# How to model the correlation between predictions in classification problems

In most of deep learning classification problem settings, the predictions $$p(y|x)$$ are often modeled to be independent, namely, $$p(y|x) = \prod_{i=1}^{N} p(y_i|x_i)$$ However, this assumption may violate our prior knowledge that the labels could be highly correlated. For example, in face attribute classification, the hair color could be highly correlated to the eye color, and the above model lacks the ability to infer the correlation between predictions, such as $$p(y_i, y_j|x)$$ or $$I(y_i;y_j|x)$$.

I would like to know if there is any literature or papers discussing modeling the correlation between predictions given only the dataset $$\{x_i, y_i\}_{i=1}^N$$. Or, if necessary, given certain additional information is it possible to model the "conditional" correlation $$p(y_i, y_j|x)$$?

Any input would be greatly appreciated.

• any idea? any inputs related to this question is highly welcome. Oct 15, 2019 at 8:12