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In a multi-target model framework - where a separate model is estimated for each target - how can one take into account for correlations between targets during the training process ? For example say I am predicting y1 and y2 separately (with a potentially different set of features). I know that corr(y1, y2) = 0.5, however upon building two models I discover that my predictions y1_pred and y2_pred have a negative correlation corr(y1_pred, y2_pred) = -0.3. Intuitively, I would expect this correlation to be around 0.5 as well. What are the ways to achieve that ? Assume features are continuous and we work with linear regressions.

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