## 3 Results
### Multivariate Prediction Models
#### 3.2.4 Neuronal Networks  
We utilized two distinct neural networks for training purposes. The first network employed a classical perceptron architecture with a single hidden layer. The neural network was trained with different architectures, using different random initial weights and training parameters. We experimented with learning rates of 0.05 and 0.1, and used the hyperbolic tangent (tanh) and logistic activation functions.  
\[\tanh(x)=\frac{e^{x}-e^{-x}}{e^{x}+e^{-x}};\;\text{logistic}(x)=\frac{1}{1+e^{ -x}}\]  
The best model was attained using an architecture of 18-5-1, indicating 18 input nodes, 5 nodes in the hidden layer, and 1 output node. A total of 101 weights were estimated, and the logistic activation function was used. The optimization function employed was cross-entropy, which measures the disparity between predictions and the actual occurrence of acidemia. The architecture of the network is visually represented in Figure 11, with positive weights depicted as black lines and negative weights shown as grey lines. The thickness of each line corresponds to the relative magnitude of the weight it represents.  
Figure 8: Minimization of error depending on the number of trees added to the model. The error rate was evaluated for the non-acidotic cases (0), acidotic cases (1), and all data, using the out-of-bag (OOB) error estimation.  
Figure 10: Variable importance in a random forest model.  
Figure 9: Minimization of error depending on the node size (minimum size of terminal node) and mtry (number of variables that possibly split at each node).  
Figure 12 illustrates the variable importance plot for the multilayer perceptron, utilizing the methodology proposed by [PERSON] in 1991 [44]. This approach involves decon-structing the model weights to determine the relative importance of explanatory variables for a single response within a supervised neural network. The variables that exerted the greatest influence were the drop, slope, and duration of the last deceleration time window. It is noteworthy that, contrary to expectations, the drop in the deceleration, rather than the slope, emerged as the most significant variable in this model.  
Additionally, a multilayer perceptron with two hidden layers was trained. We explored as an activation function the ReLU \(f(x)=\left\{\begin{array}{l}x\ \textit{if}\ x>0\\ 0\ \textit{if}\ x\leq 0\end{array}\right.\), linear \(f(x)=x\), and sigmoid \(f(x)=\frac{1}{1+e^{-x}}\), the learning rate was fixed as 0.01, the number of epochs explored ranged from 20 to 400, and the number of units of the hidden layer was set as 32, 64 or 128. The architecture of the best network was 16-64-32-2, with 3234 weights estimated. The activation  
Figure 11: Neural network architecture with input (I), hidden (H), and output (O) layers. (B) is the result obtained after applying the activation function.  
Figure 12: Variable importance in the neural network. Abs_V: absence of variability; FHR: fetal heart rate; Inest: instability; d_DArea: difference in deceleration area; d_Sl: difference in slope; Darea: deceleration area; d_amp: difference in amplitude; Rep_t: reperfusion time; d_dur: difference in duration; d_FHR: difference in fetal heart rate; Saltat: saltatory pattern; Dur: duration; Red_V: reduced variability; Nor_V: normal variability; d_drop: difference in drop; Ampl: amplitude.  
function for the first and second hidden layers was ReLU, and softmax was used for the output layer. The loss function employed was categorical crossentropy, with the optimizer set as rmsprop, and the metric used for optimization was accuracy. The model was trained for 30 epochs, with a batch size of 128, and a validation split of 0.2 was used to estimate the convergence, as shown in Figure 13. Due to the complexity of this model, it is not graphically represented.