def test_gradients():
K = 1
B = 3
T = 100
dt = 1.0
true_model = DiscreteTimeNetworkHawkesModelGammaMixture(K=K, B=B, dt=dt)
S, R = true_model.generate(T=T)
# Test with a standard Hawkes model
test_model = DiscreteTimeStandardHawkesModel(K=K, B=B, dt=dt)
test_model.add_data(S)
# Check gradients with the initial parameters
def objective(x):
test_model.weights[0, :] = np.exp(x)
return test_model.log_likelihood()
def gradient(x):
test_model.weights[0, :] = np.exp(x)
return test_model.compute_gradient(0)
print "Checking initial gradient: "
print gradient(np.log(test_model.weights[0, :]))
check_grad(objective, gradient, np.log(test_model.weights[0, :]))
print "Checking gradient at true model parameters: "
test_model.initialize_with_gibbs_model(true_model)
print gradient(np.log(test_model.weights[0, :]))
check_grad(objective, gradient, np.log(test_model.weights[0, :]))
def test_gradients():
K = 1
B = 3
T = 100
dt = 1.0
true_model = DiscreteTimeNetworkHawkesModelGammaMixture(K=K, B=B, dt=dt)
S,R = true_model.generate(T=T)
# Test with a standard Hawkes model
test_model = DiscreteTimeStandardHawkesModel(K=K, B=B, dt=dt)
test_model.add_data(S)
# Check gradients with the initial parameters
def objective(x):
test_model.weights[0,:] = np.exp(x)
return test_model.log_likelihood()
def gradient(x):
test_model.weights[0,:] = np.exp(x)
return test_model.compute_gradient(0)
print("Checking initial gradient: ")
print(gradient(np.log(test_model.weights[0,:])))
check_grad(objective, gradient,
np.log(test_model.weights[0,:]))
print("Checking gradient at true model parameters: ")
test_model.initialize_with_gibbs_model(true_model)
print(gradient(np.log(test_model.weights[0,:])))
check_grad(objective, gradient,
np.log(test_model.weights[0,:]))
if __name__ == "__main__":
"""
Create a discrete time Hawkes model and generate from it.
:return:
"""
T = 50
dt = 1.0
dt_max = 3.0
network_hypers = {'c': np.array([0], dtype=np.int),
'p': 0.5, 'kappa': 3.0, 'v': 15.0}
weight_hypers = {"kappa_0": 3.0, "nu_0": 15.0}
model = DiscreteTimeNetworkHawkesModelGammaMixture(K=1, dt=dt, dt_max=dt_max,
weight_hypers=weight_hypers,
network_hypers=network_hypers)
model.generate(T=T)
# Gibbs sample and then generate new data
N_samples = 10000
samples = []
lps = []
for itr in progprint_xrange(N_samples, perline=50):
# Resample the model
model.resample_model(resample_network=False)
samples.append(model.copy_sample())
lps.append(model.log_probability())
# Geweke step
model.data_list.pop()
model.generate(T=T)
dt = 1.0
dt_max = 3.0
network_hypers = {
'c': np.array([0], dtype=np.int),
'p': 0.5,
'kappa': 3.0,
'v': 15.0
}
weight_hypers = {"kappa_0": 3.0, "nu_0": 15.0}
model = DiscreteTimeNetworkHawkesModelGammaMixture(
K=1,
dt=dt,
dt_max=dt_max,
weight_hypers=weight_hypers,
network_hypers=network_hypers)
model.generate(T=T)
# Gibbs sample and then generate new data
N_samples = 10000
samples = []
lps = []
for itr in progprint_xrange(N_samples, perline=50):
# Resample the model
model.resample_model(resample_network=False)
samples.append(model.copy_sample())
lps.append(model.log_probability())
# Geweke step
model.data_list.pop()
model.generate(T=T)
def geweke_test():
"""
Create a discrete time Hawkes model and generate from it.
:return:
"""
T = 50
dt = 1.0
dt_max = 3.0
network_hypers = {
'c': np.array([0], dtype=np.int),
'p': 0.5,
'kappa': 3.0,
'v': 15.0
}
model = DiscreteTimeNetworkHawkesModelGammaMixture(
K=1, dt=dt, dt_max=dt_max, network_hypers=network_hypers)
model.generate(T=T)
# Gibbs sample and then generate new data
N_samples = 10000
samples = []
lps = []
for itr in xrange(N_samples):
if itr % 10 == 0:
print "Iteration: ", itr
# Resample the model
model.resample_model(resample_network=False)
samples.append(model.copy_sample())
lps.append(model.log_probability())
# Geweke step
model.data_list.pop()
model.generate(T=T)
# Compute sample statistics for second half of samples
A_samples = np.array([s.weight_model.A for s in samples])
W_samples = np.array([s.weight_model.W for s in samples])
g_samples = np.array([s.impulse_model.g for s in samples])
lambda0_samples = np.array([s.bias_model.lambda0 for s in samples])
c_samples = np.array([s.network.c for s in samples])
p_samples = np.array([s.network.p for s in samples])
v_samples = np.array([s.network.v for s in samples])
lps = np.array(lps)
offset = 0
A_mean = A_samples[offset:, ...].mean(axis=0)
W_mean = W_samples[offset:, ...].mean(axis=0)
g_mean = g_samples[offset:, ...].mean(axis=0)
lambda0_mean = lambda0_samples[offset:, ...].mean(axis=0)
print "A mean: ", A_mean
print "W mean: ", W_mean
print "g mean: ", g_mean
print "lambda0 mean: ", lambda0_mean
# Plot the log probability over iterations
plt.figure()
plt.plot(np.arange(N_samples), lps)
plt.xlabel("Iteration")
plt.ylabel("Log probability")
# Plot the histogram of bias samples
plt.figure()
p_lmbda0 = gamma(model.bias_model.alpha, scale=1. / model.bias_model.beta)
_, bins, _ = plt.hist(lambda0_samples[:, 0],
bins=20,
alpha=0.5,
normed=True)
bincenters = 0.5 * (bins[1:] + bins[:-1])
plt.plot(bincenters, p_lmbda0.pdf(bincenters), 'r--', linewidth=1)
plt.xlabel('lam0')
plt.ylabel('p(lam0)')
print "Expected p(A): ", model.network.P
print "Empirical p(A): ", A_samples.mean(axis=0)
# Plot the histogram of weight samples
plt.figure()
Aeq1 = A_samples[:, 0, 0] == 1
p_W1 = gamma(model.network.kappa, scale=1. / model.network.v[0, 0])
_, bins, _ = plt.hist(W_samples[Aeq1, 0, 0],
bins=20,
alpha=0.5,
normed=True)
bincenters = 0.5 * (bins[1:] + bins[:-1])
plt.plot(bincenters, p_W1.pdf(bincenters), 'r--', linewidth=1)
plt.xlabel('W')
plt.ylabel('p(W | A=1)')
plt.figure()
Aeq0 = A_samples[:, 0, 0] == 0
p_W1 = gamma(model.weight_model.kappa_0,
scale=1. / model.weight_model.nu_0)
_, bins, _ = plt.hist(W_samples[Aeq0, 0, 0],
bins=20,
alpha=0.5,
normed=True)
bincenters = 0.5 * (bins[1:] + bins[:-1])
plt.plot(bincenters, p_W1.pdf(bincenters), 'r--', linewidth=1)
plt.xlabel('W')
plt.ylabel('p(W | A=0)')
# Plot the histogram of impulse samples
plt.figure()
for b in range(model.B):
plt.subplot(1, model.B, b + 1)
a = model.impulse_model.gamma[b]
b = model.impulse_model.gamma.sum() - a
p_beta11b = beta(a, b)
_, bins, _ = plt.hist(g_samples[:, 0, 0, b],
bins=20,
alpha=0.5,
normed=True)
bincenters = 0.5 * (bins[1:] + bins[:-1])
plt.plot(bincenters, p_beta11b.pdf(bincenters), 'r--', linewidth=1)
plt.xlabel('g_%d' % b)
plt.ylabel('p(g_%d)' % b)
plt.show()
