Why may log(natural logarithm) transformation improve results of SVM prediction(**regression**, eps-svm)? Is SVM based on the assumption of normal distribution or something else?

update1. I use Radial basis function kernel.

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#### Best Answer

SVM doesn't assume normality. But it's still a regression that minimizes some symmetric loss function (I suppose you use symmetric kernel).

So… this is just a feeling and I'm too tired to justify/prove all this but:

- Probably your output variable has highly skewed distribution;
- And you use symmetric gaussian kernel that leads to symmetric squared loss to minimize (squared error with bump cut-off if I remember correct?);
- Then SVM still estimates something close to conditional mean of your data if you minimize this loss for original output variable;
- When you log-transform output variable and minimize that symmetric loss for it, then in terms of
*original*variable it estimates something like a conditional median; - it's well-known that mean is the thing that minimizes average squared error and median is the thing that minimizes average absolute error, so when you estimate regression using log-transformed output you get worse MSE but better MAPE.

Hope this helps.

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