## 3 Results and Discussion
### Turbidity Prediction Model with Regression Learner  
Using the Regression Learner approach, different regression machine learning models were trained. The performance of the best models (Figure 3) showed an R\({}^{2}\) within the range of 0.5 to 1 for the estimation of wine turbidity wine prior to bottling, which is considered a high representation [48]. However, the exponential Gaussian process regression (GPR) model presented better performance metrics than the other models, with an R\({}^{2}\) of 0.973 and an MSE of 0.003. Even though the MSEs are closer for every model, there is more of a difference when NRSME and AIC are compared because the exponential GRP model's AIC is the only one lower than \(-900\), and the lower the AIC, the better the model. For NRSME, only two models are lower than six, and the lowest one is exponential GRP; this is why this model was selected as the best one among all the 22 models trained with a Regression Learner for the training step; in the next section, it is compared with the best model from the Neural Net Fitting program. In contrast, between the models of Figure 3, the one with the lowest performance was the fine Gaussian support vector machine (SVM) with an R\({}^{2}\) of 0.770, an MSE of 0.026, and higher values of NRSME and AIC.  
Figure 2: Performance of the neural network model trained with the Levenberg–Marquardt algorithm with 25 neurons in the hidden layer to predict turbidity in wines.  
In the exponential GPR model, the performance values obtained resemble those found by [PERSON] et al. [49], who, in their research, trained Gaussian process models to predict solid residues, finding values of 0.982 and 0.007 for R2 and MSE, respectively. Those results were obtained because they established non-linear relationships between the data used in the training (dose and type of clarifier) using a probability distribution in a function space. On the contrary, the fine Gaussian SVM model presented a lower R2 and higher MSE than the other models, obtaining similar values to those found by [PERSON] et al. [26], who revealed an R2 of 0.77 and MSE of 0.276 to predict wine quality. The performance obtained in this study is because this model type is not flexible to abrupt changes in the turbidity data by assigning the non-linear values in a higher space using the kernel function [26].  
In contrast to this study, researchers have found that SVM method is the most suitable technique for predicting the quality of red wine from data generated over 1000 years [50], but in another study in the same field where different methods were compared, the Gradient Boosting Regressor (GBR) and its variants surpassed all other models [26; 51]. [PERSON] and [PERSON] [52] found that when the quality classification of red and white wine is needed, the most successful method was the random forest algorithm with a 99.5% accuracy, which is the same as [PERSON] and [PERSON] [53], who found more than 90% accuracy in the wine quality prediction. These two last studies worked with previous data sets taken from repositories and with more than 10 features of physicochemical data. All those studies focused on classifying wine over its quality, but in this research, the obtained model can predict the turbidity value of wine, and even though machine learning principles were used in both cases, the aims of the studies are different, which is why different methods were found to be suitable between this study and the literature.  
Figure 3: Regression Learner performance metrics: (**a**) coefficient of determination, (**b**) mean square error, (**c**) normalized root mean square error, and (**d**) Aikake information criterion.