ENNreg_cv() R function from [evreg]

Hyperparameter tuning for the ENNreg model using cross-validation

ENNreg_cv tunes parameters xi and rho of the ENNreg model using cross-validation.


ENNreg_cv(
  X,
  y,
  K,
  batch = TRUE,
  folds = NULL,
  Kfold = 5,
  XI,
  RHO,
  nstart = 100,
  c = 1,
  lambda = 0.9,
  eps = NULL,
  nu = 1e-16,
  optimProto = TRUE,
  verbose = TRUE,
  options = list(maxiter = 1000, rel.error = 1e-04, print = 10),
  opt.rmsprop = list(batch_size = 100, epsi = 0.001, rho = 0.9, delta = 1e-08, Dtmax =
    100)
)

Arguments

X: Input matrix of size n x p, where n is the number of objects and p the number of attributes.
y: Vector of length n containing observations of the response variable.
K: Number of prototypes.
batch: If TRUE (default), batch learning is used; otherwise, online learning is used.
folds: Vector of length n containing the folds (integers between 1 and Kfold).
Kfold: Number of folds (default=5, used only if folds is not provided).
XI: Vector of candidate values for hyperparameter xi.
RHO: Vector of candidate values for hyperparameter rho.
nstart: Number of random starts of the k-means algorithm (default: 100).
c: Multiplicative coefficient applied to scale parameter gamma (defaut: 1).
lambda: Parameter of the loss function (default=0.9).
eps: Parameter of the loss function (if NULL, fixed to 0.01 times the standard deviation of y).
nu: Parameter of the loss function to avoid a division par zero (default=1e-16).
optimProto: If TRUE (default), the initial prototypes are optimized.
verbose: If TRUE (default) intermediate results are displayed.
options: Parameters of the optimization algorithm (see ENNreg).
opt.rmsprop: Parameters of the RMSprop algorithm (see ENNreg).

Returns

A list with three components:

xi: Optimal value of xi.
rho: Optimal value of rho.
RMS: Matrix of root mean squared error values

Details

Either the folds (a vector of the same length as y, such that folds[i] equals the fold, between 1 and Kfold, containing observation i), or the number of folds must be provided. Arguments options and opt.rmsprop are passed to function ENNreg.

Examples


# Boston dataset

library(MASS)
X<-as.matrix(scale(Boston[,1:13]))
y<-Boston[,14]
set.seed(220322)
n<-nrow(Boston)
ntrain<-round(0.7*n)
train <-sample(n,ntrain)
cv<-ENNreg_cv(X=X[train,],y=y[train],K=30,XI=c(0.1,1,10),RHO=c(0.1,1,10))
cv$RMS
fit <- ENNreg(X[train,],y[train],K=30,xi=cv$xi,rho=cv$rho)
pred<-predict(fit,newdata=X[-train,],yt=y[-train])
print(pred$RMS)

References

Thierry Denoeux. An evidential neural network model for regression based on random fuzzy numbers. In "Belief functions: Theory and applications (proc. of BELIEF 2022)", pages 57-66, Springer, 2022.

Thierry Denoeux. Quantifying prediction uncertainty in regression using random fuzzy sets: the ENNreg model. IEEE Transactions on Fuzzy Systems, Vol. 31, Issue 10, pages 3690-3699, 2023.

ENNreg_cv function