ENNreg() R function from [evreg]

Training the ENNreg model

ENNreg trains the ENNreg model using batch or minibatch learning procedures.


ENNreg(
  X,
  y,
  init = NULL,
  K = NULL,
  batch = TRUE,
  nstart = 100,
  c = 1,
  lambda = 0.9,
  xi = 0,
  rho = 0,
  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.
init: Initial model generated by ENNreg_init (default=NULL).
K: Number of prototypes (default=NULL; must be supplied if initial model is not supplied).
batch: If TRUE (default), batch learning is used; otherwise, online learning is used.
nstart: Number of random starts of the k-means algorithm (default: 100, used only if initial model is not supplied).
c: Multiplicative coefficient applied to scale parameter gamma (defaut: 1, used only if initial model is not supplied)
lambda: Parameter of the loss function (default=0.9)
xi: Regularization coefficient penalizing precision (default=0).
rho: Regularization coefficient shrinking the solution towards a linear model (default=0).
eps: Parameter of the loss function (if NULL, set 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 procedure (see details).
opt.rmsprop: Parameters of the RMSprop algorithm (see details).

Returns

An object of class "ENNreg" with the following components:

loss: Value of the loss function.
param: Parameter values.
K: Number of prototypes.
pred: Predictions on the training set (a list containing the prototype unit activations, the output means, variances and precisions, as well as the lower and upper expectations).

Details

If batch=TRUE, function harris from package evclust is used for optimization. Otherwise, the RMSprop minibatch learning algorithm is used. The three parameters in list options are:

maxiter: Maximum number of iterations (default: 100).
rel.error: Relative error for stopping criterion (default: 1e-4).
print: Number of iterations between two displays (default: 10).

Additional parameters for the RMSprop, used only if batch=FALSE, are contained in list opt.rmsprop. They are: '

batch_size: Minibatch size.
epsi: Global learning rate.
rho: Decay rate.
delta: Small constant to stabilize division by small numbers.
Dtmax: The algorithm stops when the loss has not decreased in the last Dtmax iterations.

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)
fit <- ENNreg(X[train,],y[train],K=30)
plot(y[train],fit$pred$mux,xlab="observed response",ylab="predicted response")

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 function