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# comparisonLMS.R -- version 2011-05-17
# compare PS and DE for robust regression (LQS)
require(MASS); require(NMOF)
OF <- function(param, data) {
X <- data$X
y <- data$y
# as.vector(y) for recycling; param is a matrix
aux <- as.vector(y) - X %*% param
aux <- aux * aux
aux <- apply(aux, 2, sort, partial = data$h)
colSums(aux[1L:data$h, ]) # LTS
}
OF <- function(param, data) {
X <- data$X
y <- data$y
# as.vector(y) for recycling; param is a matrix
aux <- as.vector(y) - X %*% param
aux <- aux * aux
aux <- apply(aux, 2, sort, partial = data$h)
aux[data$h, ] # LQS
}
createData <- function(n, p,
constant = TRUE, sigma = 2, oFrac = 0.1) {
X <- array(rnorm(n * p), dim = c(n, p))
if (constant) X[ ,1L] <- 1
b <- rnorm(p)
y <- X %*% b + rnorm(n) * 0.5
nO <- ceiling(oFrac * n)
when <- sample.int(n, nO)
X[when, -1L] <- X[when, -1L] + rnorm(nO, sd = sigma)
list(X = X, y = y)
}
n <- 100 # number of observations
p <- 10 # number of regressors
constant <- TRUE; sigma <- 5; oFrac <- 0.15
h <- 70L # ...or use something like floor((n+1)/2)
aux <- createData(n, p, constant, sigma, oFrac)
X <- aux$X; y <- aux$y
data <- list(y = y, X = X, h = h)
popsize <- 100L; generations <- 400L
ps <- list(
min = rep(-10, p),
max = rep(10, p),
c1 = 1.0,
c2 = 2.0,
iner = 0.8,
initV = 0.1,
maxV = 3,
nP = popsize,
nG = generations,
loopOF = FALSE)
de <- list(
min = rep(-10, p),
max = rep(10, p),
nP = popsize,
nG = generations,
F = 0.2,
CR = 0.5,
loopOF = FALSE)
system.time(solPS <- PSopt(OF = OF,algo = ps, data = data))
system.time(solDE <- DEopt(OF = OF,algo = de, data = data))
# test: lqs. use X[ ,-1] because lqs includes constant.
system.time(test1 <- lqs(y ~ X[ ,-1L], adjust = TRUE,
nsamp = 100000L, method = "lqs", quantile = h))
res1 <- sort((y - X %*% as.matrix(coef(test1)))^2)[h]
res2 <- sort((y - X %*% as.matrix(solPS$xbest))^2)[h]
res3 <- sort((y - X %*% as.matrix(solDE$xbest))^2)[h]
cat("lqs: ", res1, "\n",
"PSopt: ", res2, "\n",
"DEopt: ", res3, "\n", sep = "")
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