## 6 Results and Discussion
Regarding computational complexity, BRNN is more time consuming on a single-user desktop computer when compared to GP and SVM, but these differences are not remarkable when using the cloud. On the other hand, there is not too much contrast in performance between the GP model and the MLP technique. In any case, all the computational efforts seem to be equated when being \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Technique** & **Best Parameter** & **RMSE (mg/dL)** & **CV RMSE (\%)** & **R\({}^{2}\)** \\ \hline GP & \(\sigma\) = 0.1 & 21.64 & 16.42 & 0.65 \\ MLP & size = 40 & 19.68 & 15.31 & 0.68 \\ SVM & cost = 2 & 15.31 & 13.59 & 0.79 \\ BRNN & neurons = 2 & 14.03 & 12.86 & 0.83 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results of the tuning for each technique. Figure 3: RMSE, CV-RMSE, and R2 for each technique. Figure 2: Boxplots comparing the RMSE differences by models pairwise. executed in a powerful cloud server. Comparing SVMs with ANNs, ANNs are considerably faster. The simple reason for this is that to train an SVM requires the solution of associated Lagrangian dual problems 30. This represents a quadratic optimization problem, which has an extremely large number of variables, equal to the number of training instances. From the derived results, we can see that there are significant differences between various machine learning models, and they may be ranked unambiguously. The ranking may appear to be wide-ranging as it is not constrained by time series that have a number of features that could promote certain models. Nevertheless, it should be noted that the ranking is applicable to DM1-time time series. Certain other time series, e.g., in chemistry, physics, or other areas, will display significantly different features related to series size, noise levels, etc. Making comparisons of the tested models in these time series could be interesting, as would investigating whether the derived conclusions are applicable for a variety of time windows in the past. It should also be noted that the derived ranking represents a general ranking; with all forecasting problems, a number of models must be tested. Various types of time series have a variety of stylized facts, resulting in variations in performance ranking. Nevertheless, this general ranking remains an extremely useful tool for a modeler selecting models for testing. The worst results are provided by the GP, but in no case are these excessively poor. This result is extremely interesting as machine learning communities have comparatively only become interested in GPs recently [27]. GP has been available for a considerable time but extensive study or application of it did not occur until very recently. We contend that there remains scope for making improvements to GPs in ways that could be a positive enhancement to its performance. The MLP model offered extremely good results partially (although not completely) due to the fact that it is able to reduce linear models [20]. Interestingly, GP is centered on the construction of locally centered weighted averages for target outputs in the training set, and while it is centered on solid probabilistic models [24], it came out lowest of the four methods tested. Although SVM ranks highly in the classification, for regression its results are not as good, but still acceptable. BRNN performs, on the whole, a little better than SVM. It has been demonstrated that MLP is capable of providing an approximation of accuracy as long as it has enough hidden neurons [20]. Nevertheless, this capacity has a drawback in that these close approximations can become approximations to the noise. This means that the model's solutions are not easily generalizable with new data, a problem known as overfitting. The NN's complexity has to be matched with the problem under examination. In this area, Bayesian techniques can offer probabilistic interpretations of NN learning. There are significant advantages to BRNN modeling as compared to classical MLP learning processes.