cv_gam: Robust Cross-Validation
In gamreg: Robust and Sparse Regression via Gamma-Divergence

Description Usage Arguments Details Value Author(s) References Examples

Compute Robust Cross-Validation for selecting best model.

  cv.gam(X, Y, init.mode = c("sLTS", "RLARS", "RANSAC"),
         lambda.mode = "lambda0", lmax = 1, lmin = 0.05, nlambda = 50,
         fold = 10, ncores = 1, gam = 0.1, gam0 = 0.5, intercept = "TRUE",
         alpha = 1, ini.subsamp = 0.2, ini.cand = 1000, alpha.LTS = 0.75,
         nlambda.LTS = 40)

`X`	Predictor variables Matrix.
`Y`	Response variables Matrix.
`init.mode`	`"sLTS"`: a initial point is the estimate of sparse least trimmed squares. `"RLARS"`: a initial point is the estimate of Robust LARS. `"RANSAC"`: a initial point is the estimate of RANSAC algorithm.
`lambda.mode`	`"lambda0"`: Robust Cross-Validation uses grids on range [0.05lambda0,lambda0] with log scale, where lambda0 is an estimator of sparse tuning parameter which would shrink regression coefficients to zero.
`lmax`	When `lambda.mode` is not lambda0, upper bound of range of grids is lmax.
`lmin`	When `lambda.mode` is not lambda0, lower bound of range of grids is lmin.
`nlambda`	The number of grids for Robust Cross-Validation.
`fold`	the number of folds for K-fold Robust Cross-Validation. If `fold` equals to sample size, Robust Cross-Validation is leave-one-out method.
`ncores`	positive integer giving the number of processor cores to be used for parallel computing (the default is 1 for no parallelization).
`gam`	Robust tuning parameter of gamma-divergence for regression.
`gam0`	tuning parameter of Robust Cross-Validation.
`intercept`	Should intercept be fitted `TRUE` or set to zero `FALSE`
`alpha`	The elasticnet mixing parameter, with 0 ≤ α ≤ 1. `alpha=1` is the lasso penalty, and `alpha=0` the ridge penalty.
`ini.subsamp`	The fraction of subsamples in "`RANSAC`".
`ini.cand`	The number of candidates for estimating itnial points in "`RANSAC`".
`alpha.LTS`	The fraction of subsamples for trimmed squares in "`sLTS`".
`nlambda.LTS`	The number of grids for sparse tuning parameter in "`sLTS`".

If the "RANSAC" is used as the initial point, the parameter ini.subsamp and ini.cand can be determined carefully. The smaller ini.subsamp is, the more robust initial point is. However, less efficiency.

`lambda`	A numeric vector giving the values of the penalty parameter.
`fit`	All results at each lambda.
`Rocv`	The result of best model by Robust Cross-Validation.

Takayuki Kawashima

Kawashima, T. and Fujisawa, H. (2017). Robust and Sparse Regression via gamma-divergence, Entropy, 19(11).
Fujisawa, H. and Eguchi, S. (2008). Robust parameter estimation with a small bias against heavy contamination, Journal of Multivariate Analysis, 99(9), 2053-2081.

  ## generate data
  library(mvtnorm)
  n <- 30                      # number of observations
  p <- 10                      # number of expalanatory variables

  epsilon <- 0.1               # contamination ratio

  beta0 <- 0.0                 # intercept
  beta <- c(numeric(p))        # regression coefficients
  beta[1] <- 1
  beta[2] <- 2
  beta[3] <- 3
  beta[4] <- 4

  Sigma <- 0.2^t(sapply(1:p, function(i, j) abs(i-j), 1:p))
  X <- rmvnorm(n, sigma=Sigma) # explanatory variables
  e <- rnorm(n) # error terms

  i <- 1:ceiling(epsilon*n)    # index of outliers
  e[i] <- e[i] + 20            # vertical outliers
  Y <- beta0*(numeric(n)+1) + X%*%beta


  res <- cv.gam(X,Y,nlambda = 5, nlambda.LTS=20 ,init.mode="sLTS")