# Variational Inference for Gaussian Process with Panel Count Data

## TL;DR

This paper introduces a novel variational inference framework for Gaussian process-modulated Poisson processes tailored to panel count data, enabling efficient modeling when exact event times are unknown.

## Contribution

It is the first to develop a variational inference method for Gaussian process-based models with panel count data, addressing intractability issues.

## Key findings

- Algorithm outperforms classical methods on synthetic data
- Effective in real panel count datasets
- Provides a tractable lower bound for inference

## Abstract

We present the first framework for Gaussian-process-modulated Poisson processes when the temporal data appear in the form of panel counts. Panel count data frequently arise when experimental subjects are observed only at discrete time points and only the numbers of occurrences of the events between subsequent observation times are available. The exact occurrence timestamps of the events are unknown. The method of conducting the efficient variational inference is presented, based on the assumption of a Gaussian-process-modulated intensity function. We derive a tractable lower bound to alleviate the problems of the intractable evidence lower bound inherent in the variational inference framework. Our algorithm outperforms classical methods on both synthetic and three real panel count sets.