ENNreg_cv {evreg}

Hyperparameter tuning for the ENNreg model using cross-validation

Description

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

Usage

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).

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.

Value

A list with three components:

xi

Optimal value of xi.

rho

Optimal value of rho.

RMS

Matrix of root mean squared error values

.

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.

See Also

ENNreg, ENNreg_holdout

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)