Efficient Simulation of Sparse Graphs of Point Processes

TL;DR

This paper introduces efficient algorithms for simulating sparse marked point process graphs by integrating local independence structures with activity tracking, significantly reducing computational complexity.

Contribution

It presents a novel coupling of local independence graphs with activity tracking algorithms for high-performance asynchronous simulation of sparse point process graphs.

Findings

Reduced computational complexity for sparse graphs

Effective simulation of marked point processes

Improved performance over classical algorithms

Abstract

We derive new discrete event simulation algorithms for marked time point processes. The main idea is to couple a special structure, namely the associated local independence graph, as defined by Didelez arXiv:0710.5874, with the activity tracking algorithm [muzy, 2019] for achieving high performance asynchronous simulations. With respect to classical algorithm, this allows reducing drastically the computational complexity, especially when the graph is sparse. [muzy, 2019] A. Muzy. 2019. Exploiting activity for the modeling and simulation of dynamics and learning processes in hierarchical (neurocognitive) systems. (Submitted to) Magazine of Computing in Science & Engineering (2019)