ENNreg_holdout() R function from [evreg]

Hyperparameter tuning for the ENNreg model using the hold-out method

ENNreg_holdout tunes parameters xi and rho of the ENNreg model usingthe hold-out method.


ENNreg_holdout(
  X,
  y,
  K,
  batch = TRUE,
  val = NULL,
  nval = NULL,
  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.
val: Vector of indices of the validation instances (nval integers between 1 and n). Needed only if nval is not provided.
nval: Number of validation instances (needed only if val 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 validation set (a vector of indices), or the number nval of validation instances 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)
hold.out<-ENNreg_holdout(X,y,K=30,nval=round(n/3),XI=c(0.1,1,10),RHO=c(0.1,1,10))
hold.out$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_holdout function