def test_model_hawkes_least_sq_multiple_events(self):
"""...Test that multiple events list for ModelHawkesFixedExpKernLeastSq
is consistent with direct integral estimation
"""
# precision of the integral approximation (and the corresponding
# tolerance)
precison = 1
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)
intensities_list = [
hawkes_sumexp_kernel_intensities(self.baseline, self.decays,
self.adjacency, timestamps)
for timestamps in self.timestamps_list
]
integral_approx = sum([
hawkes_least_square_error(intensities,
timestamps,
end_time,
precision=precison)
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=precison)
def test_model_hawkes_loglik_multiple_events(self):
"""...Test that multiple events list for ModelHawkesFixedSumExpKernLogLik
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)
intensities_list = [
hawkes_sumexp_kernel_intensities(self.baseline, self.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 test_model_hawkes_sum_exp_kernel_least_sq_loss(self):
"""...Test that computed losses are consistent with approximated
theoretical values
"""
timestamps = self.timestamps_list[self.realization]
intensities = hawkes_sumexp_kernel_intensities(
self.baseline, self.decays, self.adjacency, timestamps)
integral_approx = hawkes_least_square_error(
intensities, timestamps,
self.model.end_times[self.realization])
integral_approx /= self.model.n_jumps
self.assertAlmostEqual(integral_approx,
self.model.loss(self.coeffs),
places=2)
def test_model_hawkes_losses(self):
"""...Test that computed losses are consistent with approximated
theoretical values
"""
timestamps = self.timestamps_list[self.realization]
intensities = hawkes_sumexp_kernel_intensities(self.baseline,
self.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)