Can `bw_selection.py` return a value when root finding did not converge?

[Kaiyangshi-Ito]

When ISJ bandwidth's root finding does not converge, can it return bandwidth selection using another method (e.g. Silverman) automatically just with a warning message? Or can it use some other root finding method? I think currently it uses brent method, but if the feasible set it uses doesn't contain a root, this should be the source of the problem. I encountered this problem quite often ever since upgrading to 1.1.1, though on a different data. So I'm not sure whether it's due to my data or due to change of implementation.

  File "KDEpy/FFTKDE.py", line 104, in fit
    super().fit(data, weights)
  File "KDEpy/BaseKDE.py", line 131, in fit
    self.bw = self.bw_method(self.data, self.weights)
  File "KDEpy/bw_selection.py", line 188, in improved_sheather_jones
    t_star = _root(_fixed_point, N, args=(N, I_sq, a2))
  File "KDEpy/bw_selection.py", line 120, in _root
    raise ValueError("Root finding did not converge. Need more data.")
ValueError: Root finding did not converge. Need more data.

[tommyod]

I've chosen to be explicit about failures rather than implicit. If I remember correctly version 1.1.1 introduces no changes in ISJ code, so the upgrade should not cause it.

Try:

• Scaling (standardizing) your data before fitting the KDE (you can transform the data back afterwards). If values are roughly in the 0-1 range, the algorithm probably has better chance of convergence.
• Putting the entire thing in a try..except.

I won't be making any changes to make these errors more "silent", since I personally prefer to be explicit when things fail. The user can always wrap the code in try..except to silence it :)

Also, do you have relatively little data? If so, that might also be the cause of it.