# Forecasting Electricity Prices: A Machine Learning Approach
## 4 Experimental Phase
### Comparison with Other State-of-the-Art Machine Learning Techniques  
In the second part of the experimental phase, the performance of LSGP was compared to that achieved with the other machine learning and statistical techniques commonly used to address forecasting problems. The objective of this section is to assess if, besides outperforming GSGP, LSGP is able to produce better models with respect to the other techniques considered. \begin{table}
\begin{tabular}{c c c} \hline \hline  & \multicolumn{2}{c}{**Running Time(s)**} \\ \hline  & **Median** & **Standard Deviation** \\ \hline GSGP & 35.73 & 0.59 \\ \hline LSGP & 36.18 & 0.81 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Median and standard deviation of the running time (in seconds) for the two GP based systems. Figure 3: Test MAE. The plots show the median over 100 runs. The Test MAE is expressed in Euros. The light gray line represents Geometric Semantic Genetic Programming, while the black line represents Geometric Semantic Genetic Programming with Local Search. The techniques considered to perform this comparison are the following: linear regression (LIN) [52], ordinary least square regression (SQ) [53], isotonic regression (ISO) [54], radial basis function network (RBF) [55], multilayer perceptron trained with backpropagation (NN) [55], and support vector machine (SVM) [56] with a polynomial kernel. The implementation provided by the WEKA machine learning software [57] was used in this experimental phase. A tuning phase was performed with the objective of finding suitable values for the parameters that characterize the techniques considered. The tuning phase was performed by using the grid search functionality provided by Weka, which allows searching for the best parameters' values. The boxplots reported in Figures 4 and 5 show a comparison between the performance achieved by using the different machine learning techniques considered. On each box, the central mark is the median, the edges of the box are the 25 th and 75 th percentiles, and the whiskers extend to the most extreme data points not considered outliers. In the boxplots, SVM refers to support vector machines with a polynomial kernel of degree 1, while SVM-2 refers to support machines with a polynomial kernel of the second degree. Figure 4: Boxplots of the training MAE calculated over 100 runs. On each box, the central mark is the median, the edges of the box are the 25 th and 75 th percentiles, and the whiskers extend to the most extreme data points not considered outliers. The MAE is expressed in Euros. LIN stands for linear regression, SQ stands for ordinary least square regression, ISO stands for isotonic regression, RBF stands for radial basis function network, NN stands for multilayer perceptron trained with backpropagation, and SVM stands for support vector machine with a polynomial kernel (of second degree for SVM2). Figure 5: Boxplots of the test MAE calculated over 100 runs. On each box, the central mark is the median, the edges of the box are the 25 th and 75 th percentiles, and the whiskers extend to the most extreme data points not considered outliers. The MAE is expressed in Euros. LIN stands for linear regression, SQ stands for ordinary least square regression, ISO stands for isotonic regression, RBF stands for radial basis function network, NN stands for multilayer perceptron trained with backpropagation, and SVM stands for support vector machine with a polynomial kernel (of second degree for SVM2). Considering the MAE on the training instances, the LSGP is observably the best performer, with MAE values that are comparable to the ones achieved with SVM-2. The worst technique on the training set is the multilayer perceptron, followed by SQ and RBF. ISO, LIN, and SVM produce results that are better than the latter techniques but still worse than the results achieved with LSGP. To summarize the results observed with the training set, LSGP is the best performer, and, among the other techniques taken into account, SVM-2 is able to produce comparable good quality solutions.