Deep Learning BAMLSS

This function interfaces keras infrastructures for high-level neural networks. The function can be used as a standalone model fitting engine such as bamlss or as an on top model engine to capture special features in the data that could not be captures by other model fitting engines.

## Deep learning bamlss.
dl.bamlss(object, offset = NULL, weights = NULL,
  eps = .Machine$double.eps^0.25, maxit = 100,
  force.stop = TRUE, epochs = 30, optimizer = NULL,
  batch_size = NULL, keras.model = NULL,
  verbose = TRUE, digits = 4, ...)

## Predict method.
# S3 method for dl.bamlss
predict(object, newdata, model = NULL, drop = TRUE, ...)

Arguments

object	An object of class "bamlss" or a bamlss.formula.
offset	A list or data.frame. Can be used to supply model offsets for use in fitting, e.g., fitted values from an initial model fit.
weights	Prior weights on the data.
eps	The relative convergence tolerance of the algorithm.
maxit	Integer, maximum number of iterations of the algorithm.
force.stop	Logical. should the algorithm stop if relative change is smaller than eps.
epochs	Number of times to iterate over the training data arrays, see fit.
optimizer	Character or call to optimizer functions to be used within fit. For character, options are: "adam" "sgd", "rmsprop", "adagrad", "adadelta", "adamax", "nadam". The default is optimizer_rmsprop with learning rate set to 1e-04.
batch_size	Number of samples per gradient update, see fit.
keras.model	A compiled model using keras, e.g., using keras_model_sequential and compile. Note that the last layer only has one unit with linear activation function.
verbose	Print information during runtime of the algorithm.
digits	Set the digits for printing when verbose = TRUE.
newdata	A list or data.frame that should be used for prediction.
model	Character or integer specifying for which distributional parameter predictions should be computed.
drop	If predictions for only one model are returned, the list structure is dropped.
…	For function dl.boost(), arguments passed to bamlss.frame.

Details

The default keras model is a sequential model with two hidden layers with "relu" activation function and 100 units in each layer. Between each layer is a dropout layer with 0.1 dropout rate.

Value

For function dl.bamlss() an object of class "dl.bamlss". Note that extractor functions fitted and residuals.bamlss can be applied. For function predict.dl.bamlss() a list or vector of predicted values.

WARNINGS

The BAMLSS deep learning infrastructure is still experimental!

See also

bamlss.frame, bamlss

Examples

# NOT RUN {
## Simulate data.
set.seed(123)
n <- 300
x <- runif(n, -3, 3)
fsigma <- -2 + cos(x)
y <- sin(x) + rnorm(n, sd = exp(fsigma))

## Setup model formula.
f <- list(
  y ~ x,
  sigma ~ x
)

## Fit neural network.
library("keras")
b <- dl.bamlss(f)

## Plot estimated functions.
par(mfrow = c(1, 2))
plot(x, y)
plot2d(fitted(b)$mu ~ x, add = TRUE)
plot2d(fitted(b)$sigma ~ x,
  ylim = range(c(fitted(b)$sigma, fsigma)))
plot2d(fsigma ~ x, add = TRUE, col.lines = "red")

## Another example identifying structures that are
## not captured by the initial model.
set.seed(123)
d <- GAMart()
b1 <- bamlss(num ~ s(x1) + s(x2) + s(x3), data = d, sampler = FALSE)
b2 <- dl.bamlss(num ~ lon + lat, data = d, offset = fitted(b1))
p <- predict(b2, model = "mu")
par(mfrow = c(1, 1))
plot3d(p ~ lon + lat, data = d, symmetric = FALSE)
# }