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"coef.lars" <-
function(object, ...)
{
predict(object, type = "coefficient", ...)$coef
}
"cv.folds" <-
function(n, folds = 10)
{
split(sample(1:n), rep(1:folds, length = n))
}
"cv.lars" <-
function(x, y, K = 10, fraction = seq(from = 0, to = 1, length = 100),
trace = FALSE, plot.it = TRUE, se = TRUE, ...)
{
all.folds <- cv.folds(length(y), K)
residmat <- matrix(0, length(fraction), K)
for(i in seq(K)) {
omit <- all.folds[[i]]
fit <- lars(x[ - omit, ], y[ - omit], trace = trace, ...)
fit <- predict(fit, x[omit, ,drop=FALSE], mode = "fraction", s = fraction
)$fit
if(length(omit)==1)fit<-matrix(fit,nrow=1)
residmat[, i] <- apply((y[omit] - fit)^2, 2, mean)
if(trace)
cat("\n CV Fold", i, "\n\n")
}
cv <- apply(residmat, 1, mean)
cv.error <- sqrt(apply(residmat, 1, var)/K)
object<-list(fraction = fraction, cv = cv, cv.error = cv.error)
if(plot.it) plotCVLars(object,se=se)
invisible(object)
}
"downdateR" <-
function(R, k = p)
{
p <- dim(R)[1]
if(p == 1)
return(NULL)
R <- delcol(R, rep(1, p), k)[[1]][ - p, , drop = FALSE]
attr(R, "rank") <- p - 1
R # Built-in Splus utility
}
"error.bars" <-
function(x, upper, lower, width = 0.02, ...)
{
xlim <- range(x)
barw <- diff(xlim) * width
segments(x, upper, x, lower, ...)
segments(x - barw, upper, x + barw, upper, ...)
segments(x - barw, lower, x + barw, lower, ...)
range(upper, lower)
}
"lars" <-
function(x, y, type = c("lasso","plasso", "lar", "forward.stagewise"), trace = FALSE, Gram,
eps = .Machine$double.eps, max.steps, use.Gram = TRUE)
{
### program automatically centers and standardizes predictors.
###
### Original program by Brad Efron September 2001
### Recoded by Trevor Hastie November 2001
### Computational efficiency December 22, 2001
### Bug fixes and singularities February 2003
### Conversion to R April 2003
### Copyright Brad Efron and Trevor Hastie
###
### Extension for "plasso" by Bernhard Renard, Marc Kirchner, January 2007
call <- match.call()
type <- match.arg(type)
TYPE <- switch(type,
lasso = "LASSO",
plasso = "PLASSO",
lar = "LAR",
forward.stagewise = "Forward Stagewise")
if(trace)
cat(paste(TYPE, "sequence\n"))
nm <- dim(x)
n <- nm[1]
m <- nm[2]
im <- inactive <- seq(m)
one <- rep(1, n)
vn <- dimnames(x)[[2]]
### Center x and y, and scale x, and save the means and sds
meanx <- drop(one %*% x)/n
x <- scale(x, meanx, FALSE) # centers x
normx <- sqrt(drop(one %*% (x^2)))
nosignal<-normx/sqrt(n) < eps
if(any(nosignal))# ignore variables with too small a variance
{
ignores<-im[nosignal]
inactive<-im[-ignores]
normx[nosignal]<-eps*sqrt(n)
if(trace)
cat("LARS Step 0 :\t", sum(nosignal), "Variables with Variance < \\eps; dropped for good\n") #
}
else ignores <- NULL #singularities; augmented later as well
names(normx) <- NULL
x <- scale(x, FALSE, normx) # scales x
if(use.Gram & missing(Gram)) {
if(m > 500 && n < m)
cat("There are more than 500 variables and n<m;\nYou may wish to restart and set use.Gram=FALSE\n"
)
if(trace)
cat("Computing X'X .....\n")
Gram <- t(x) %*% x #Time saving
}
mu <- mean(y)
y <- drop(y - mu)
Cvec <- drop(t(y) %*% x)
ssy <- sum(y^2) ### Some initializations
residuals <- y
if(missing(max.steps))
max.steps <- 8*min(m, n-1)
beta <- matrix(0, max.steps + 1, m) # beta starts at 0
Gamrat <- NULL
arc.length <- NULL
R2 <- 1
RSS <- ssy
first.in <- integer(m)
active <- NULL # maintains active set
actions <- as.list(seq(max.steps))
# a signed index list to show what comes in and out
drops <- FALSE # to do with type=="lasso" or "forward.stagewise"
Sign <- NULL # Keeps the sign of the terms in the model
R <- NULL ###
### Now the main loop over moves
###
k <- 0
#NN# added Indicator Plasso in while and setting Indicator accordingly
if (type=="plasso"){
IndPlasso<-1
} else {
IndPlasso<-0
}
while((k < max.steps) & (length(active) <( min(m - length(ignores),n-1))-IndPlasso)) {
action <- NULL
k <- k + 1
C <- Cvec[inactive] #
### identify the largest nonactive gradient
#NN# if added
if (type=="plasso"){
Cmax <- max(C)
if (Cmax <= 0)
break;
} else {
Cmax <- max(abs(C))
}
### Check if we are in a DROP situation
if(!any(drops)) {
#NN# if added
if (type=="plasso"){
new <- C >= Cmax - eps
} else {
new <- abs(C) >= Cmax - eps
}
C <- C[!new] # for later
new <- inactive[new] # Get index numbers
print(paste("Cmax:", Cmax, "new:", paste(as.character(new))))
### We keep the choleski R of X[,active] (in the order they enter)
for(inew in new) {
if(use.Gram) {
R <- updateR(Gram[inew, inew], R, drop(Gram[
inew, active]), Gram = TRUE,eps=eps)
}
else {
R <- updateR(x[, inew], R, x[, active], Gram
= FALSE,eps=eps)
}
if(attr(R, "rank") == length(active)) {
##singularity; back out
nR <- seq(length(active))
R <- R[nR, nR, drop = FALSE]
attr(R, "rank") <- length(active)
ignores <- c(ignores, inew)
action <- c(action, - inew)
if(trace)
cat("LARS Step", k, ":\t Variable", inew,
"\tcollinear; dropped for good\n") #
}
else {
if(first.in[inew] == 0)
first.in[inew] <- k
active <- c(active, inew)
#NN# if added
if (type=="plasso"){
Sign <- c(Sign, 1)
} else {
Sign <- c(Sign, sign(Cvec[inew]))
}
action <- c(action, inew)
if(trace)
cat("LARS Step", k, ":\t Variable", inew,
"\tadded\n") #
}
}
}
else action <- - dropid
Gi1 <- backsolve(R, backsolvet(R, Sign))
### Now we have to do the forward.stagewise dance
### This is equivalent to NNLS
dropouts<-NULL
if(type == "forward.stagewise") {
directions <- Gi1 * Sign
if(!all(directions > 0)) {
if(use.Gram) {
nnls.object <- nnls.lars(active, Sign, R,
directions, Gram[active, active], trace =
trace, use.Gram = TRUE,eps=eps)
}
else {
nnls.object <- nnls.lars(active, Sign, R,
directions, x[, active], trace = trace,
use.Gram = FALSE,eps=eps)
}
positive <- nnls.object$positive
dropouts <-active[-positive]
action <- c(action, -dropouts)
active <- nnls.object$active
Sign <- Sign[positive]
Gi1 <- nnls.object$beta[positive] * Sign
R <- nnls.object$R
C <- Cvec[ - c(active, ignores)]
}
}
A <- 1/sqrt(sum(Gi1 * Sign))
w <- A * Gi1 # note that w has the right signs
if(!use.Gram) u <- drop(x[, active, drop = FALSE] %*% w) ###
### Now we see how far we go along this direction before the
### next competitor arrives. There are several cases
###
### If the active set is all of x, go all the way
if(length(active) >= min(n-1, m - length(ignores) ) ) {
gamhat <- Cmax/A
}
else {
if(use.Gram) {
a <- drop(w %*% Gram[active, - c(active,ignores), drop = FALSE])
}
else {
a <- drop(u %*% x[, - c(active, ignores), drop=FALSE])
}
#NN# if plasso
if (type=="plasso"){
gam <- c((Cmax - C)/(A - a))
#browser();
} else {
gam <- c((Cmax - C)/(A - a), (Cmax + C)/(A + a))
}
### Any dropouts will have gam=0, which are ignored here
#NN# if plasso
if (type=="plasso"){
gamhat <- min(gam[gam > eps])
} else {
gamhat <- min(gam[gam > eps], Cmax/A)
}
}
if(type == "lasso"|type=="plasso") {
dropid <- NULL
b1 <- beta[k, active] # beta starts at 0
z1 <- - b1/w
zmin <- min(z1[z1 > eps], gamhat)
if(zmin < gamhat) {
gamhat <- zmin
drops <- z1 == zmin
}
else drops <- FALSE
}
beta[k + 1, ] <- beta[k, ]
beta[k + 1, active] <- beta[k + 1, active] + gamhat * w
if(use.Gram) {
Cvec <- Cvec - gamhat * Gram[, active, drop = FALSE] %*% w
}
else {
residuals <- residuals - gamhat * u
Cvec <- drop(t(residuals) %*% x)
}
Gamrat <- c(Gamrat, gamhat/(Cmax/A))
arc.length <- c(arc.length, gamhat)
### Check if we have to drop any guys
if((type == "lasso"|type=="plasso") && any(drops)) {
dropid <- seq(drops)[drops]
#turns the TRUE, FALSE vector into numbers
for(id in rev(dropid)) {
if(trace)
cat("Lasso Step", k+1, ":\t Variable", active[
id], "\tdropped\n")
R <- downdateR(R, id)
}
dropid <- active[drops] # indices from 1:m
beta[k+1,dropid]<-0 # added to make sure dropped coef is zero
active <- active[!drops]
Sign <- Sign[!drops]
}
if(!is.null(vn))
names(action) <- vn[abs(action)]
actions[[k]] <- action
inactive <- im[ - c(active, ignores)]
}
beta <- beta[seq(k + 1), ] #
dimnames(beta) <- list(paste(0:k), vn) ### Now compute RSS and R2
if(trace)
cat("Computing residuals, RSS etc .....\n")
residuals <- y - x %*% t(beta)
beta <- scale(beta, FALSE, normx)
RSS <- apply(residuals^2, 2, sum)
#Problem with RSS for plasso by the fact that the last estimates do give some weired results
R2 <- 1 - RSS/RSS[1]
Cp <- ((n - k - 1) * RSS)/rev(RSS)[1] - n + 2 * seq(k + 1)
object <- list(call = call, type = TYPE, R2 = R2, RSS = RSS, Cp = Cp,
actions = actions[seq(k)], entry = first.in, Gamrat = Gamrat,
arc.length = arc.length, Gram = if(use.Gram) Gram else NULL,
beta = beta, mu = mu, normx = normx, meanx = meanx)
class(object) <- "lars"
object
}
"nnls.lars" <-
function(active, Sign, R, beta, Gram, eps = 1e-10, trace = FALSE, use.Gram = TRUE)
{
### Modified 05/15/03 to allow for more than one addition to the set
### Lawson and Hanson page 161
### Go back to the first positive coefficent vector; can assume its in order
### Note that X'y is constant for all these guys;
### we assume WOLOG this constant is 1
### We also assume we have come into this because we have a negative coeff
### If use.Gram is FALSE, then Gram comes in as x
if(!use.Gram) x <- Gram # to avoid confusion
M<-m <- length(active)
im <- seq(m)
positive <- im
zero <- NULL
### Get to the stage where beta.old is all positive
while(m>1) {
zero.old<-c(m,zero)
R.old <- downdateR(R, m)
beta0 <- backsolve(R.old, backsolvet(R.old, Sign[ - zero.old]))*Sign[-zero.old]
beta.old <- c(beta0,rep(0,length(zero.old)))
if(all(beta0 >0))break
m <-m-1
zero<-zero.old
positive<-im[-zero]
R<-R.old
beta<-beta.old
}
### Now we do the NNLS backtrack dance
while(TRUE) {
while(!all(beta[positive] > 0)) {
alpha0 <- beta.old/(beta.old - beta)
alpha <- min(alpha0[positive][(beta <= 0)[positive]])
beta.old <- beta.old + alpha * (beta - beta.old)
dropouts<-match(alpha,alpha0[positive],0)
### Used to have the following line, but this failed occasionally
### dropouts <- seq(positive)[abs(beta.old[positive]) < eps]
for(i in rev(dropouts)) R <- downdateR(R, i)
positive <- positive[ - dropouts]
# there is an order in R
zero <- im[ - positive]
beta0 <- backsolve(R, backsolvet(R, Sign[positive])) *
Sign[positive]
beta <- beta.old * 0
beta[positive] <- beta0
}
### Now all those in have a positive coefficient
if(use.Gram) {
w <- 1 - Sign * drop(Gram %*% (Sign * beta))
#should be zero for some
}
else {
jw <- x %*% (Sign * beta)
w <- 1 - Sign * drop(t(jw) %*% x)
}
if((length(zero) == 0) || all(w[zero] <= 0))
break
add <- order(w)[M]
if(use.Gram) {
R <- updateR(Gram[add, add], R, drop(Gram[add,
positive]), Gram = TRUE,eps=eps)
}
else {
R <- updateR(x[, add], R, x[, positive], Gram = FALSE,eps=eps)
}
positive <- c(positive, add)
zero <- setdiff(zero, add)
beta0 <- backsolve(R, backsolvet(R, Sign[positive])) * Sign[
positive]
beta[positive] <- beta0
}
if(trace)
{
dropouts<-active[-positive]
for(i in dropouts){
cat("NNLS Step:\t Variable", i, "\tdropped\n")
}
}
list(active = active[positive], R = R, beta = beta, positive = positive
)
}
"plotCVLars" <-
function(cv.lars.object,se=TRUE){
attach(cv.lars.object)
plot(fraction, cv, type = "b", ylim = range(cv, cv + cv.error,
cv - cv.error))
if(se)
error.bars(fraction, cv + cv.error, cv - cv.error,
width = 1/length(fraction))
detach(cv.lars.object)
invisible()
}
"plot.lars" <-
function(x, xvar=c("norm","df","arc.length"), breaks = TRUE, plottype = c("coefficients", "Cp"),
omit.zeros = TRUE, eps = 1e-10, ...)
{
object <- x
plottype <- match.arg(plottype)
xvar <- match.arg(xvar)
coef1 <- object$beta ### Get rid of many zero coefficients
coef1 <- scale(coef1, FALSE, 1/object$normx)
if(omit.zeros) {
c1 <- drop(rep(1, nrow(coef1)) %*% abs(coef1))
nonzeros <- c1 > eps
cnums <- seq(nonzeros)[nonzeros]
coef1 <- coef1[, nonzeros]
}
else cnums <- seq(ncol(coef1))
s1<-switch(xvar,
norm={
s1 <- apply(abs(coef1), 1, sum)
s1/max(s1)
},
df=seq(length(object$arc.length)+1),
arc.length=cumsum(c(0,object$arc.length))
)
xname<-switch(xvar,
norm="|beta|/max|beta|",
df="Df",
arc.length="Arc Length"
)
if(plottype == "Cp") {
Cp <- object$Cp
plot(s1, Cp, type = "b", xlab=xname,main = object$type, ...)
}
else {
matplot(s1, coef1, xlab = xname, ..., type = "b",
pch = "*", ylab = "Standardized Coefficients")
title(object$type,line=2.5)
abline(h = 0, lty = 3)
axis(4, at = coef1[nrow(coef1), ], label = paste(cnums
), cex = 0.80000000000000004, adj = 0)
if(breaks) {
axis(3, at = s1, labels = paste(seq(s1)-1),cex=.8)
abline(v = s1)
}
}
invisible()
}
"predict.lars" <-
function(object, newx, s, type = c("fit", "coefficients"), mode = c("step",
"fraction", "norm"), ...)
{
mode <- match.arg(mode)
type <- match.arg(type)
if(missing(newx) & type == "fit") {
warning("Type=fit with no newx argument; type switched to coefficients"
)
type <- "coefficients"
}
betas <- object$beta
sbetas <- scale(betas, FALSE, 1/object$normx) #scaled for unit norm x
kp <- dim(betas)
k <- kp[1]
p <- kp[2]
steps <- seq(k)
if(missing(s)) {
s <- steps
mode <- "step"
}
sbeta <- switch(mode,
step = {
if(any(s < 0) | any(s > k))
stop("Argument s out of range")
steps
}
,
fraction = {
if(any(s > 1) | any(s < 0))
stop("Argument s out of range")
nbeta <- drop(abs(sbetas) %*% rep(1, p))
nbeta/nbeta[k]
}
,
norm = {
nbeta <- drop(abs(sbetas) %*% rep(1, p))
if(any(s > nbeta[k]) | any(s < 0))
stop("Argument s out of range")
nbeta
}
)
sfrac <- (s - sbeta[1])/(sbeta[k] - sbeta[1])
sbeta <- (sbeta - sbeta[1])/(sbeta[k] - sbeta[1])
usbeta<-unique(sbeta)
useq<-match(usbeta,sbeta)
sbeta<-sbeta[useq]
betas<-betas[useq,]
coord <- approx(sbeta, seq(sbeta), sfrac)$y
left <- floor(coord)
right <- ceiling(coord)
newbetas <- ((sbeta[right] - sfrac) * betas[left, , drop = FALSE] + (sfrac -
sbeta[left]) * betas[right, , drop = FALSE])/(sbeta[right] - sbeta[
left])
newbetas[left == right, ] <- betas[left[left == right], ]
robject <- switch(type,
coefficients = list(s = s, fraction = sfrac, mode = mode,
coefficients = drop(newbetas)),
fit = list(s = s, fraction = sfrac, mode = mode, fit = drop(
scale(newx, object$meanx, FALSE) %*% t(newbetas)) + object$
mu))
robject
}
"print.lars" <-
function(x, ...)
{
cat("\nCall:\n")
dput(x$call)
cat("R-squared:", format(round(rev(x$R2)[1], 3)), "\n")
actions <- x$actions
jactions <- unlist(actions)
jsteps <- rep(seq(along = actions), sapply(actions, length))
actmat <- rbind(jsteps, jactions)
vn <- names(jactions)
if(is.null(vn))
vn <- rep("", length(jactions))
dimnames(actmat) <- list(c("Step", "Var"), vn)
cat(paste("Sequence of", x$type, "moves:\n"))
print(actmat[2:1, ])
invisible(x)
}
"updateR" <-
function(xnew, R = NULL, xold, eps = .Machine$double.eps, Gram = FALSE)
{
###Gram argument determines the nature of xnew and xold
xtx <- if(Gram) xnew else sum(xnew^2)
norm.xnew <- sqrt(xtx)
if(is.null(R)) {
R <- matrix(norm.xnew, 1, 1)
attr(R, "rank") <- 1
return(R)
}
Xtx <- if(Gram) xold else drop(t(xnew) %*% xold)
r <- backsolvet(R, Xtx)
rpp <- norm.xnew^2 - sum(r^2)
rank <- attr(R, "rank") ### check if R is machine singular
if(rpp <= eps)
rpp <- eps
else {
rpp <- sqrt(rpp)
rank <- rank + 1
}
R <- cbind(rbind(R, 0), c(r, rpp))
attr(R, "rank") <- rank
R
}
"backsolvet"<-
function(r, x, k=ncol(r))
{
backsolve(r,x,k,transpose=TRUE)
}
"delcol" <-
function(r, z, k = p)
{
p <- dim(r)[1]
r <- r[, - k, drop = FALSE]
z <- as.matrix(z)
dz <- dim(z)
storage.mode(r) <- storage.mode(z) <- "double"
.Fortran("delcol",
r,
as.integer(p),
as.integer(k),
z,
as.integer(dz[1]),
as.integer(dz[2]),
PACKAGE="iwrlars")[c(1, 4)]
}
".First.lib" <-
function (lib, pkg)
library.dynam("iwrlars", pkg, lib)
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