Note

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UNHaP on simulated univariate Hawkes processesΒΆ

This example demonstrates inference performed by UNHaP on univariate Hawkes processes simulated with a truncated gaussian kernel.

# Authors: Guillaume Staerman <guillaume.staerman@inria.fr>
#          Virginie Loison <virginie.loison@inria.fr>
#          Thomas Moreau <thomas.moreau@inria.fr>
#
# License: MIT

Let us first define the parameters of our model. %% Imports

import numpy as np
import matplotlib.pyplot as plt

from fadin.utils.utils_simu import simulate_marked_data
from fadin.solver import UNHaP
from fadin.utils.vis import plot

baseline = np.array([0.3])
baseline_noise = np.array([0.05])
alpha = np.array([[1.45]])
mu = np.array([[0.4]])
sigma = np.array([[0.1]])

delta = 0.01
end_time = 1000
seed = 0
max_iter = 2000
batch_rho = 200

ev, noisy_marks, true_rho = simulate_marked_data(
    baseline, baseline_noise.item(), alpha, end_time, mu, sigma, seed=0
)

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print('Type of ev object', type(ev))
# ev is a list of numpy arrays, one for each dimension
print('Number of events', len(ev[0]))
print('Shape of first event array', ev[0].shape)
# Each dimension is stored as a numpy array of shape (n_events, 2).
print('First 10 events timestamps and marks', ev[0][:10])
# Each event is stored as [timestamp, mark].
# This is the expected data format for UNHaP.
print('First event timestamp', ev[0][0][0])
print('First event mark', ev[0][0][1])
print('Second event timestamp', ev[0][1][0])
print('Second event mark', ev[0][1][1])

Type of ev object <class 'list'>
Number of events 4051
Shape of first event array (4051, 2)
First 10 events timestamps and marks [[ 4.69547619  0.74068982]
 [11.71408419  0.84561144]
 [13.23685776  0.7762665 ]
 [13.64455959  0.32854968]
 [13.92911594  0.52535543]
 [14.34636819  0.70410709]
 [14.91771101  0.86337427]
 [16.42962959  0.73803117]
 [18.52179446  0.6507131 ]
 [18.78980044  0.80357712]]
First event timestamp 4.695476192547066
First event mark 0.7406898228281054
Second event timestamp 11.714084185001973
Second event mark 0.8456114395619337

solver = UNHaP(
    n_dim=1,
    kernel="truncated_gaussian",
    kernel_length=1.0,
    init='moment_matching_mean',
    delta=delta,
    optim="RMSprop",
    params_optim={"lr": 1e-3},
    max_iter=max_iter,
    batch_rho=batch_rho,
    density_hawkes="linear",
    density_noise="uniform",
)
solver.fit(ev, end_time)

sum of marks per channel: tensor([2465.4731])
number of events is: tensor([3721.])
precomput: 0.5338568687438965
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Fitting model...  42.3%
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Fitting model...  44.3%
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iterations in  3.8175885677337646

<fadin.solver.UNHaP object at 0x7f4e6bc81640>

print("Estimated baseline is: ", solver.baseline_.item())
print("Estimated alpha is: ", solver.alpha_.item())
print("Estimated kernel mean is: ", solver.kernel_[0].item())
print("Estimated kernel sd is: ", solver.kernel_[1].item())
print("Estimated noise baseline is: ", solver.baseline_noise_.item())
# error on params
error_bl = (solver.baseline_.item() - baseline.item()) ** 2
error_bl_noise = (
    solver.baseline_noise_.item() - baseline_noise.item()
) ** 2
error_alpha = (solver.alpha_.item() - alpha.item()) ** 2
error_mu = (solver.kernel_[0].item() - mu.item()) ** 2
error_sigma = (solver.kernel_[1].item() - sigma.item()) ** 2
sum_error = error_bl + error_bl_noise + error_alpha + error_mu + error_sigma
error_params = np.sqrt(sum_error)

print("L2 square error of the vector of parameters is:", error_params)

Estimated baseline is:  0.3127627372741699
Estimated alpha is:  1.3615236282348633
Estimated kernel mean is:  0.4037073254585266
Estimated kernel sd is:  0.10070288926362991
Estimated noise baseline is:  0.47099992632865906
L2 square error of the vector of parameters is: 0.4304022910110504

fig, axs = plot(
    solver,
    plotfig=False,
    bl_noise=True,
    title="UNHaP fit",
    savefig=None
)
plt.show(block=True)
UNHaP fit, 0-> 0

Total running time of the script: (0 minutes 5.542 seconds)

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