Prove it

I have a kernel method that works. Intuitively, it makes sense. Empirically, it yields correct results (at least, asymptotically; it's a bit conservative early on, which isn't a bad thing). But, I don't yet have a solid mathematical basis for it. It's really the result of just messing with the simulation.

There are two problems with that. First off, the simulation is just that: a simulation. You can fairly easily cook up a simulation to support just about anything. Simply bake your assumptions into the sim. The real world may not be so accommodating. The other problem is that "proofs" by simulation don't give people good insight into the assumptions of the method. No method works everywhere. Only by knowing what situations are supported can one know when NOT to use a method.

So, I'm now working on the mathematical basis for my method. It's a fairly heavy lift. These correlated data sets have been largely ignored for the simple reason that they don't yield easy answers and one can usually just work around the problem with heuristics.

However, this is one thing my adviser and I agree on: there really isn't much to this paper without a solid theoretical grounding. The result in and of themselves aren't that interesting. It's only with the theory in place that we will have an adequate foundation for a dissertation.

More late nights to follow.