# 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.

If вЂњSettledвЂќ means good and вЂњPast DueвЂќ is described as negative, then utilizing the design of this confusion matrix plotted in Figure 6, the four areas are split as real Positive (TN), False Positive (FP), False bad (FN) and real Negative (TN). 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 keen on those two regions. To normalize the values, two widely used mathematical terms are defined: real good Rate (TPR) and False Positive Rate (FPR). Their equations are shown below:

## In this application, TPR may be the hit price of great loans, plus it represents the ability of creating funds from loan interest; FPR is the lacking rate of standard, also it represents the probability of losing profits.

Receiver Operational Characteristic (ROC) curve is considered the most widely used plot to visualize the performance of a category model at all thresholds. In Figure 7 left, the ROC Curve associated with 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 also have the ROC curve over the red standard, sitting by the вЂњrandom classifierвЂќ. The region Under Curve (AUC) can be a metric for assessing the classification model besides precision. The AUC for the Random Forest model is 0.82 away from 1, which will be decent.

Although the ROC Curve plainly shows the connection between TPR and FPR, the limit is an implicit adjustable. The optimization task cannot be performed solely by the ROC Curve. Consequently, another measurement is introduced to add the limit adjustable, as plotted in Figure 7 right. Because the orange TPR represents the capacity of creating 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 can find restrictions for this approach: the FPR and TPR are ratios. Also we no credit check payday loans Clarks Summit PA 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 really maybe not. Individuals who default on loans may have a greater loan quantity and interest that have to be repaid, and it adds uncertainties towards the results that are modeling.

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

The one thing staying is to get a method to link all of them with the threshold and model predictions. It’s not hard to determine a manifestation for revenue. By presuming the income is solely through the interest gathered through the settled loans additionally the price is entirely through the total loan quantity that clients standard, those two terms could be determined utilizing 5 understood factors as shown below in dining table 2: