Network Hawkes processes in Julia.
Author cswaney
2 Stars
Updated Last
10 Months Ago
Started In
December 2022

Build Status


Network Hawkes processes in Julia.


This package implements methods to simulate and estimate mutually-exciting Hawkes processes with network structure as described in Linderman, 2016. It allows researchers to construct models from a flexible set of model components, run inference from a list of compatible methods (including maximum-likelihood estimation, Markov chain Monte Carlo sampling, and variational inference), and explore results with visualization and diagnostic utilities.

Key Features

  • Supports continuous and discrete processes
  • Uses modular design to support extensible components
  • Implements simulation via Poisson thinning
  • Provides multiple estimation/inference methods
  • Supports a wide range of network specifications
  • Supports non-homogeneous baselines
  • Accelerates methods via Julia's built-in Threads module


using Pkg;


using NetworkHawkesProcesses
nnodes = 2
weight = 0.1
duration = 1000.0
Δtmax = 1.0
baseline = NetworkHawkesProcesses.HomogeneousProcess(ones(nnodes))
weights = NetworkHawkesProcesses.DenseWeightModel(weight .* ones(nnodes, nnodes))
impulses = NetworkHawkesProcesses.ExponentialImpulseResponse(ones(nnodes, nnodes))
process = NetworkHawkesProcesses.ContinuousStandardHawkesProcess(baseline, impulses, weights)
data = NetworkHawkesProcesses.rand(process, duration)
ll = NetworkHawkesProcesses.loglikelihood(process, data)
res = NetworkHawkesProcesses.mle!(process, data; verbose=true, regularize=true)


In addition to improved testing and documentation, we plan to add the following features in future releases:

  • Support for (distributed) multiple-trial inference
  • Support stochastic variational inference
  • Implement additional network models (e.g., stochastic block and latent distance networks)
  • Implement network models for weights
  • Support for time-varying network models
  • Support baselines processes with exogenous covariates


Contributions and feedback are welcome. Please report issues and feature requests to our GitHub page,

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