Learning Generalization and Regularization of Nonhomogeneous Temporal
  Poisson Processes
Son Nguyen Van Hoai Nguyen Xuan
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.