cv.MRFA {MRFA}

Compute K-fold cross-validated error for Multi-Resolution Functional ANOVA (MRFA) Model

Description

Computes the K-fold cross validated mean squared prediction error for multiresolution functional ANOVA model.

Usage

cv.MRFA(
  X,
  Y,
  order = 10,
  level = 10,
  lambda = exp(seq(log(500), log(0.001), by = -0.01)),
  K = 10,
  plot.it = TRUE,
  parallel = FALSE,
  verbose = FALSE,
  ...
)

Arguments

X

input for MRFA_fit.

Y

input for MRFA_fit.

order

input for MRFA_fit.

level

input for MRFA_fit.

lambda

lambda values at which CV curve should be computed.

K

a positive integer specifying the number of folds.

plot.it

logical. If TRUE, a CV curve will be shown. The default is TRUE.

parallel

logical. If TRUE, apply cross-validation function in parallel using parallel backend provided by foreach. The default is FALSE.

verbose

logical. If TRUE, additional diagnostics are printed. The default is FALSE.

...

additional arguments to MRFA_fit.

Value

lambda

lambda values at which CV curve is computed.

cv

the CV curve at each value of lambda.

cv.error

the standard error of the CV curve

Author(s)

Chih-Li Sung <[e-mail]>

See Also

MRFA_fit for fitting a multiresolution functional ANOVA model.

Examples

## Not run: 

#####             Testing function: GRAMACY & LEE (2009) function             #####
#####   Thanks to Sonja Surjanovic and Derek Bingham, Simon Fraser University #####
grlee09 <- function(xx)
{
  x1 <- xx[1]
  x2 <- xx[2]
  x3 <- xx[3]
  x4 <- xx[4]
  x5 <- xx[5]
  x6 <- xx[6]

  term1 <- exp(sin((0.9*(x1+0.48))^10))
  term2 <- x2 * x3
  term3 <- x4

  y <- term1 + term2 + term3
  return(y)
}

library(MRFA)
#####   Training data and testing data   #####
set.seed(2)
n <- 100; n_rep <- 3; n_new <- 50; d <- 6
X.train <- matrix(runif(d*n), ncol = d)
X.train <- matrix(rep(X.train, each = n_rep), ncol = d)
Y.train <- apply(X.train, 1, grlee09)
Y.train <- Y.train + rnorm(n*n_rep, 0, 0.05)
X.test <- matrix(runif(d*n_new), ncol = d)
Y.test <- apply(X.test, 1, grlee09)

#####   Fitting    #####
MRFA_model <- MRFA_fit(X.train, Y.train)

#####   Computes the K-fold cross validated   #####
cv.out <- cv.MRFA(X.train, Y.train, K = 5, lambda = seq(0.01,3,0.1))

#####   Prediction : CV  ######
lambda_cv <- cv.out$lambda[which.min(cv.out$cv)]
Y.pred <- predict(MRFA_model, X.test, lambda = lambda_cv)$y_hat
print(sqrt(mean((Y.test - Y.pred)^2)))

## End(Not run)