Fixed error in KDE calculation - #9
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…earn's implementation assumed standardized data
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In
sklearn's implementation of KDE, undersite-packages/sklearn/neighbors/_kde.py, we see the following:When given a bandwidth of "scott", it calculates:
Which in our case is$\sigma \cdot n^{-\frac{1}{5}}$ .$\sigma=1$ , in other words, that the data has already been standardized, which isn't the case.
n ** (-1/5).But the standard Scott's rule formula is
So
sklearnis assumingAs a result, the KDE estimate overfits or underfits the data, which then results in erroneous ID_OOD splits down the line.
A fix could be to standardize the data before calculating the KDE, or to just pass the Scott's formula bandwidth directly, which is what I opted to do in this fix.
Let me know if you think I missed anything :)