SH), scale="none",
# cluster_rows=FALSE, cluster_cols=FALSE)
#
# #With high Strong heredity: all possible interactions
# Y_high_SH <- as.vector(w.tr%*%as.vector(B_high_SH))+rnorm(100)
# Y_high_SH.te <- as.vector(w.te%*%as.vector(B_high_SH))+rnorm(100)
#
# ############################## FIT SOME MODELS ########################################
#
# #high Strong heredity with l_2 norm
# fit_high_SH<- FAMILY(X.tr, X.tr, Y_high_SH, lambdas ,
# alphas, quad = FALSE,iter=500, verbose = TRUE )
# yhat_hSH<- predict(fit_high_SH, X.te, X.te)
# mse_hSH <-apply(yhat_hSH,c(2,3), "-" ,Y_high_SH.te)
# mse_hSH<- apply(mse_hSH^2,c(2,3),sum)
#
# #Find optimal model and plot matrix
# im<- which(mse_hSH==min(mse_hSH),TRUE)
# plot(fit_high_SH$Estimate[[im[2] ]][[im[1]]])
#
#
# #Plot some matrices for different alpha values
# #Low alpha, higher penalty on groups
# plot(fit_high_SH$Estimate[[ 1 ]][[ 50 ]])
# #Medium alpha, equal penalty on groups and individual interactions
# plot(fit_high_SH$Estimate[[ 2 ]][[ 50 ]])
# #High alpha, more penalty on individual interactions
# plot(fit_high_SH$Estimate[[ 3 ]][[ 50 ]])
#
#
# #View Coefficients
# coef(fit_high_SH,XequalZ = TRUE)[[im[2]]][[im[1]]]
FAMILY documentation built on May 2, 2019, noon
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Description Usage Arguments Value Author(s) References See Also Examples
Description
Similar to R's generic coef function which extracts the coefficients from the model for each value of alpha and lambda.
Usage
1 2 |
Arguments
object |
The fitted object from the output of the main function |
XequalZ |
A logical variable indicating if X = Z. |
Bias.corr |
A logical variable indicating if we wish to re-fit the selected variables using |
... |
Extra arguments for the generic S3 |
Value
The function returns a list of dimensions length(alphas)*length(lambdas) where each element is a list with the following components:
Intercept |
The estimated coefficient for the intercept of the model. |
mains, mainsX, mainsZ |
A matrix with two columns which show the selected non-zero coefficients in the model and the estimated coefficient. When |
interacts |
The matrix showing the estimated non-zero interaction terms with corresponding coefficient estimates. |
alpha |
The alpha value used for the particular fitted model |
lambda |
The lambda value used for the particular fitted model |
Author(s)
Asad Haris
References
Haris, Witten and Simon (2014). Convex Modeling of Interactions with Strong Heredity. Available on ArXiv at http://arxiv.org/abs/1410.3517
See Also
Examples
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library(pROC)
library(pheatmap)
#####################################################################################
#####################################################################################
############################# EXAMPLE - CONTINUOUS RESPONSE #########################
#####################################################################################
#####################################################################################
############################## GENERATE DATA ########################################
#Generate training set of covariates X and Z
set.seed(1)
X.tr<- matrix(rnorm(10*100),ncol = 10, nrow = 100)
Z.tr<- matrix(rnorm(15*100),ncol = 15, nrow = 100)
#Generate test set of covariates X and Z
X.te<- matrix(rnorm(10*100),ncol = 10, nrow = 100)
Z.te<- matrix(rnorm(15*100),ncol = 15, nrow = 100)
#Scale appropiately
meanX<- apply(X.tr,2,mean)
meanY<- apply(Z.tr,2,mean)
X.tr<- scale(X.tr, scale = FALSE)
Z.tr<- scale(Z.tr, scale = FALSE)
X.te<- scale(X.te,center = meanX,scale = FALSE)
Z.te<- scale(Z.te,center = meanY,scale = FALSE)
#Generate full matrix of Covariates
w.tr<- c()
w.te<- c()
X1<- cbind(1,X.tr)
Z1<- cbind(1,Z.tr)
X2<- cbind(1,X.te)
Z2<- cbind(1,Z.te)
for(i in 1:16){
for(j in 1:11){
w.tr<- cbind(w.tr,X1[,j]*Z1[,i])
w.te<- cbind(w.te, X2[,j]*Z2[,i])
}
}
#Generate response variables with signal from
#First 5 X features and 5 Z features.
#We construct the coefficient matrix B.
#B[1,1] contains the intercept
#B[-1,1] contains the main effects for X.
# For instance, B[2,1] is the main effect for the first feature in X.
#B[1,-1] contains the main effects for Z.
# For instance, B[1,10] is the coefficient for the 10th feature in Z.
#B[i+1,j+1] is the coefficient of X_i Z_j
B<- matrix(0,ncol = 16,nrow = 11)
rownames(B)<- c("inter" , paste("X",1:(nrow(B)-1),sep = ""))
colnames(B)<- c("inter" , paste("Z",1:(ncol(B)-1),sep = ""))
# First, we simulate data as follows:
# The first five features in X, and the first five features in Z, are non-zero.
# And given the non-zero main effects, all possible interactions are involved.
# We call this "high strong heredity"
B_high_SH<- B
B_high_SH[1:6,1:6]<- 1
#View true coefficient matrix
pheatmap(as.matrix(B_high_SH), scale="none",
cluster_rows=FALSE, cluster_cols=FALSE)
Y_high_SH <- as.vector(w.tr%*%as.vector(B_high_SH))+rnorm(100,sd = 2)
Y_high_SH.te <- as.vector(w.te%*%as.vector(B_high_SH))+rnorm(100,sd = 2)
# Now a new setting:
# Again, the first five features in X, and the first five features in Z, are involved.
# But this time, only a subset of the possible interactions are involved.
# Strong heredity is still maintained.
# We call this "low strong heredity"
B_low_SH<- B_high_SH
B_low_SH[2:6,2:6]<-0
B_low_SH[3:4,3:5]<- 1
#View true coefficient matrix
pheatmap(as.matrix(B_low_SH), scale="none",
cluster_rows=FALSE, cluster_cols=FALSE)
Y_low_SH <- as.vector(w.tr%*%as.vector(B_low_SH))+rnorm(100,sd = 1.5)
Y_low_SH.te <- as.vector(w.te%*%as.vector(B_low_SH))+rnorm(100,sd = 1.5)
############################## FIT SOME MODELS ########################################
#Define alphas and lambdas
#Define 3 different alpha values
#Low alpha values penalize groups more
#High alpha values penalize individual Interactions more
alphas<- c(0.01,0.5,0.99)
lambdas<- seq(0.1,1,length = 50)
#high Strong heredity with l2 norm
fit_high_SH<- FAMILY(X.tr, Z.tr, Y_high_SH, lambdas ,
alphas, quad = TRUE,iter=500, verbose = TRUE )
yhat_hSH<- predict(fit_high_SH, X.te, Z.te)
mse_hSH <-apply(yhat_hSH,c(2,3), "-" ,Y_high_SH.te)
mse_hSH<- apply(mse_hSH^2,c(2,3),sum)
#Find optimal model and plot matrix
im<- which(mse_hSH==min(mse_hSH),TRUE)
plot(fit_high_SH$Estimate[[im[2] ]][[im[1]]])
#Plot some matrices for different alpha values
#Low alpha, higher penalty on groups
plot(fit_high_SH$Estimate[[ 1 ]][[ 25 ]])
#Medium alpha, equal penalty on groups and individual interactions
plot(fit_high_SH$Estimate[[ 2 ]][[ 25 ]])
#High alpha, more penalty on individual interactions
plot(fit_high_SH$Estimate[[ 3 ]][[ 40 ]])
#View Coefficients
coef(fit_high_SH)[[im[2]]][[im[1]]]
############################## Uncomment code for EXAMPLE ###########################
# #high Strong heredity with l_infinity norm norm
# fit_high_SH<- FAMILY(X.tr, Z.tr, Y_high_SH, lambdas ,
# alphas, quad = TRUE,iter=500, verbose = TRUE,
# norm = "l_inf")
# yhat_hSH<- predict(fit_high_SH, X.te, Z.te)
# mse_hSH <-apply(yhat_hSH,c(2,3), "-" ,Y_high_SH.te)
# mse_hSH<- apply(mse_hSH^2,c(2,3),sum)
#
# #Find optimal model and plot matrix
# im<- which(mse_hSH==min(mse_hSH),TRUE)
# plot(fit_high_SH$Estimate[[im[2] ]][[im[1]]])
#
#
# #Plot some matrices for different alpha values
# #Low alpha, higher penalty on groups
# plot(fit_high_SH$Estimate[[ 1 ]][[ 30 ]])
# #Medium alpha, equal penalty on groups and individual interactions
# plot(fit_high_SH$Estimate[[ 2 ]][[ 10 ]])
# #High alpha, more penalty on individual interactions
# plot(fit_high_SH$Estimate[[ 3 ]][[ 20 ]])
#
#
# #View Coefficients
# coef(fit_high_SH)[[im[2]]][[im[1]]]
############################## Uncomment code for EXAMPLE ###########################
# #Redefine lambdas
# lambdas<- seq(0.1,0.5,length = 50)
#
# #low Strong heredity with l_2 norm
# fit_low_SH<- FAMILY(X.tr, Z.tr, Y_low_SH, lambdas ,
# alphas, quad = TRUE,iter=500, verbose = TRUE )
# yhat_lSH<- predict(fit_low_SH, X.te, Z.te)
# mse_lSH <-apply(yhat_lSH,c(2,3), "-" ,Y_low_SH.te)
# mse_lSH<- apply(mse_lSH^2,c(2,3),sum)
#
# #Find optimal model and plot matrix
# im<- which(mse_lSH==min(mse_lSH),TRUE)
# plot(fit_low_SH$Estimate[[im[2] ]][[im[1]]])
#
#
# #Plot some matrices for different alpha values
# #Low alpha, higher penalty on groups
# plot(fit_low_SH$Estimate[[ 1 ]][[ 25 ]])
# #Medium alpha, equal penalty on groups and individual interactions
# plot(fit_low_SH$Estimate[[ 2 ]][[ 10 ]])
# #High alpha, more penalty on individual interactions
# plot(fit_low_SH$Estimate[[ 3 ]][[ 10 ]])
#
#
# #View Coefficients
# coef(fit_low_SH)[[im[2]]][[im[1]]]
#####################################################################################
#####################################################################################
############################### EXAMPLE - BINARY RESPONSE ###########################
#####################################################################################
#####################################################################################
############################## GENERATE DATA ########################################
#Generate data for logistic regression
Yp_high_SH<- as.vector((w.tr)%*%as.vector(B_high_SH))
Yp_high_SH.te<- as.vector((w.te)%*%as.vector(B_high_SH))
Yprobs_high_SH<- 1/(1+exp(-Yp_high_SH))
Yprobs_high_SH.te<- 1/(1+exp(-Yp_high_SH.te))
Yp_high_SH<- rbinom(100, size = 1, prob = Yprobs_high_SH)
Yp_high_SH.te<- rbinom(100, size = 1, prob = Yprobs_high_SH.te)
lambdas<- seq(0.01,0.15,length = 50)
############################## FIT SOME MODELS ########################################
#Fit glm via l_2 norm
fit_high_SH<- FAMILY(X.tr, Z.tr, Yp_high_SH, lambdas ,
alphas, quad = TRUE,iter=500, verbose = TRUE,
family = "binomial")
yhp_hSH<- predict(fit_high_SH, X.te, Z.te)
mse_high_SH <-apply(yhp_hSH,c(2,3), "-" ,Yp_high_SH.te)
mse_hSH<- apply(mse_high_SH^2,c(2,3),sum)
im<- which(mse_hSH==min(mse_hSH),TRUE)
plot(fit_high_SH$Estimate[[im[2] ]][[im[1]]])
roc( Yp_high_SH.te,yhp_hSH[,im[1],im[2]],plot = TRUE)
#View Coefficients
coef(fit_high_SH)[[im[2]]][[im[1]]]
############################## Uncomment code for EXAMPLE ###########################
# #Fit glm via l_infinity norm
# fit_high_SH<- FAMILY(X.tr, Z.tr, Yp_high_SH, lambdas , norm = "l_inf",
# alphas, quad = TRUE,iter=500, verbose = TRUE,
# family = "binomial")
# yhp_hSH<- predict(fit_high_SH, X.te, Z.te)
# mse_high_SH <-apply(yhp_hSH,c(2,3), "-" ,Yp_high_SH.te)
# mse_hSH<- apply(mse_high_SH^2,c(2,3),sum)
# im<- which(mse_hSH==min(mse_hSH),TRUE)
# plot(fit_high_SH$Estimate[[im[2] ]][[im[1]]])
# roc( Yp_high_SH.te,yhp_hSH[,im[1],im[2]],plot = TRUE)
#
# #View Coefficients
# coef(fit_high_SH)[[im[2]]][[im[1]]]
#####################################################################################
#####################################################################################
############################## EXAMPLE WHERE X=Z ####################################
######################## Uncomment Code for EXAMPLE #################################
#####################################################################################
############################## GENERATE DATA ########################################
# #Redefine Lambdas
# lambdas<- seq(0.01,0.3,length = 50)
#
#
# #We consider the case X=Z now
# w.tr<- c()
# w.te<- c()
# X1<- cbind(1,X.tr)
# X2<- cbind(1,X.te)
#
# for(i in 1:11){
# for(j in 1:11){
# w.tr<- cbind(w.tr,X1[,j]*X1[,i])
# w.te<- cbind(w.te, X2[,j]*X2[,i])
# }
# }
#
# B<- matrix(0,ncol = 11,nrow = 11)
# rownames(B)<- c("inter" , paste("X",1:(nrow(B)-1),sep = ""))
# colnames(B)<- c("inter" , paste("X",1:(ncol(B)-1),sep = ""))
#
#
# B_high_SH<- B
# B_high_SH[1:6,1:6]<- 1
# #We exclude quadratic terms in this example
# diag(B_high_SH)[-1]<-0
# #View true coefficient matrix
# pheatmap(as.matrix(B_high_SH), scale="none",
# cluster_rows=FALSE, cluster_cols=FALSE)
#
# #With high Strong heredity: all possible interactions
# Y_high_SH <- as.vector(w.tr%*%as.vector(B_high_SH))+rnorm(100)
# Y_high_SH.te <- as.vector(w.te%*%as.vector(B_high_SH))+rnorm(100)
#
# ############################## FIT SOME MODELS ########################################
#
# #high Strong heredity with l_2 norm
# fit_high_SH<- FAMILY(X.tr, X.tr, Y_high_SH, lambdas ,
# alphas, quad = FALSE,iter=500, verbose = TRUE )
# yhat_hSH<- predict(fit_high_SH, X.te, X.te)
# mse_hSH <-apply(yhat_hSH,c(2,3), "-" ,Y_high_SH.te)
# mse_hSH<- apply(mse_hSH^2,c(2,3),sum)
#
# #Find optimal model and plot matrix
# im<- which(mse_hSH==min(mse_hSH),TRUE)
# plot(fit_high_SH$Estimate[[im[2] ]][[im[1]]])
#
#
# #Plot some matrices for different alpha values
# #Low alpha, higher penalty on groups
# plot(fit_high_SH$Estimate[[ 1 ]][[ 50 ]])
# #Medium alpha, equal penalty on groups and individual interactions
# plot(fit_high_SH$Estimate[[ 2 ]][[ 50 ]])
# #High alpha, more penalty on individual interactions
# plot(fit_high_SH$Estimate[[ 3 ]][[ 50 ]])
#
#
# #View Coefficients
# coef(fit_high_SH,XequalZ = TRUE)[[im[2]]][[im[1]]]
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