predict.FAMILY: predict.FAMILY

Description Usage Arguments Value Author(s) References See Also Examples

View source: R/ADMM_0.1.19.R

Description

Similar to R's generic predict function which predicts the model for new data for different values of α and λ.

Usage

1
2
## S3 method for class 'FAMILY'
predict(object, new.X, new.Z, Bias.corr = FALSE, XequalZ = FALSE, ...)

Arguments

object

The fitted object as the output from the main function FAMILY.

new.X

Matrix of covariates X. Must have the same number of columns used for fitting the model.

new.Z

Matrix of covariates Z. Must have the same number of columns used for fitting the model.

Bias.corr

A logical variable indicating if we wish to re-fit the selected variables using glm or lm.

XequalZ

A logical variable indicating if X = Z or if we have two different sets of covariates.

...

Extra arguments for the generic S3 predict function

Value

The function returns an array of dimensions [n, length(alphas), length(lambdas)] where n = nrow(new.X). This array contains one the following:

yhat

The fitted values using the data given

phat

The fitted estimated probabilities for logistic regression

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

FAMILY

Examples

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
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 30, 2017, 3:10 a.m.