# Learning Generalization and Regularization of Nonhomogeneous Temporal Poisson Processes

arXiv: https://arxiv.org/abs/2402.12808 · HTML: https://mlsanity.com/paper/2402.12808/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 41 references that are in the map.
- First posted on arXiv 20 Feb 2024.

## Builds on (most cited first, 3 of 3)

- [Contextualized Spatial-Temporal Network for Taxi Origin-Destination Demand Prediction](https://mlsanity.com/paper/1905.06335/) (2019)
- [Multi-output Gaussian Process Modulated Poisson Processes for Event Prediction](https://mlsanity.com/paper/2011.03172/) (2020)
- [Estimation of Poisson arrival processes under linear models](https://mlsanity.com/paper/1803.00980/) (2018)

## Abstract (arXiv)

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.