def test_model_hawkes_loglik_multiple_events(self):
"""...Test that multiple events list for ModelHawkesFixedExpKernLogLik
is consistent with direct integral estimation
"""
end_times = np.array([max(map(max, e)) for e in self.timestamps_list])
end_times += 1.
self.model_list.fit(self.timestamps_list, end_times=end_times)
decays = np.ones((self.n_nodes, self.n_nodes)) * self.decay
intensities_list = [
hawkes_exp_kernel_intensities(self.baseline, decays,
self.adjacency, timestamps)
for timestamps in self.timestamps_list
]
integral_approx = sum([hawkes_log_likelihood(intensities,
timestamps, end_time)
for (intensities, timestamps, end_time) in zip(
intensities_list, self.timestamps_list,
self.model_list.end_times
)])
integral_approx /= self.model_list.n_jumps
self.assertAlmostEqual(integral_approx,
self.model_list.loss(self.coeffs),
places=2)
def approximate_likelihood(em, events, end_times, precision=2):
n_total_jumps = sum(map(len, events))
kernels_func = [[
lambda t, i=i, j=j: em.get_kernel_values(i, j, np.array([t]))[
0] for j in range(n_nodes)
] for i in range(n_nodes)]
intensities = hawkes_intensities(events, em.baseline, kernels_func)
return hawkes_log_likelihood(
intensities, events, end_times,
precision=precision) / n_total_jumps
def test_model_hawkes_losses(self):
"""...Test that computed losses are consistent with approximated
theoretical values
"""
timestamps = self.timestamps_list[self.realization]
decays = np.ones((self.n_nodes, self.n_nodes)) * self.decay
intensities = hawkes_exp_kernel_intensities(
self.baseline, decays, self.adjacency, timestamps)
precision = 3
integral_approx = hawkes_log_likelihood(
intensities, timestamps, self.end_time, precision=precision)
integral_approx /= self.model.n_jumps
self.assertAlmostEqual(integral_approx, self.model.loss(self.coeffs),
places=precision)