  The Poisson process, especially the nonhomogeneous Poisson process (NHPP), is
an essentially important counting process with numerous real-world
applications. Up to date, almost all works in the literature have been on the
estimation of NHPPs with infinite data using non-data driven binning methods.
In this paper, we formulate the problem of estimation of NHPPs from finite and
limited data as a learning generalization problem. We mathematically show that
while binning methods are essential for the estimation of NHPPs, they pose a
threat of overfitting when the amount of data is limited. We propose a
framework for regularized learning of NHPPs with two new adaptive and
data-driven binning methods that help to remove the ad-hoc tuning of binning
parameters. Our methods are experimentally tested on synthetic and real-world
datasets and the results show their effectiveness.
