I have a more theoretical question on how real world data is gathered when constructing class scores. The formula for class scores according to the assignment is:

π πππππ,π=ππΓππ: the probability that there is an object ππ times the probability that the object is a certain class ππ.

In the exercise both pc and ci values are assigned randomly. In the real world how one would collect this data for each box of an image ? Is there a real algorithm to assign probabilities and create those values ? Or is this data collected manually by a human by inspecting each box and guessing a probability value for pc and ci ?

Training data for object detection has zero uncertainty about where a bounding box is and what is inside it. Whether it is human or machine generated, you start off with an object of known type and location so those probabilities are 1.0

Itβs only during prediction, either during training or at runtime, that there is uncertainty. During training, the computed \delta between the prediction and 1. is what drives learning.