## 4 Experimental Results
The distribution function was set to Poisson and in order to avoid overfitting, the regularization parameter (Lambda) has been set to 0.001. The other two parameters (\(\rho\) and \(\epsilon\)) were set as default as in [36]. The DT algorithm is based on a greedy algorithm [53] that performs a recursive binary partitioning of the feature space in order to build a decision tree. This algorithm uses the information gain in order to build the decision trees, and we used the default parameter as in the package _rpart_ of R [54]. For the GBM, we used the GBM package of R [55] with Gaussian distribution, 3000 gradient boosting interactions, learning rate of 0.9 and 40 as maximum depth of variable interactions. For RF, we used the implementation from provided by the randomForest package of R [56], using 100 as the number of trees to be built by algorithm and 100 as the maximum number of terminal nodes trees in the forest can have. For ANN we used the nnet package of R [57], with maximum 10 number of hidden units, 10,000 maximum number of weights allowed and 1000 maximum number of iterations. EV is an evolutionary algorithm for producing regression trees, and we used the R evtree package (from now on EVTree) [58], with parameters as in [14]. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \(h\) & **Layers** & **Neurons** & \(\lambda\) & \(\rho\) & \(\epsilon\) & **Activation** & **Distribution** & **End Metric** \\ \hline
1 & 52 & 942 & 4.09\(\times 10^{-10}\) & 1.00 & \(6.43\times 10^{-12}\) & Tanh & Gaussian & Deviance \\
2 & 68 & 921 & 0 & 1.00 & 0 & Maxout & Huber & MSE \\
3 & 75 & 880 & 0 & 1.00 & 0 & Maxout & Huber & Deviance \\
4 & 68 & 921 & 0 & 1.00 & 0 & Maxout & Huber & MSE \\
5 & 88 & 504 & 0 & 1.00 & 0 & Maxout & Huber & Deviance \\
6 & 80 & 789 & 0 & 1.00 & 0 & Maxout & Huber & MSE \\
7 & 74 & 892 & 0 & 1.00 & 0 & Maxout & Huber & RMSE \\
8 & 46 & 300 & 0 & 1.00 & 0 & Maxout & Huber & MAE \\
9 & 75 & 889 & \(5.57\times 10^{-10}\) & 0.99 & \(6.74\times 10^{-10}\) & Tanh & Gaussian & Mean per class error \\
10 & 25 & 852 & 0 & 1.00 & 0 & Maxout & Huber & RMSE \\
11 & 58 & 843 & \(3.69\times 10^{-10}\) & 1.00 & \(2.45\times 10^{-10}\) & Tanh & Gaussian & RMSE \\
12 & 41 & 491 & 0 & 1.00 & 0 & Maxout & Huber & RMSE \\
13 & 17 & 552 & 0 & 0.99 & 0 & Maxout & Huber & MSE \\
14 & 26 & 661 & 0 & 0.99 & 0 & Maxout & Huber & MAE \\
15 & 89 & 811 & \(5.61\times 10^{-10}\) & 0.99 & \(4.23\times 10^{-10}\) & Tanh & Gaussian & RMSE \\
16 & 98 & 697 & 0 & 1.00 & 0 & Maxout & Huber & MAE \\
17 & 74 & 478 & \(1.46\times 10^{-10}\) & 1.00 & \(3.58\times 10^{-10}\) & Tanh & Gaussian & Deviance \\
18 & 62 & 705 & \(2.74\times 10^{-10}\) & 0.99 & \(6.64\times 10^{-10}\) & Tanh & Gaussian & MAE \\
19 & 65 & 879 & 0 & 0.99 & 0 & Maxout & Huber & MAE \\
20 & 81 & 780 & \(7.62\times 10^{-10}\) & 0.99 & \(5.21\times 10^{-10}\) & Tanh & Gaussian & MSE \\
21 & 27 & 931 & 0 & 1.00 & 0 & Maxout & Huber & MAE \\
22 & 95 & 745 & 0 & 1.00 & 0 & Maxout & Huber & Deviance \\
23 & 41 & 923 & 0 & 1.00 & 0 & Maxout & Huber & MSE \\
24 & 80 & 754 & 0 & 1.00 & 0 & Maxout & Huber & MAE \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameters found by the GA for \(w=168\). The ensemble method [14] uses a two layer strategy, where in the first layer random forests, neural networks and an evolutionary algorithm are used. The results produced by these three algorithms are then used by an algorithm based on Gradient Boosting in order to produce the final prediction. All the parameters of the ML based techniques were established after several preliminary runs. Table 5 shows the results obtained by the various methods for each value of \(w\). We can notice that all the methods obtained better results with a historical window of 168 reads. NDL obtained the lowest MRE in all the cases, while the ensemble strategy obtains the second best results. Moreover, we can see that NDL outperforms all other methods even when only a historical window of 96 is used, confirming the extremely good performances of such strategy.