Train a Replicator Neural Network using Stohastic Gradient descent with optional batch learning. See Hawkins et al. (2002) for details on Replicator Neural Networks.
replicator(X, hiddenLayers = c(10, 5, 10), lossFunction = "pseudo-huber",
dHuber = 1, stepLayers = 2, nSteps = 5, smoothSteps = 25,
rampLayers = NA, rectifierLayers = NA, sigmoidLayers = NA,
standardize = TRUE, learnRate = 1e-06, maxEpochs = 1000,
batchSize = 32, momentum = 0.2, L1 = 0, L2 = 0, validLoss = TRUE,
validProp = 0.1, verbose = TRUE, earlyStop = FALSE,
earlyStopEpochs = 50, earlyStopTol = -1e-07, lrSched = FALSE,
lrSchedEpochs = 800, lrSchedLearnRates = 1e-07, robErrorCov = FALSE)matrix with explanatory variables
vector specifying the number of nodes in each layer. Set
to NA for a Network without any hidden layers
which loss function should be used. Options are "log", "quadratic", "absolute", "huber" and "pseudo-huber"
used only in case of loss functions "huber" and "pseudo-huber". This parameter controls the cut-off point between quadratic and absolute loss.
vector or integer specifying which layers should have stepwise activation in its nodes
numeric integer specifying how many steps the step function should have on the interval [0, 1]
numeric indicating the smoothness of the step function. Smaller values result in smoother steps. Recommended to keep below 50 for stability. If set to high, the derivative of the stepfunction will also be large
vector or integer specifying which layers should have ramplike activation in its nodes. This is equivalent to a stepfunction with an infinite number of steps (limit of step function when nSteps and smoothSteps go to infinity) but more efficient than using step function layer with a large number for nSteps.
vector or integer specifying which layers should have rectifier activation in its nodes
vector or integer specifying which layers should have sigmoid activation in its nodes
logical indicating if X and y should be standardized before
training the network. Recommended to leave at TRUE for faster
convergence.
the size of the steps made in gradient descent. If set too large, optimization can become unstable. Is set too small, convergence will be slow.
the maximum number of epochs (one iteration through training data).
the number of observations to use in each batch. Batch learning is computationally faster than stochastic gradient descent. However, large batches might not result in optimal learning, see Le Cun for details.
numeric value specifying how much momentum should be used. Set to zero for no momentum, otherwise a value between zero and one.
L1 regularization. Non-negative number. Set to zero for no regularization.
L2 regularization. Non-negative number. Set to zero for no regularization.
logical indicating if loss should be monitored during training.
If TRUE, a validation set of proportion validProp is randomly
drawn from full training set. Use function plot to assess convergence.
proportion of training data to use for validation
logical indicating if additional information (such as lifesign) should be printed to console during training.
logical indicating if early stopping should be used based on
the loss on a validation set. Only possible with validLoss set to TRUE
after how many epochs without sufficient improvement
(as specified by earlyStopTol) should training be stopped.
numerical value specifying tolerance for early stopping. Can be either positive or negative. When set negative, training will be stopped if improvements are made but improvements are smaller than tolerance.
logical indicating if a schedule for the learning rate should
be used. If TRUE, schedule as specified by lrSchedEpochs and
vector with elements specifying the epoch after which the
corresponding learn rate from vector lrSchedLearnRates. Length of vector
shoud be the same as length of learnSchedLearnRates.
vector with elements specifying the learn rate to be used after epochs determined by lrSchedEpochs.
logical indicating if robust covariance should be estimated in
order to assess Mahalanobis distances of reconstruction errors
lrSchedLearnRates .
An ANN object. Use function plot(<object>) to assess
loss on training and optionally validation data during training process. Use
function predict(<object>, <newdata>) for prediction.
A function for training an Replicator Neural Network.
Hawkins, Simon, et al. "Outlier detection using replicator neural networks." DaWaK. Vol. 2454. 2002.
# NOT RUN {
# Replicator
repNN <- replicator(faithful, hiddenLayers = c(4,1,4), batchSize = 5,
learnRate = 1e-5, momentum = 0.5, L1 = 1e-3, L2 = 1e-3,
robErrorCov = TRUE)
plot(repNN)
rX <- reconstruct(repNN, faithful)
plot(rX, alpha = 0.05)
plot(faithful, col = (rX$mah_p < 0.05)+1, pch = 16)
# }
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