# On Predicting Ticket Reopening for Improving Customer Service in 5G Fiber Optic Networks
## 4 A Bayesian Network Classifier Trained on a Further Reduced Dataset
### Bayesian Network Classifier  
Based on the reduced dataset, we trained a classifier resorting to a Bayesian network. A Bayesian network is a probabilistic graphical model that, by representing a set of variables and their conditional dependencies via a directed acyclic graph \(\mathcal{G}\), allows for predicting the likelihood that one of several possible known causes is the contributing factor behind the occurrence of a specific event. In the considered case, the aim is that of predicting if a combination of network QoS parameters belongs to the discrete class variable Repeated ticket. In more detail, we learned a Naive Bayes network structure \(\mathcal{G}\) as in Figure 3, revolving around the following input variables, which therefore compose the new reduced dataset \(X^{\prime}_{red}\) as a \(p^{\prime}\times n\) matrix, with \(p^{\prime}=7\):  
* Repeated ticket;
* Ticket close code;
* Signal-to-noise ratio (downstream);
* SAC;
* Constant bitrate (downstream);
* Power (upstream);
* Attenuation (upstream). We set the Upstream Attenuation node as root node and the SAC and Repeated ticket nodes as leaf nodes. Figure 3: Naive Bayes network structure \(\mathcal{G}\) behind the chosen Bayesian network classifier. The variables' alarm tag and percentage of 3G data availability for backup have been preliminarily excluded from the ABT because, from a statistical viewpoint, they were not suitable for the algorithm procedure that is behind training a Bayesian network classifier. In addition, before training the classifier, we chose to perform _discretization_--referred to as the process of grouping values into intervals in order to limit the number of possible states--on the input data according to the type and distribution of each variable, in order to optimize the performance in the creation of the Bayesian network graph. The following two methods were applied onto the continuous variables of the ABT: namely, quantile (subdivision by frequency) and uniform (subdivision into a suitable number of groups of the same size) discretization. Quantile discretization was performed onto the constant bitrate (downstream), signal-to-noise ratio (downstream), attenuation (upstream) and power (upstream) variables, by grouping the values of each variable into four same size bins, split based on percentiles. Uniform discretization, instead, was performed onto the ticket close code and SAC, grouping the values of each variable into four same-width discrete bins depending on the span of possible values for each considered variable. The Repeated ticket variable was discretized into two disjoint bins, of which 15% are repeated tickets and the rest are non-repeated. Table 4 shows the characteristics of the Bayesian network in detail. The value of the Pearson correlation coefficient (denoted with 'Strength' in the table) indicates the existing degree of correlation between the variables considered: the closer this value is to 1, the greater the correlation between the variables. On the other hand, the 'Direction' column indicates the degree of reliability of the links that introduce a hierarchy between the variables: in this case, too, the closer the value is to 1, the more the direction of the link accounting for the existing relationship between the considered variables is reliable. It is clear from Figure 3 and Table 4 that the correlation coefficient with the variables closest to the Repeated ticket variable is always greater than 0.93, which implies that the proposed tree structure can be considered as highly reliable for our classification purpose. The combinations of conditional probabilities calculated by the Bayesian network as a result of discretization generate a number of scenarios to which it is possible to associate the probability of occurrence of the event of ticket reopening. For the considered reduced dataset \(X^{\prime}_{red}\), more than one thousand different simulation scenarios were generated.