However, this might not be practical at all: in image processing, the "cloud" pixel of a pixel showing the blue sky of a picture are more likelihood to co-occur in the same picture; in natural language processing, the word "mythical" is more likely to co-occur with the word "unicorn", rather than the word "popcorn".
by modeling the correlations among marginal CDFs, the copula model has gained the insights on the dependency structures of the random variables, and thus, the performance of the regression task is boosted.