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Let's suppose that I'm trying to predict a stochastic forecast with machine learning models, and I don't have missing, null/NaN values and outliers. Also suppose that there is an error for the predictive model which decreases if I normalize and standardize the data:

a) I put the raw data in the machine learning model

Raw_data

b I use normalization and standarization. Let's call f the normalization function and g de standarization function:

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For case b), now my data is inside a normalized and standardized space, so it's not my actual values. To return to have the real value I must apply the inverse functions.

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Mathematically I'm moving between spaces, like this:

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Question: In b), will the accuracy have a value of 97% once the inverse functions are applied? If the answer is yes, why are the values ​​obtained in a space transferred to the original?

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  • $\begingroup$ On the one hand, you are not telling us how you define "accuracy". There are many, many, many different forecast accuracy measures. On the other hand, almost no accuracy measure will be invariant under transformations. (And transformations are nontrivial: IMO, most people forget the bias correction when back-transforming a log.) $\endgroup$ Commented Jun 19, 2023 at 13:42
  • $\begingroup$ I was thinking accuracy as variance $\endgroup$ Commented Jun 19, 2023 at 14:05
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    $\begingroup$ I think you need to be a bit more precise. I do not think you mean the variance of the forecast (which may easily be zero, and more importantly, is no accuracy because it has nothing to do with the actual outcome). Are you thinking of the Mean Squared Error? That will only be invariant under transformations that additively shift forecasts by a fixed number, $\hat{y}\mapsto\hat{y}\pm a$, which is not a very helpful transformation. $\endgroup$ Commented Jun 19, 2023 at 14:09

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