Let's say we have basic
MNIST dataset, and we have the same goal to predict the digit, BUT we're swapping all the labels by
BLUE. The label becomes
BLUE with probability
DIGIT/10. So if the digit is
FIVE, then probability of label
BLUE is 50%, so we have equal number of
BLUE labels. And if that digit is
TWO, then probability of
BLUE is only
20% and we have mostly
This on one hand seems like an extremely trivial task, but on the other hand I can't see any way of approaching it, despite many years in the fields of ML and programming.
My question: what architecture or methodology could be used to approach this kind of a model? I understand that traditional feed-forward neural networks won't be able to deal with probabilistic nature of this problem. While Probabilistic Programming tools aren't suitable either. I would appreciate links to similar problems solved or any proposals on how can this be conceptually approached. Right now it doesn't seem that traditional neural network will do any good on this problem.