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[D] Multidimensional regression: Should I / how to make sure the error variances are the same along different dimensions

[Posted this yesterday, but i think it got removed for some reason]

I have data that has equal variance along each of the target dimensions, but if i analyze the results of training i notice that that my trained model does not have the same error variances along each of the dimensions, which means some dimensions are more erroneous than others.

Does this say anything about me missing some sort of regularization, or is this not something I should be fretting over? Is there a way I can regularize to make sure the errors along different dimensions have the same variance?

submitted by /u/journeymango
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Toronto AI is a social and collaborative hub to unite AI innovators of Toronto and surrounding areas. We explore AI technologies in digital art and music, healthcare, marketing, fintech, vr, robotics and more. Toronto AI was founded by Dave MacDonald and Patrick O'Mara.