Parameter free divergences for point processes
Recently, my dear collaborator Sohan Seth brought me some new ideas of designing divergence measures using the ideas from cumulative distribution functions (CDF) estimation. Unlike probability density functions (PDF), CDF can be estimated without binning or smoothing. The empirical CDF consisting of step functions is very simple, and by Glivenko–Cantelli theorem it can be shown that it converges to the true CDF in probability. We have derived a couple of CDF based divergence measures for point processes together, and sometimes they perform better than the parametric divergences I have discusses before. The best part of course is that it does not require a parameter! We are writing a conference paper this week about this, and I’m very excited about it.