## 5 Experimentation and Results
### Evaluation Metrics  
The metrics used for evaluation are some of the most common ones in the field of classification. In this context, classical concepts of binary classification are re-defined to our specific problem of having success in a course (passing it with or without distinction) or not having it (failure or dropout) as follow:  
* \(t_{p}\) is the number of students correctly identified to pass the course.
* \(t_{n}\) is the number of students correctly identified to fail the course.
* \(f_{p}\) is the number of students do not correctly identified to pass the course (it is predicted that students pass the course, but they really do not pass).
* \(f_{n}\) is the number of students do not correctly identified to fail the course (it is predicted that students do pass the course, but they really pass).  
\begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Algorithm** & **Parameter** & **Value** & **Algorithm** & **Parameter** & **Value** \\ \hline \multirow{8}{*}{LibSVM} & SVMType & C-SVC & & decay & False \\  & coef0 & 0 & hiddenLayers & a \\  & cost & 1.0 & & learningRate & 0.3 \\  & degree & 3 & & momentum & 0.2 \\  & doNotReplace & Multilayer & normalize & True \\  & MissingValues & False & Perceptron & Attributes & True \\  & eps & 0.001 & & reset & True \\  & gamma & 0.0 & & trainingTime & 500 \\  & kernelType & radial & & validation & 20 \\  & normalize & False & & & \\  & probability & False & & minStdDev & 0.1 \\  & Estimates & True & & numClusters & 2 \\ \hline \multirow{8}{*}{SGD} & dontNormalize & False & & ridge & \(1\times 10^{-8}\) \\  & dontReplace & False & & & \\  & Missing & & & & \\  & epochs & 500 & AdaBoost-Random & numIterations & 10 \\  & lambda & \(1\times 10^{-4}\) & Forest & useResampling & False \\  & learningRate & 0.01 & & weightThreshold & 100 \\  & lossFunction & SVM & & numIterations & 10 \\ \hline \multirow{8}{*}{SMO} & buildCalibration & False & & useResampling & False \\  & Models & 1.0 & & weightThreshold & 100 \\  & c & 1.0 & & & \\  & epsilon & \(1\times 10^{-12}\) & AdaBoost-Naive & numIterations & 10 \\  & filterType & Normalize & Bayes & useResampling & False \\  & filterType & training & & weightThreshold & 100 \\  & kernel & PolyKernel & & Bagging—Random & bagSizePercent & 100 \\  & tolerance & 0.001 & Forest & numIterations & 10 \\ \hline \multirow{8}{*}{SPegasos} & dontNormalize & False & & bagSizePercent & 100 \\  & dontReplace & False & & numIterations & 10 \\ \cline{1-1}  & Missing & & & bagSizePercent & 100 \\ \cline{1-1}  & epochs & 500 & Bayes & numIterations & 10 \\ \cline{1-1}  & lambda & \(1\times 10^{-4}\) & & bagSize & \\ \cline{1-1}  & lossFunction & SVM & & & \\ \hline \hline \end{tabular}
\end{table}
Table 8: Configuration of the studied algorithms II.  
\begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Wrapper** & **Comparison** & \(R^{+}\) & \(R^{-}\) & \(p\)**-Value** \\ \hline SimpleMI & **Conf. 1** vs. Conf. 2 & 12,740.5 & 300.5 & \(4.78\times 10^{-25}\) \\ \hline \multirow{4}{*}{MIWrapper} & **Conf. 1** vs. Conf. 2 & 8274.0 & 4606.0 & \(5.19\times 10^{-4}\) \\  & **Conf. 1** vs. Conf. 3 & 12,846.0 & 195.0 & \(2.32\times 10^{-25}\) \\  & **Conf. 2** vs. Conf. 3 & 12,847.0 & 194.0 & \(2.28\times 10^{-25}\) \\ \hline \hline \end{tabular}
\end{table}
Table 9: Wilcoxon signed-rank test between MIL wrappers.  
Given the nature of the problem, in this context it is specially interesting to focus on students who are likely to fail. Thus, the metrics studied are [70]:  
* _Accuracy_ is the proportion of correctly classified students, i.e., identifying if they pass or not the course. \[Acc=\frac{t_{p}+t_{n}}{t_{p}+t_{n}+f_{p}+f_{n}}\] (1)
* _Sensitivity_ is the proportion of students correctly classified that pass the course. \[Se=\frac{t_{p}}{t_{p}+f_{n}}\] (2)
* _Specificity_ is the proportion of students correctly classified that do not pass the course. \[Sp=\frac{t_{n}}{t_{n}+f_{p}}\] (3)