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Before training the model, I convert a target value to the log scale since range of the target is quite large.

After training the model, the Absolute Mean error was estimated as, for instance, 0.5.

If I want to re-convert the predicted target value to linear scale, how can I handle the error on the target value?

For example:

A predicted target value = 2.5 (at log scale)
The Absolute Mean error = 0.5 (at log scale)

When re-converting the predicted target value to the linear scale while including the error, would the range of the target value be exp(2.5-0.5) ~ exp(2.5+0.5)?

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1 Answer 1

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I think this is incorrect.

If on the log scale you have log(value) + log(error), in order to get back something of the form value + error onthe linear scale, you would need to use these exponents separately, in other words value + error = exp(log(value)) + exp((log(error)).

With your method, you get exp(log(value) + log(error)) = exp(log(value))*exp(log(error))=value*error which is not the desired value + error.

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