Learning Generalization and Regularization of Nonhomogeneous Temporal Poisson Processes
This work addresses a domain-specific challenge in statistical learning for temporal data analysis, offering incremental improvements by reducing ad-hoc tuning in NHPP estimation.
The paper tackles the problem of estimating nonhomogeneous Poisson processes (NHPPs) from limited data, showing that traditional binning methods risk overfitting, and proposes a regularized learning framework with adaptive binning methods that improve effectiveness in experiments.
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.