Our framework is a very simple framework used to calculate the area under the curve in the given axis-parallel rectangle. We will use a numerical method that is the simplification of the Monte Carlo method to calculate the integral of a function. The following image illustrates the idea. To calculate the area under the curve in a given rectangle, we will take a lot of points from the rectangle and evaluate the curve equation at those points using the x coordinate. If the evaluation is less than the y coordinates of the point, the point is below the curve at that x coordinate. We will count all such points. The area under the curve can be calculated as,
Area under curve = Area of the rectangle * (pointsBelowCurve/totalPoints)
Axis-parallel rectangle with arbitrary function f(x)
The grey area is the value that we are interested in.
The accuracy of the AUC calculated by this method depends on how many points we take. The more points we take, the more accurate our area under...