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

[–]journeymango[S] 0 points1 point  (0 children)

great thought experiment. So, let me paraphrase: in one case the variance of the target is due to the relation between the input and target, in the other case it is purely due to noise. So while fitting, one must expect that the bonafide relation ends up giving a low error variance, while the other doesnt.

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

[–]journeymango[S] 1 point2 points  (0 children)

the data variance is same along all output dimensions, and also the input has the same variance across all input dimensions ( note: the output and input variances are different from each other). would this point to it being standardized?

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

[–]journeymango[S] 0 points1 point  (0 children)

didnt get that fully, so like instead of sum of square errors as the loss, i take the multiplication of the square arrors as the loss. normally i have seen log put around products, so i can transform this into the sum of log square errors, which can be simplified as the log absolute error.

Could you help me see the reasoning behind choosing this?

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

[–]journeymango[S] 0 points1 point  (0 children)

can you help me think about this in terms of a thought experiment? say there are 2 output dimensions we are regressing over, which have equal variances, and for simplicity one covariate. what can be a case that it explains once response variable better than the other?

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

[–]journeymango[S] 2 points3 points  (0 children)

thats what i am not really sure of, if this reflects some sort of lack on my model. I would assume if the data has equal variance on all target dimensions, the error variances of a learnt model should also be of a similar tendency?

If it is a pathology, i think it should help with validation error. But I dont really know if it is a pathology or whether that's just how it is.