## 5 Experimentation and Results
### Configuration of Wrappers for MIL  
With respect to MIL representation based on multiple instance, it is proposed the use of two different wrappers available in Weka [49] to adapt the MIL problem to single instance or traditional learning problem. Once that the problem is transformed, the same algorithms used in single instance representation (presented in previous Section 5.1) can be used with MIL representation. Thus, it is a more fair comparison because same algorithms and configurations are used. The proposals of MIL wrappers are the following:  
* SimpleMI [67]: this wrapper makes a summary of all the instances of a bag in order to build a unique instance that can be processed by a simple instance algorithm. * MIWrapper [68]: this wrapper assumes that all instances contribute equally and independently to the bag's label. Thus, the method breaks up the bag into its individual instances labeling each one with the bag label and assigning weights proportional to the number of instances in a bag. At evaluation time, the final class of the bag is derived from the classes assigned to its instances. In the case of SimpleMI, there are two possible configurations to compute the summary of the instances of a bag into a single instance:  
* Configuration 1: computing arithmetic mean of each attribute using all instances of the bag and using it in the summarized instance. * Configuration 2: computing geometric mean of each attribute using all instances of the bag and using it in the summarized instance. In the case of MIWrapper, three configurations to compute the final class of the bag, extracted from the classes assigned at evaluation time:  
* Configuration 1: computing the arithmetic average of the class probabilities of all the individual instances of the bag. * Configuration 2: computing the geometric average of the class probabilities of all the individual instances of the bag. * Configuration 3: checking the maximum probability of single positive instances. If there is at least one instance with its positive probability greater than 0.5, the entire bag is positive. This study evaluates the accuracy of the different configurations to predict if a student will pass or fail the course. The experimentation consists of a 10-fold stratified cross-validation for every combination of wrapper configuration, algorithm and course. The complete results of this experimentation can be downloaded from the web repository associated to this work ([[http://www.uco.es/kdis/mildistanceeducation/](http://www.uco.es/kdis/mildistanceeducation/)]([http://www.uco.es/kdis/mildistanceeducation/](http://www.uco.es/kdis/mildistanceeducation/)), accessed on 23 October 2021). With the average accuracy of the cross-validation, a statistical analysis is carried out in order to find significant differences between configurations in each MIL wrapper. Concretely, it is used the non-parametric Wilcoxon signed-rank test [69] to carry out a pairwise statistical procedure between every two configurations. In each comparison is applied the test and obtained a \(p\)-value independent to show if algorithms obtain significantly better accuracy values with a specific configuration. Table 9 shows the \(R^{+}\), \(R^{-}\) and \(p\)-values for all pairwise comparisons carried out. For both wrappers and considering a confidence level of 99%, the configuration 1 obtains significantly higher accuracy values than the others. Thus, for SimpleMI is more convenient to summarize the bag with the