For evaluation, k-fold cross validation with k = 5 was applied [36]: the data was randomly categorized into training set (80%) and testing set (20%). Hyper-parameters were selected based on the number of features in the data set. Tables Tables77 and and88 presents the parameters of the hazard ratio network and the parameters of the distribution function network for each data set, respectively. Both the architecture of the two networks and the number of parameters are similar. 4-layers neural networks were used for each data set. The network was trained through Adam optimization method with a learning rate of 10–5. Xavier initialization was applied for all the layers, and a dropout probability of 0.5 was implemented only for the third layer.

The parameters of the hazard ratio network

The parameters of the distribution function network

To improve a model, the optimal hyper parameter values should be determined. However, it is hard to find the optimal hyper parameter. Thus, we employ a grid search method to find optimal hyper parameter. Grid search is an effective way to tune parameters in supervised learning and improve the generalization performance of a model. With grid search, we try as many combinations of the parameters of interest as possible and find the best ones. In order to find optimal parameter, we typically set the range of parameters. The combinations of the parameter are defined as

{‘num_hidden_layers’: between 2 and 7, ‘hidden_layer_size’: between 8 and 64, ‘activation’: ['sigmoid', 'relu', 'tanh'], ‘dropout_rate’: between 0 and 0.9}

In GridSearch, we try every combination of the set of parameters defined above.

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