Implementing probabilistic KDE error bounds - Week 1

Current state of KDE in mlpack

The current KDE codebase takes advantage of one property: Many kernel functions decrease their value the further away two points are. If it's affodable to have an approximation, then it's possible to avoid many calculations by relaxing the problem (i.e. setting an absolute or relative error bound).

Let's relax even more

It's summertime so let's take those error bounds on vacation so they can relax :)

By setting a probabilistic relative error bound, researchers in this paper made the error bound more flexible (e.g. the KDE, with a 95% probability, will differ as much as 5% from the real value).

During the week I have been working on implementing this into the existing mlpack codebase. So far, the implementation for single trees is almost ready, but I haven't been able to figure out some issues yet. At the moment approximations get really close to the real value, but still not close enough.