-
Notifications
You must be signed in to change notification settings - Fork 1
/
theme_backward.r
230 lines (211 loc) · 9.89 KB
/
theme_backward.r
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
#' @title Theme Backward selection
#' @description Perform component selection by cross-validation backward approach
#' @export
#' @param formula an object of class "\code{Formula}" (or one that can be coerced
#' to that class): a symbolic description of the model to be fitted. The details
#' of model specification are given under Details.
#' @param data data frame.
#' @param H vector of R integer. Number of components to keep for each theme
#' @param folds number of folds - default is 10. Although folds can be as large as the sample size (leave-one-out CV),
#' it is not recommended for large datasets. Smallest value allowable is folds=2.
#' folds can also be provided as a vector (same length as data) of fold identifiers.
#' @param family a vector of character of the same length as the number of dependent variables:
#' "bernoulli", "binomial", "poisson" or "gaussian" is allowed.
#' @param size describes the number of trials for the binomial dependent variables.
#' A (number of statistical units * number of binomial dependent variables) matrix is expected.
#' @param weights weights on individuals (not available for now)
#' @param offset used for the poisson dependent variables.
#' A vector or a matrix of size: number of observations * number of Poisson dependent variables is expected.
#' @param na.action a function which indicates what should happen when the data contain NAs. The default is set to \code{na.omit}.
#' @param crit a list of two elements : maxit and tol, describing respectively the maximum number of iterations and
#' the tolerance convergence criterion for the Fisher scoring algorithm. Default is set to 50 and 10e-6 respectively.
#' @param method structural relevance criterion. Object of class "method.SCGLR"
#' built by \code{\link{methodSR}} for Structural Relevance.
#' @param type loss function to use for cross-validation.
#' Currently six options are available depending on whether the responses are of the same distribution family.
#' If the responses are all bernoulli distributed, then the prediction performance may be measured
#' through the area under the ROC curve: type = "auc"
#' In any other case one can choose among the following five options ("likelihood","aic","aicc","bic","mspe").
#' @param st logical (FALSE) theme build and fit order. TRUE means random, FALSE means sequential (T1, ..., Tr)
#' @details
#' Models for theme are specified symbolically.
#'
#' A model as the form \code{response ~ terms} where \code{response}
#' is the numeric response vector and terms is a series of R themes composed of predictors.
#'
#' Themes are separated by "|" (pipe) and are composed.\cr
#' y1 + y2 + \dots ~ x11 + x12 + \dots + x1_ | x21 + x22 + \dots | \dots + x1_ + \dots | a1 + a2 + \dots
#'
#' See \code{\link{multivariateFormula}}.
#' @return a list containing the path followed along the selection process, the associated mean square predictor error and the best configuration.
#' @examples \dontrun{
#' library(SCGLR)
#'
#' # load sample data
#' data(genus)
#'
#' # get variable names from dataset
#' n <- names(genus)
#' n <- n[!n %in% c("geology","surface","lon","lat","forest","altitude")]
#' ny <- n[grep("^gen",n)] # Y <- names that begins with "gen"
#' nx1 <- n[grep("^evi",n)] # X <- remaining names
#' nx2 <- n[-c(grep("^evi",n),grep("^gen",n))]
#'
#'
#' form <- multivariateFormula(ny,nx1,nx2,A=c("geology"))
#' fam <- rep("poisson",length(ny))
#' testcv <- scglrThemeBackward(form,data=genus,H=c(2,2),family=fam,offset = genus$surface,folds=3)
#'
#' # Cross-validation pathway
#' testcv$H_path
#'
#' # Plot criterion
#' plot(testcv$cv_path)
#'
#' # Best combination
#' testcv$H_best
#' }
scglrThemeBackward <- function(formula, data, H, family, size = NULL, weights = NULL,
offset = NULL, na.action = na.omit, crit = list(), method = methodSR(), folds=10,type="mspe",st=FALSE){
if(!inherits(formula,"MultivariateFormula"))
formula <- multivariateFormula(formula,data=data)
additional <- formula$additional
# check family
Y_vars <- attr(formula,"Y_vars")
if(!is.character(family)||any(!(family %in% c("gaussian","poisson","bernoulli","binomial"))))
stop("Expecting character vector of gaussian, poisson, bernoulli or binomial for family")
if(!(length(family) %in% c(1,length(Y_vars))))
stop("Length of family must be equal to one or number of Y variables")
if(length(family)==1)
family <- rep(family, length(Y_vars))
X_expand <- lapply(formula$X,function(X){
f <- as.formula(paste0("~",paste0(trim(deparse(X)),collapse=" ")))
return(model.matrix(f,data)[,-1])
})
invsqrtm <- lapply(formula$X, function(X){
nms <- all.vars(as.formula(paste0("~",paste0(trim(deparse(X)),collapse=" "))))
metric(data[,nms])
})
X_expand <- lapply(1:length(H),function(l) scale(X_expand[[l]],TRUE,FALSE)%*%invsqrtm[[l]])
if(formula$additional)
A_expand <- model.matrix(as.formula(paste0("~",paste0(trim(deparse(formula$A)),collapse=" "))),data)[,-1,drop=F]
else
A_expand <- NULL
nobs <- nrow(data)
# fold provided as a vector of user groups
if(length(folds)>1) {
if(length(folds)!=nobs)
stop("length of folds must be the same as the number of observations!")
folds <- as.factor(folds)
kfolds <- length(levels(folds))
foldid <- as.integer(folds)
} else {
kfolds <- folds
foldid <- sample(rep(seq(kfolds), length = nobs))
}
if(kfolds<2) stop("kfolds must be at least equal to two")
#Full model evaluation
message("full model")
full_fold <- function(k) {
out <- try(
scglrTheme(
formula=formula,
data=data,
H=H,
family=family,
size=size,
weights=weights,
offset=offset,
subset=(1:nrow(data))[foldid!=k],
na.action = na.action,
crit=crit,
method=method,
st=st
), silent = TRUE)
..progressor..()
if(inherits(out, "try-error")) {
stop("In fold ", k, attr(out, "condition")$message)
}
result <- list(
u=lapply(out$themes,function(t) as.matrix(t$u)),
gamma=out$gamma
)
return (result)
}
..progressor.. <- getProgressor(kfolds)
thm <- getParallel("lapply", seq(kfolds), full_fold)
cv <- lapply(1:kfolds,function(k){
XU_new <- as.matrix(do.call(cbind,lapply(which(H>0),function(l) as.matrix(X_expand[[l]][foldid==k,,drop=F])%*%thm[[k]]$u[[l]])))
if(!is.null(A_expand))
A_new <- A_expand[foldid==k,,drop=F]
else
A_new <- NULL
X_new <- cbind(1,XU_new,A_new)
pred <- multivariatePredictGlm(X_new,family=family,beta=thm[[k]]$gamma,offset = offset[foldid==k])
if(!(type%in%c("mspe","auc"))) npar <- ncol(X_new) else npar <- 0
qual <- infoCriterion(ynew=as.matrix(data[foldid==k,formula$Y_vars]),pred=pred,family=family,type=type,size=size[foldid==k,,drop=FALSE],npar=npar)
})
cv <- mean(log(Reduce("+",cv)/kfolds))
message("[",paste(H,collapse=","),"] = ",cv)
#backward evaluation
message("backward")
H_cur <- H
cv_path <- cv
H_path <- list(H)
while(sum(H_cur)>1) {
H_new <- lapply(which(H_cur>0),function(i) {h <- H_cur; h[i]<-h[i]-1;h})
cv_new <- lapply(H_new,function(h){
cv <- lapply(1:kfolds, function(k){
XU_fit <- as.matrix(do.call(cbind,lapply(which(h>0),function(l) as.matrix(X_expand[[l]][foldid!=k,,drop=F])%*%thm[[k]]$u[[l]][,1:h[l],drop=FALSE])))
colnames(XU_fit) <- paste0("c",1:ncol(XU_fit))
if(!is.null(A_expand))
A_fit <- A_expand[foldid!=k,,drop=FALSE]
else
A_fit <- NULL
X_fit <- cbind(XU_fit,A_fit)##Ajouter drop =FALSE dans data en dessous
fit <- multivariateGlm.fit(Y=data[foldid!=k,formula$Y_vars,drop=FALSE],comp=X_fit,family=family,offset=offset[foldid!=k],size=size[foldid!=k,,drop=FALSE])
gamma <- sapply(fit, coef)
XU_new <- as.matrix(do.call(cbind,lapply(which(h>0),function(l) as.matrix(X_expand[[l]][foldid==k,,drop=F])%*%thm[[k]]$u[[l]][,1:h[l],drop=FALSE])))
colnames(XU_new) <- paste0("c",1:ncol(XU_new))
if(!is.null(A_expand))
A_new <- A_expand[foldid==k,,drop=FALSE]
else
A_new <- NULL
X_new <- cbind(1,XU_new,A_new)
pred <- multivariatePredictGlm(X_new,family=family,beta=gamma,offset = offset[foldid==k])
if(!(type%in%c("mspe","auc"))) npar <- ncol(X_new) else npar <- 0
qual <- infoCriterion(ynew=as.matrix(data[foldid==k,formula$Y_vars]),pred=pred,family=family,type=type,size=size[foldid==k,,drop=FALSE],npar=npar)
})
return(mean(log(Reduce("+",cv)/kfolds)))
})
cv_new <- unlist(cv_new)
H_cur <- H_new[[which.min(cv_new)]]
cv_path <- c(cv_path,min(cv_new))
H_path <- c(H_path,list(H_cur))
message("[",paste(H_cur,collapse=","),"] = ",min(cv_new))
}
message("NULL model")
cvNull <- lapply(1:kfolds,function(k){
if(!is.null(A_expand))
A_fit <- A_expand[foldid!=k,,drop=FALSE]
else
A_fit <- NULL
#idem ajouter des drop = FALSE dans data en dessous
fit <- multivariateGlm.fit(Y=data[foldid!=k,formula$Y_vars,drop=FALSE],comp=A_fit,family=family,offset=offset[foldid!=k],size=size[foldid!=k,,drop=FALSE])
gamma <- sapply(fit, coef)
if(!is.null(A_expand))
A_new <- A_expand[foldid==k,,drop=FALSE]
else
A_new <- NULL
X_new <- cbind(rep(1,sum(foldid==k)),A_new)
pred <- multivariatePredictGlm(X_new,family=family,beta=gamma,offset = offset[foldid==k])
if(!(type%in%c("mspe","auc"))) npar <- ncol(X_new) else npar <- 0
qual <- infoCriterion(ynew=as.matrix(data[foldid==k,formula$Y_vars]),pred=pred,family=family,type=type,size=size[foldid==k,,drop=FALSE],npar=npar)
})
message("[",paste(rep(0,length(H)),collapse=","),"] = ",mean(log(Reduce("+",cvNull)/kfolds)))
cv_path <- c(cv_path,mean(log(Reduce("+",cvNull)/kfolds)))
H_path <- c(H_path,list(rep(0,length(H))))
H_path <- do.call(rbind,H_path)
colnames(H_path) <- paste0("thm",1:length(H))
return(list(H_path=H_path,cv_path=cv_path,H_best=H_path[which.min(cv_path),]))
}