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I have a regression task for which my best models has a Mean Absolute Error (MAE) of approximately 15,000. The median value of the target variable is approximately 150,000.

I want to report that the error is ~10% of the median. Is there a name for such metric? i.e. dividing the MAE by the median?

If not, is there an alternative error that quantifies percentage?

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You are encoding a Laplace prior over your targets... now, by itself a loss has no much meaning, however, if you associate it with a distribution, you can understand how good it is

the Mean Absolute Error is the MLE of the "variance" $b$ of the Laplace distribution (variance is a bit abusive as term since the variance is actually $2b^2$)

However, this is the result of an assumptions... homoscedasticity... which might be true, or might be false

In other words, saying that the ratio between the loss and the target is 10%, just explains how much noise on average your data has... with respect to your model

This means, that there is no much to say about the ratio, since it depends on a strong assumption, and on the model you are fitting (maybe using a very thick and deep NN you can get much better than that, but that does not mean that it performs as better as reported by the ratio)

In my opinion then, you might want to avoid using that "measure" since it's missleading, and does not convey much information (to a human, but you can use that to compare your model to other models)

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