# ROC- AUC(Reciever Operating Characteristics)

This is one of the popularly used model evaluation technique. Many more model evaluation techniques are also there, like confusion matrix etc.

In ROC also, we deal with confusion matrix i.e, we use TPR(True positive rate) and FPR(False positive rate) for, drawing the conclusion from the curve based on these two parameters.

Further to this, would like to add two more terms sensitivity and specificity related to TPR and FPR only.

First, see this confusion matrix will give more idea about TP, FP, TN, FN.

## Sensitivity = TP/(TP+FN)

## Specificity = TN/(TN + FP)

If we go to the curve of Specificity and Sensitivity, will get this kind of curve.

So, for the evaluation, we will use **sensitivity i.e, TPR** and **1- specificity i.e, FPR.** See like this we will get a curve.

Therefore, we can conclude the performance of the model with the help of this curve shown above. After that will calculate the Area Under the Curve(AUC). If AUC has high value then its good otherwise not. Let’s see some rules for deducing the conclusion-:

- 90-1 = excellent
- .80-.90 = good
- .70-.80 = fair
- .60-.70 = poor
- .50-.60 = fail

This is all about ROC, in the upcoming discussion will discuss * “Gini Coefficient” *which is one of the evaluation metrics.

# Gini Coefficient

It is generally used in the classification problem. It is basically derived from Area Under the curve and ROC. It is the ratio of the area between the ROC curve and the diagonal line & the area of the above triangle. It will be more clear through this figure.

## Figure for gini

The formula used for calculating Gini Coefficient is as follows-:

## Gini = 2*AUC -1

Higher the Gini index, better the predictive model is.

I hope it gives you a clear description of the ROC, AUC and Gini Index.

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