Let's say Morpheus has multiple users to offer colored pills(from an infinite set of colored pills), there are in total 3 unique colored pills(red, blue, green) Morpheus can offer. The trick is, Morpheus can offer only one pill to a user and the user has a choice to either take the pill or deny it. (Also, user's decisions are independent of each other)
Now Morpheus wants to be smart about his offer and wants to model the user such that the user selects the pill he is offering. The users are moody and there is some uncertainty that they would randomly take a choice.
Rejection can be because of multiple unknown reasons such as
I didn't like the color of the pill,
I will choose the pill later,
I want to understand more about this pill,
Show me other pills before I decide
Now there are two ways I can think of modeling this:
- Treating this as binary classification
- Treating this as multi-class classification
When I treat this as binary classification, I pass
pill color as feature with other
user features to the model, and my output is the probability of user taking or rejecting a pill given the pill color.
Morpheus can then offer the pill color with the highest probability. This will use both
Reject decisions of a user while modeling, but there is some uncertainty and the same type of users can accept or reject randomly.
When I treat this as a multi-class classification, where I try to predict the pill color itself. I would not use the rejected case in my training and would only consider cases when the user chose something. In this way, I can reduce uncertainty in this case but would have to completely ignore rejected cases. Morpheus then can either use softmax or sigmoid for each class and take argmax to get the best choice to offer.
I am not sure if there are other ways to model this problem, but out of these two which can be a better way?