Poisson Log-Normal Process for Count Data Prediction

TL;DR

The paper introduces the Poisson Log-Normal (PoLoN) process, a non-parametric Gaussian process-based framework for modeling and predicting count data, capable of detecting localized signals in scientific datasets.

Contribution

It presents the PoLoN process that models Poisson log-rates with Gaussian processes, enabling non-parametric count data prediction and signal detection, including in high-energy physics applications.

Findings

PoLoN predicts count data effectively in synthetic and real datasets.

The method successfully detects weak signals in noisy backgrounds.

It offers an alternative to parametric models for count data analysis.

Abstract

Modeling count data is important in physics and other scientific disciplines, where measurements often involve discrete, non-negative quantities such as photon or neutrino detection events. Traditional parametric approaches can be trained to generate integer-count predictions but may struggle with capturing complex, non-linear dependencies often observed in the data. Gaussian process (GP) regression provides a robust non-parametric alternative to modeling continuous data; however, it cannot generate integer outputs. We propose the Poisson Log-Normal (PoLoN) process, a framework that employs GP to model Poisson log-rates. As in GP regression, our approach relies on the correlations between data points captured via GP kernel structure rather than explicit functional parameterizations. We demonstrate that the PoLoN predictive distribution is Poisson-LogNormal and provide an algorithm for optimizing kernel hyperparameters. Furthermore, we adapt the PoLoN approach to the problem of detecting weak localized signals superimposed on a smoothly varying background - a task of considerable interest in many areas of science and engineering. Our framework allows us to predict the strength, location and width of the detected signals. We evaluate PoLoN's performance using both synthetic and real-world datasets, including the open dataset from CERN which was used to detect the Higgs boson at the Large Hadron Collider. Our results indicate that the PoLoN process can be used as a non-parametric alternative for analyzing, predicting, and extracting signals from integer-valued data.