This non parametric Hawkes cumulants matching
(tick.hawkes.HawkesCumulantMatching) algorithm estimates directly
kernels norms without making any assumption on kernel shapes.
It has been originally described in this paper:
Achab, M., Bacry, E., Gaiffas, S., Mastromatteo, I., & Muzy, J. F. (2017, July). Uncovering causality from multivariate Hawkes integrated cumulants. In International Conference on Machine Learning (pp. 1-10).
Script output:
tensorflow not found, skipping HawkesCumulantMatching
Python source code: plot_hawkes_cumulants_matching.py
skip = True
try:
import tensorflow
skip = False
except ImportError:
print("tensorflow not found, skipping HawkesCumulantMatching")
if not skip:
import numpy as np
from tick.hawkes import (HawkesCumulantMatching, SimuHawkesExpKernels,
SimuHawkesMulti)
from tick.plot import plot_hawkes_kernel_norms
np.random.seed(7168)
n_nodes = 3
baselines = 0.3 * np.ones(n_nodes)
decays = 0.5 + np.random.rand(n_nodes, n_nodes)
adjacency = np.array([
[1, 1, -0.5],
[0, 1, 0],
[0, 0, 2],
], dtype=float)
adjacency /= 4
end_time = 1e5
integration_support = 5
n_realizations = 5
simu_hawkes = SimuHawkesExpKernels(baseline=baselines, adjacency=adjacency,
decays=decays, end_time=end_time,
verbose=False, seed=7168)
simu_hawkes.threshold_negative_intensity(True)
multi = SimuHawkesMulti(simu_hawkes, n_simulations=n_realizations,
n_threads=-1)
multi.simulate()
nphc = HawkesCumulantMatching(integration_support, cs_ratio=.15, tol=1e-10,
step=0.3)
nphc.fit(multi.timestamps)
plot_hawkes_kernel_norms(nphc)
Total running time of the example: 0.00 seconds ( 0 minutes 0.00 seconds)