# An optimization problem has to be solved by adjusting the threshold and seeking the optimum in order to balance the trade-off between the decrease in revenue and a decrease in cost.

An optimization problem has to be solved by adjusting the threshold and seeking the optimum in order to balance the trade-off between the decrease in revenue and a decrease in cost.

Then by using the layout of the confusion matrix plotted in Figure 6, the four regions are divided as True Positive (TN), False Positive (FP), False Negative (FN) and True Negative (TN) ifвЂњSettledвЂќ is defined as positive and вЂњPast DueвЂќ is defined as negative,. Aligned with all the confusion matrices plotted in Figure 5, TP could be the good loans hit, and FP could be the defaults missed. Our company is interested in those two areas. To normalize the values, two widely used mathematical terms are defined: true rate that is positiveTPR) and False Positive Rate (FPR). Their equations are shown below:

## In this application, TPR may be the hit price of good loans, and it also represents the ability of earning cash from loan interest; FPR is the rate that is missing of, plus it represents the likelihood of taking a loss.

Receiver Operational Characteristic (ROC) bend is considered the quick and easy payday loans Chapel Hill most widely used plot to visualize the performance of the category model at all thresholds. In Figure 7 left, the ROC Curve associated with the Random Forest model is plotted. This plot really shows the partnership between TPR and FPR, where one always goes into the direction that is same one other, from 0 to at least one. a classification that is good would will have the ROC curve above the red standard, sitting by the вЂњrandom classifierвЂќ. The location Under Curve (AUC) can be a metric for assessing the category model besides precision. The AUC associated with the Random Forest model is 0.82 away from 1, which can be decent.

Even though the ROC Curve demonstrably shows the connection between TPR and FPR, the limit is an implicit adjustable. The optimization task cannot be achieved solely by the ROC Curve. Consequently, another measurement is introduced to add the limit adjustable, as plotted in Figure 7 right. Considering that the orange TPR represents the capacity of getting cash and FPR represents the possibility of losing, the instinct is to look for the limit that expands the gap between curves whenever you can. The sweet spot is around 0.7 in this case.

You will find limits for this approach: the FPR and TPR are ratios. Also we still cannot infer the exact values of the profit that different thresholds lead to though they are good at visualizing the impact of the classification threshold on making the prediction. Having said that, the FPR, TPR vs Threshold approach makes the presumption that the loans are equal (loan quantity, interest due, etc.), however they are actually maybe not. Individuals who default on loans may have a greater loan quantity and interest that require become repaid, plus it adds uncertainties towards the modeling outcomes.

## Luckily, detail by detail loan amount and interest due are available from the dataset it self.

The only thing staying is to get ways to link these with the limit and model predictions. It isn’t tough to determine a manifestation for revenue. By presuming the income is entirely through the interest gathered through the settled loans plus the price is entirely through the total loan quantity that clients standard, both of these terms may be determined making use of 5 understood factors as shown below in dining table 2: