# Estimation of Poisson arrival processes under linear models

arXiv: https://arxiv.org/abs/1803.00980 · HTML: https://mlsanity.com/paper/1803.00980/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Mar 2018.

## Built on by (most cited first, 1 of 1)

- [Learning Generalization and Regularization of Nonhomogeneous Temporal Poisson Processes](https://mlsanity.com/paper/2402.12808/) (2024)

## Abstract (arXiv)

In this paper we consider the problem of estimating the parameters of a Poisson arrival process where the rate function is assumed to lie in the span of a known basis. Our goal is to estimate the basis expansions coefficients given a realization of this process. We establish novel guarantees concerning the accuracy achieved by the maximum likelihood estimate. Our initial result is near-optimal, with the exception of an undesirable dependence on the dynamic range of the rate function. We then show how to remove this dependence through a process of "noise regularization", which results in an improved bound. We conjecture that a similar guarantee should be possible when using a more direct (deterministic) regularization scheme. We conclude with a discussion of practical applications and an empirical examination of the proposed regularization schemes.