Given an input, I want to predict 0/1 for each of N output classes. The output can be 1 for multiple classes. So I'm training with individual binary cross-entropies for each of the output classes. This works very well for the most part. However, I have some prior knowledge that I'd like to be able to incorporate to decrease the number of false positives.
Specifically I have a confusion matrix that states whether any pair of classes is or is not mutually exclusive. In other words, if class A has output 1, then I can look up the table and see that classes B, D, and F must be 0. This is where I get false positives. Class A has output 1, but class B might also incorrectly predict 1. Roughly 75% of the class pairs are mutually exclusive.
Is there a way to incorporate this confusion matrix (which is known) into the training?
