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A bunch of ML regression models are defined only for predicting the value of a single variable. Or have standard implementation that are only for the univariate case. For example support vector machine and random forest regression models.

I am contemplating the naive (but generic) way to extend them for multivariate regression, via training seperate models for each output variables.

Am I right in saying this would only be correct if the output variables are conditionally independent, when conditioning upon the input feature variables?

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