def test_HawkesKernelExp_str(self):
"""...Test HawkesKernelExp string representation
"""
intensity = 3
decay = 2
hawkes_kernel_exp = HawkesKernelExp(intensity, decay)
self.assertEqual(str(hawkes_kernel_exp), "3 * 2 * exp(- 2 * t)")
intensity = 3
decay = 0
hawkes_kernel_exp = HawkesKernelExp(intensity, decay)
self.assertEqual(str(hawkes_kernel_exp), "3")
intensity = 0
decay = 2
hawkes_kernel_exp = HawkesKernelExp(intensity, decay)
self.assertEqual(str(hawkes_kernel_exp), "0")
def test_HawkesKernelExp_repr(self):
"""...Test HawkesKernelExp string in list representation
"""
intensity = 3
decay = 2
hawkes_kernel_exp = HawkesKernelExp(intensity, decay)
self.assertEqual(str([hawkes_kernel_exp]), "[3*2*exp(-2*t)]")
intensity = 3
decay = 0
hawkes_kernel_exp = HawkesKernelExp(intensity, decay)
self.assertEqual(str([hawkes_kernel_exp]), "[3]")
intensity = 0
decay = 2
hawkes_kernel_exp = HawkesKernelExp(intensity, decay)
self.assertEqual(str([hawkes_kernel_exp]), "[0]")
def setUp(self):
self.decay = 2
self.intensity = 3
self.hawkes_kernel_exp = HawkesKernelExp(self.intensity, self.decay)
self.multiplier = 0.1
self.cutoff = 0.01
self.exponent = 1.2
self.support = 10000
self.hawkes_kernel_power_law = HawkesKernelPowerLaw(
self.multiplier, self.cutoff, self.exponent, self.support)
def setUp(self):
np.random.seed(28374)
self.kernels = np.array([[HawkesKernel0(),
HawkesKernelExp(0.1, 3)],
[
HawkesKernelPowerLaw(0.2, 4, 2),
HawkesKernelSumExp([0.1, 0.4], [3, 4])
]])
self.baseline = np.random.rand(2)
def test_HawkesKernelExp_pickle(self):
"""...Test pickling ability of HawkesKernelExp
"""
obj = HawkesKernelExp(decay=2, intensity=3)
pickled = pickle.loads(pickle.dumps(obj))
self.assertTrue(str(obj) == str(pickled))
self.assertEqual(obj.decay, pickled.decay)
self.assertEqual(obj.intensity, pickled.intensity)
np.testing.assert_array_equal(obj.get_values(self.random_times),
obj.get_values(self.random_times))
def simulate_hawkes(self, model_name):
self.model_name = model_name
def y_func_pos(t_values):
y_values = 0.02 * np.exp(-t_values)
return y_values
def y_func_neg(t_values):
y_values = -0.1 * np.exp(-t_values)
return y_values
if model_name == 'hawkes_neg':
y_func = y_func_neg
elif model_name == 'hawkes_pos':
y_func = y_func_pos
t_values = np.linspace(0, 101, 100)
y_values = y_func(t_values)
tf = TimeFunction([t_values, y_values],
inter_mode=TimeFunction.InterLinear,
dt=0.1)
tf_kernel = HawkesKernelTimeFunc(tf)
N_enodes = self.G_e2n.number_of_nodes() # regarded as 'N_enodes' types
base_int = 0.2
baselines = [base_int for i in range(N_enodes)]
kernels = [[] for i in range(N_enodes)]
for i in range(N_enodes):
for j in range(N_enodes):
if i == j:
# kernels[i].append(HawkesKernel0())
kernels[i].append(HawkesKernelExp(.1, 4)) # self influence
else:
if self.G_e2n.has_edge(self.idx_elabel_map[i],
self.idx_elabel_map[j]):
kernels[i].append(tf_kernel)
else:
kernels[i].append(HawkesKernel0())
hawkes = SimuHawkes(kernels=kernels,
baseline=baselines,
verbose=False,
seed=self.seed)
hawkes.threshold_negative_intensity(allow=True)
run_time = 100
hawkes.end_time = run_time
hawkes.simulate()
timestamps = hawkes.timestamps
self.save(timestamps, self.model_name)
def test_HawkesKernelExp_strtex(self):
"""...Test HawkesKernelExp latex string representation
"""
decay = 2
intensity = 3
hawkes_kernel_exp = HawkesKernelExp(intensity, decay)
self.assertEqual(hawkes_kernel_exp.__strtex__(), "$6 e^{-2 t}$")
intensity = 3
decay = 0
hawkes_kernel_exp = HawkesKernelExp(intensity, decay)
self.assertEqual(hawkes_kernel_exp.__strtex__(), "$3$")
intensity = 0
decay = 2
hawkes_kernel_exp = HawkesKernelExp(intensity, decay)
self.assertEqual(hawkes_kernel_exp.__strtex__(), "$0$")
intensity = 0.5
decay = 2
hawkes_kernel_exp = HawkesKernelExp(intensity, decay)
self.assertEqual(hawkes_kernel_exp.__strtex__(), "$e^{-2 t}$")
decay = 1
intensity = 3
hawkes_kernel_exp = HawkesKernelExp(intensity, decay)
self.assertEqual(hawkes_kernel_exp.__strtex__(), "$3 e^{- t}$")
decay = 1
intensity = 1
hawkes_kernel_exp = HawkesKernelExp(intensity, decay)
self.assertEqual(hawkes_kernel_exp.__strtex__(), "$e^{-t}$")
def test_hawkes_negative_intensity_fail(self):
"""...Test simulation with negative kernel without threshold_negative_intensity
"""
run_time = 40
hawkes = SimuHawkes(n_nodes=1, end_time=run_time, verbose=False,
seed=1398)
kernel = HawkesKernelExp(-1.3, .8)
hawkes.set_kernel(0, 0, kernel)
hawkes.set_baseline(0, 0.3)
msg = 'Simulation stopped because intensity went negative ' \
'\(you could call ``threshold_negative_intensity`` to allow it\)'
with self.assertRaisesRegex(RuntimeError, msg):
hawkes.simulate()
def setUp(self):
np.random.seed(28374)
self.kernels = np.array([
[HawkesKernel0(), HawkesKernelExp(0.1, 3)],
[HawkesKernelPowerLaw(0.2, 4, 2),
HawkesKernelSumExp([0.1, 0.4], [3, 4])]
])
t_values = np.linspace(0, 10, 10)
y_values = np.maximum(0.5 + np.sin(t_values), 0)
self.time_func_kernel = HawkesKernelTimeFunc(t_values=t_values,
y_values=y_values)
self.baseline = np.random.rand(2)
def test_simu_hawkes_force_simulation(self):
"""...Test force_simulation parameter of SimuHawkes
"""
diverging_kernel = [[HawkesKernelExp(2, 3)]]
hawkes = SimuHawkes(kernels=diverging_kernel, baseline=[1],
verbose=False)
hawkes.end_time = 10
msg = '^Simulation not launched as this Hawkes process is not ' \
'stable \(spectral radius of 2\). You can use ' \
'force_simulation parameter if you really want to simulate it$'
with self.assertRaisesRegex(ValueError, msg):
hawkes.simulate()
msg = "^This process has already be simulated until time 0.000000$"
with self.assertWarnsRegex(UserWarning, msg):
hawkes.end_time = 0
hawkes.force_simulation = True
hawkes.simulate()
def generate_points(n_processes, mu, alpha, decay, window, seed, dt=0.01):
"""
Generates points of an marked Hawkes processes using the tick library
"""
hawkes = SimuHawkes(n_nodes=n_processes,
end_time=window,
verbose=False,
seed=seed)
for i in range(n_processes):
for j in range(n_processes):
hawkes.set_kernel(i=i,
j=j,
kernel=HawkesKernelExp(intensity=alpha[i][j] /
decay[i][j],
decay=decay[i][j]))
hawkes.set_baseline(i, mu[i])
hawkes.track_intensity(dt)
hawkes.simulate()
return hawkes.timestamps
def test_hawkes_negative_intensity(self):
"""...Test simulation with negative kernel
"""
run_time = 40
hawkes = SimuHawkes(n_nodes=1, end_time=run_time, verbose=False,
seed=1398)
kernel = HawkesKernelExp(-1.3, .8)
hawkes.set_kernel(0, 0, kernel)
hawkes.set_baseline(0, 0.3)
hawkes.threshold_negative_intensity()
dt = 0.1
hawkes.track_intensity(dt)
hawkes.simulate()
self.assertAlmostEqual(hawkes.tracked_intensity[0].min(), 0)
self.assertAlmostEqual(hawkes.tracked_intensity[0].max(),
hawkes.baseline[0])
self.assertGreater(hawkes.n_total_jumps, 1)
from tick.plot import plot_hawkes_kernels
from tick.hawkes import (SimuHawkes, SimuHawkesMulti, HawkesKernelExp,
HawkesKernelTimeFunc, HawkesKernelPowerLaw,
HawkesKernel0, HawkesSumGaussians)
end_time = 1000
n_nodes = 2
n_realizations = 10
n_gaussians = 5
timestamps_list = []
kernel_timefunction = HawkesKernelTimeFunc(
t_values=np.array([0., .7, 2.5, 3., 4.]),
y_values=np.array([.3, .03, .03, .2, 0.]))
kernels = [[HawkesKernelExp(.2, 2.),
HawkesKernelPowerLaw(.2, .5, 1.3)],
[HawkesKernel0(), kernel_timefunction]]
hawkes = SimuHawkes(baseline=[.5, .2],
kernels=kernels,
end_time=end_time,
verbose=False,
seed=1039)
multi = SimuHawkesMulti(hawkes, n_simulations=n_realizations)
multi.simulate()
learner = HawkesSumGaussians(n_gaussians, max_iter=10)
learner.fit(multi.timestamps)
import numpy as np
import matplotlib.pyplot as plt
from tick.hawkes import HawkesKernel0, HawkesKernelExp, HawkesKernelPowerLaw, \
HawkesKernelTimeFunc
kernel_0 = HawkesKernel0()
kernel_exp = HawkesKernelExp(.7, 1.3)
kernel_pl = HawkesKernelPowerLaw(.1, .2, 0.7)
t_values = np.array([0, 1, 1.5, 1.8, 2.7])
y_values = np.array([0, .6, .34, .2, .1])
kernel_tf = HawkesKernelTimeFunc(t_values=t_values, y_values=y_values)
kernels = [[kernel_0, kernel_exp], [kernel_pl, kernel_tf]]
fig, ax = plt.subplots(2, 2, sharex=True, sharey=True, figsize=(10, 4))
t_values = np.linspace(0, 3, 100)
for i in range(2):
for j in range(2):
ax[i, j].plot(t_values, kernels[i][j].get_values(t_values),
label=kernels[i][j])
ax[i, j].legend()
plt.show()
def setUp(self):
self.decay = 2
self.intensity = 3
self.hawkes_kernel_exp = HawkesKernelExp(self.intensity, self.decay)
inter_mode=TimeFunction.InterConstRight,
dt=0.1)
kernel1 = HawkesKernelTimeFunc(tf1)
t_values2 = np.linspace(0, 4, 20)
y_values2 = np.maximum(0., np.sin(t_values2) / 4)
tf2 = TimeFunction([t_values2, y_values2])
kernel2 = HawkesKernelTimeFunc(tf2)
baseline = np.array([0.1, 0.3])
hawkes = SimuHawkes(baseline=baseline,
end_time=run_time,
verbose=False,
seed=2334)
hawkes.set_kernel(0, 0, kernel1)
hawkes.set_kernel(0, 1, HawkesKernelExp(.5, .7))
hawkes.set_kernel(1, 1, kernel2)
hawkes.simulate()
em = HawkesEM(4, kernel_size=16, n_threads=8, verbose=False, tol=1e-3)
em.fit(hawkes.timestamps)
fig = plot_hawkes_kernels(em, hawkes=hawkes, show=False)
for ax in fig.axes:
ax.set_ylim([0, 1])
plt.show()
def test_HawkesEM():
print('\n##############################')
print('\nstarting: test_HawkesEM()\n')
run_time = 30000
t_values1 = np.array([0, 1, 1.5, 2., 3.5], dtype=float)
y_values1 = np.array([0, 0.2, 0, 0.1, 0.], dtype=float)
tf1 = TimeFunction([t_values1, y_values1],
inter_mode=TimeFunction.InterConstRight,
dt=0.1)
kernel1 = HawkesKernelTimeFunc(tf1)
t_values2 = np.linspace(0, 4, 20)
y_values2 = np.maximum(0., np.sin(t_values2) / 4)
tf2 = TimeFunction([t_values2, y_values2])
kernel2 = HawkesKernelTimeFunc(tf2)
baseline = np.array([0.1, 0.3])
### ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ###
realizations = list()
for i in range(0, 1000):
print('')
temp_seed = int(1000 + 1000 * random.random())
print('i = ' + str(i) + ', temp_seed = ' + str(temp_seed))
hawkes = SimuHawkes(baseline=baseline,
end_time=run_time,
verbose=False,
seed=temp_seed)
hawkes.set_kernel(0, 0, kernel1)
hawkes.set_kernel(0, 1, HawkesKernelExp(.5, .7))
hawkes.set_kernel(1, 1, kernel2)
hawkes.simulate()
temp_realization = hawkes.timestamps
print('i = ' + str(i) + ', ' + 'event counts = (' +
str(len(temp_realization[0])) + ',' +
str(len(temp_realization[1])) + ')')
print(temp_realization)
realizations.append(temp_realization)
### ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ###
em = HawkesEM(4, kernel_size=16, n_threads=8, verbose=False, tol=1e-3)
em.fit(events=realizations)
fig = plot_hawkes_kernels(em, hawkes=hawkes, show=False)
outputFILE = 'test-HawkesEM.png'
for ax in fig.axes:
ax.set_ylim([0, 1])
plt.savefig(fname=outputFILE, bbox_inches='tight', pad_inches=0.2)
### ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ###
print('\nexitng: test_HawkesEM()')
print('\n##############################')
return (None)
t_values = np.array([0, 1, 1.5], dtype=float)
y_values = np.array([0, .2, 0], dtype=float)
tf1 = TimeFunction([t_values, y_values],
inter_mode=TimeFunction.InterConstRight,
dt=0.1)
kernel_1 = HawkesKernelTimeFunc(tf1)
t_values = np.array([0, .1, 2], dtype=float)
y_values = np.array([0, .4, -0.2], dtype=float)
tf2 = TimeFunction([t_values, y_values],
inter_mode=TimeFunction.InterLinear,
dt=0.1)
kernel_2 = HawkesKernelTimeFunc(tf2)
hawkes = SimuHawkes(kernels=[[kernel_1, kernel_1],
[HawkesKernelExp(.07, 4), kernel_2]],
baseline=[1.5, 1.5],
verbose=False,
seed=23983)
run_time = 40
dt = 0.01
hawkes.track_intensity(dt)
hawkes.end_time = run_time
hawkes.simulate()
fig, ax = plt.subplots(hawkes.n_nodes, 1, figsize=(14, 8))
plot_point_process(hawkes, t_max=20, ax=ax)
plt.show()
initparam = [np.log(0.5), 0, 0, 0, 0]
nTrain = 100
nTest = 1000
# Kernel Param -------------------------------------------
mu = 1.
param = [None] * Kclass
param[0] = np.array([mu, 0.7, 1.3])
param[1] = np.array([mu, 0.2, 3])
kernelSim = [None] * Kclass
kernelBayes = [None] * Kclass
for k in range(Kclass):
kernelSim[k] = HawkesKernelExp(param[k][1], param[k][2])
kernelBayes[k] = kernelSim[k].get_values
##############################################################
# Risks computation -------------------------------------------
##############################################################
# TrainSample
listJumptimesTrain, Ytrain = simulHawkesTraj(Klass=Kclass,
mu=mu,
Tmax=Tmax,
nSample=nTrain,
kernelSim=kernelSim)
# TestSample
listJumptimesTest, Ytest = simulHawkesTraj(Klass=Kclass,
mu=mu,