MLE for Exponential Hawkes Process

Source code for Inference of multivariate exponential Hawkes processes with inhibition and application to neuronal activity [1].

It includes a class to simulate an univariate Hawkes process and functions to compute the log-likelihood presented in the aforementioned paper along with the approximated version from Lemonnier's work [2].

Example

We include two examples of application, one for simple plotting with the exp_thinning_hawkes class, shown below, and another one implementing the algorithm of estimation with the estimator_class.

import numpy as np
from matplotlib import pyplot as plt
from code.hawkes_process import exp_thinning_hawkes

if __name__ == "__main__":

    # Set seed
    np.random.seed(0)

    lambda_0 = 1.05
    alpha = -0.7
    beta = 0.8
    
    # Create a process with given parameters and maximal number of jumps.
    hawkes = exp_thinning_hawkes(lambda_0=lambda_0, alpha=alpha, beta=beta, max_jumps=15)
    hawkes.simulate()
    
    # Plotting function of intensity and step functions.
    hawkes.plot_intensity()

    plt.show()

This example must yield the following plot:

Dependencies

This code was implemented using Python 3.8.5 and needs Numpy, Matplotlib and Scipy.

For graphics/boxplots_errors.py, pickle is necessary though this is not at all required to use all functions and classes implemented in this repository.

Installation

Copy all files in the current working directory.

Author

Miguel Alejandro Martinez Herrera

References

[1] A. Bonnet, M. Martinez Herrera, M. Sangnier, Inference of multivariate exponential Hawkes processes with inhibition and application to neuronal activity. arXiv:2205.04107

[2] R. Lemonnier, N. Vayatis, Nonparametric markovian learning of triggering kernels for mutually exciting and mutually inhibiting multivariate hawkes processes, in: Machine Learning and Knowledge Discovery in Databases, Springer Berlin Heidelberg, 2014, p. 161–176