NetworkHawkesProcesses.jl

Network Hawkes processes in Julia.

Description

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

Installation

using Pkg;
Pkg.add("https://github.com/cswaney/NetworkHawkesProcesses.jl.git")

Usage

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)

Roadmap

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

Contributing

Contributions and feedback are welcome. Please report issues and feature requests to our GitHub page, https://github.com/cswaney/NetworkHawkesProcesses.jl.