ann {validann}

Fit Artificial Neural Networks.

Description

Fits a single hidden layer ANN model to input data x and output data y.

Usage

ann(x, y, size, act_hid = c("tanh", "sigmoid", "linear", "exp"),
  act_out = c("linear", "sigmoid", "tanh", "exp"), Wts = NULL, rang = 0.5,
  objfn = NULL, method = "BFGS", maxit = 1000, abstol = 1e-04,
  reltol = 1e-08, trace = TRUE, ...)

Arguments

x

matrix, data frame or vector of numeric input values, with ncol(x) equal to the number of inputs/predictors and nrow(x) equal to the number of examples. A vector is considered to comprise examples of a single input or predictor variable.

y

matrix, data frame or vector of target values for examples.

size

number of hidden layer nodes. Can be zero.

act_hid

activation function to be used at the hidden layer. See ‘Details’.

act_out

activation function to be used at the output layer. See ‘Details’.

Wts

initial weight vector. If NULL chosen at random.

rang

initial random weights on [-rang,rang]. Default value is 0.5.

objfn

objective function to be minimised when fitting weights. This function may be user-defined with the first two arguments corresponding to y (the observed target data) and y_hat (the ANN output). If this function has additional parameters which require optimizing, these must be defined in argument par_of (see AR(1) case in ‘Examples’). Default is sse (internal function to compute sum squared error, with error given by y - y_hat) when objfn = NULL.

method

the method to be used by optim for minimising the objective function. May be “Nelder-Mead”, “BFGS”, “CG”, “L-BFGS-B”, “SANN” or “Brent”. Can be abbreviated. Default is “BFGS”.

maxit

maximum number of iterations used by optim. Default value is 1000.

abstol

absolute convergence tolerance (stopping criterion) used by optim. Default is 1e-4.

reltol

relative convergence tolerance (stopping criterion) used by optim. Optimization stops if the value returned by objfn cannot be reduced by a factor of reltol * (abs(val) + reltol) at a step. Default is 1e-8.

trace

logical. Should optimization be traced? Default = TRUE.

...

arguments to be passed to user-defined objfn. Initial values of any parameters (in addition to the ANN weights) requiring optimization must be supplied in argument par_of (see AR(1) case in ‘Examples’).

Details

The “linear” activation, or transfer, function is the identity function where the output of a node is equal to its input f(x) = x.

The “sigmoid” function is the standard logistic sigmoid function given by f(x) = \frac{1}{1+e^{-x}}.

The “tanh” function is the hyperbolic tangent function given by f(x) = \frac{e^{x}-e^{-x}}{e^{x}+e^{-x}}

The “exp” function is the exponential function given by f(x) = e^{x}

The default configuration of activation functions is act_hid = "tanh" and act_out = "linear".

Optimization (minimization) of the objective function (objfn) is performed by optim using the method specified.

Derivatives returned are first-order partial derivatives of the hidden and output nodes with respect to their inputs. These may be useful for sensitivity analyses.

Value

object of class ‘ann’ with components describing the ANN structure and the following output components:

wts

best set of weights found.

par_of

best values of additional objfn parameters. This component will only be returned if a user-defined objfn is supplied and argument par_of is included in the function call (see AR(1) case in ‘Examples’).

value

value of objective function.

fitted.values

fitted values for the training data.

residuals

residuals for the training data.

convergence

integer code returned by optim. 0 indicates successful completion, see optim for possible error codes.

derivs

matrix of derivatives of hidden (columns 1:size) and output (final column) nodes.

See Also

predict.ann, validann

Examples

## fit 1-hidden node ann model with tanh activation at the hidden layer and
## linear activation at the output layer.
## Use 200 random samples from ar9 dataset.
## ---
data("ar9")
samp <- sample(1:1000, 200)
y <- ar9[samp, ncol(ar9)]
x <- ar9[samp, -ncol(ar9)]
x <- x[, c(1,4,9)]
fit <- ann(x, y, size = 1, act_hid = "tanh", act_out = "linear", rang = 0.1)

## fit 3-hidden node ann model to ar9 data with user-defined AR(1) objective
## function
## ---
ar1_sse <- function(y, y_hat, par_of) {
  err <- y - y_hat
  err[-1] <- err[-1] - par_of * err[-length(y)]
  sum(err ^ 2)
}
fit <- ann(x, y, size = 3, act_hid = "tanh", act_out = "linear", rang = 0.1,
           objfn = ar1_sse, par_of = 0.7)