dnnFit {dnn}

Fitting a Deep Learning model with a given loss function

Description

dnnFit is used to train a deep learning neural network model based on a specified loss function.

Usage

dnnFit(x, y, model, control)

Arguments

x

covariates for the neural network model

y

output (target) value for neural network model

model

the neural network model, see below for details

control

a list of control values, in the format produced by 'dnnControl'. The default value is dnnControl(loss='mse')

Details

The 'dnnFit' function takes the input data, the target values, the network architecture, and the loss function as arguments, and returns a trained model that minimizes the loss function. The function also supports various options for regularization and optimization of the model.

See dNNmodel for details on how to specify a deep learning model.

Parameters in dnnControl will be used to control the model fit process. The loss function can be specified as dnnControl(loss = "lossFunction"). Currently, the following loss functions are supported:

'mse': Mean square error loss = 0.5*sum(dy^2)

'cox': Cox partial likelihood loss = -sum(delta*(yhat - log(S0)))

'bin': Cross-entropy = -sum(y*log(p) + (1-y)*log(1-p))

'log': Log linear cost = -sum(y*log(lambda)-lambda)

'mae': Mean absolute error loss = sum(abs(dy))

Additional loss functions will be added to the library in the future.

{ dnnFit2 } is a C++ version of dnnFit, which runs about 20% faster, however, only loss = 'mse' and 'cox' are currently supported.

When the variance for covariance matrix X is too large, please use xbar = scale(x) to standardize X.

Value

An object of class "dnnFit" is returned. The dnnFit object contains the following list components:

cost

cost at the final epoch.

dW

the gradient at the final epoch dW = dL/dW.

fitted.values

predictor value mu = f(x).

history

a cost history at each epoch.

lp

predictor value mu = f(x).

logLik

-2*log Likelihood = cost.

model

a dNNmodel object.

residuals

raw residual dy = d log(L)/dmu

dvi

deviance dvi = dy*dy

Author(s)

Chen, B. E. and Norman P.

References

Buckley, J. and James, I. (1979). Linear regression with censored data. Biometrika, 66, page 429-436.

Norman, P. and Chen, B. E. (2019). DeepAFAT: A nonparametric accelerated failure time model with artificial neural network. Manuscript to be submitted.

Chollet, F. and Allaire J. J. (2017). Deep learning with R. Manning.

See Also

deepAFT, deepGlm, deepSurv, dnnControl

Examples

## Example for dnnFit with MSE loss function to do a non-linear regression
  set.seed(101)
### define model layers
  model = dNNmodel(units = c(4, 3, 1), activation = c("elu", "sigmoid", "sigmoid"), 
                   input_shape = 3)
  x = matrix(runif(15), nrow = 5, ncol = 3)
  y = exp(x[, 1])
  control = dnnControl(loss='mse')
  fit = dnnFit(x, y, model, control)