CoOL_2_train_neural_network {CoOL}

Training the non-negative neural network

Description

This function trains the non-negative neural network. Fitting the model is done in a step-wise procedure one individual at a time, where the model estimates individual's risk of the disease outcome, estimates the prediction's residual error and adjusts the model parameters to reduce this error. By iterating through all individuals for multiple epochs (one complete iterations through all individuals is called an epoch), we end with parameters for the model, where the errors are smallest possible for the full population. The model fit follows the linear expectation that synergism is a combined effect larger than the sum of independent effects. The initial values, derivatives, and learning rates are described in further detail in the Supplementary material. The non-negative model ensures that the predicted value cannot be negative. The model does not prevent estimating probabilities above 1, but this would be unlikely, as risks of disease and mortality even for high risk groups in general are far below 1. The use of a test dataset does not seem to assist deciding on the optimal number of epochs possibly due to the constrains due to the non-negative assumption. We suggest splitting data into a train and test data set, such that findings from the train data set can be confirmed in the test data set before developing hypotheses.

Usage

CoOL_2_train_neural_network(
  X_train,
  Y_train,
  X_test,
  Y_test,
  C_train = 0,
  C_test = 0,
  model,
  lr = c(1e-04, 1e-05, 1e-06),
  epochs = 2000,
  patience = 100,
  monitor = TRUE,
  plot_and_evaluation_frequency = 50,
  input_parameter_reg = 0.001,
  spline_df = 10,
  restore_par_options = TRUE,
  drop_out = 0,
  fix_baseline_risk = -1,
  ipw = 1
)

Arguments

X_train

The exposure data for the training data.

Y_train

The outcome data for the training data.

X_test

The exposure data for the test data (currently the training data is used).

Y_test

The outcome data for the test data (currently the training data is used).

C_train

One variable to adjust the analysis for such as calendar time (training data).

C_test

One variable to adjust the analysis for such as calendar time (currently the training data is used).

model

The fitted non-negative neural network.

lr

Learning rate (several LR can be provided, such that the model training will train for each LR and continue to the next).

epochs

Epochs.

patience

The number of epochs allowed without an improvement in performance.

monitor

Whether a monitoring plot will be shown during training.

plot_and_evaluation_frequency

The interval for plotting the performance and checking the patience.

input_parameter_reg

Regularisation decreasing parameter value at each iteration for the input parameters.

spline_df

Degrees of freedom for the spline fit for the performance plots.

restore_par_options

Restore par options.

drop_out

To drop connections if their weights reaches zero.

fix_baseline_risk

To fix the baseline risk at a value.

ipw

a vector of weights per observation to allow for inverse probability of censoring weighting to correct for selection bias

Value

An updated list of connection weights, bias weights and meta data.

References

Rieckmann, Dworzynski, Arras, Lapuschkin, Samek, Arah, Rod, Ekstrom. 2022. Causes of outcome learning: A causal inference-inspired machine learning approach to disentangling common combinations of potential causes of a health outcome. International Journal of Epidemiology <https://doi.org/10.1093/ije/dyac078>

Examples

#See the example under CoOL_0_working_example