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Let's assume I'm modeling a process like:

$$y=log(x1+x2+x3+N)$$

Where $x_i$ are features and $N$ is some error/noise value.

With the way that decision trees work and the way that LightGBM works, will this be modeled correctly? Or will it be necessary for me to train using $e^y$?

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The underlying model will be a stepwise function. I don't see any garanty that it will work better (or worse) with the transformation, in the general case. This may be different depending on you variable (for binary variables you may want to work directly on the linear predictor).

However, in practice, if you know there is an underlying link transformation, I would suggest you to use it. This will often ease the model intepretation.

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  • $\begingroup$ I suspect the main difference will be in the errors: the transformation affects the scale of the loss function as well! $\endgroup$
    – Ben Reiniger
    Mar 20, 2020 at 2:29

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