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)
# 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])
def demo(seed=None):
"""
Fit a weakly sparse
:return:
"""
if seed is None:
seed = np.random.randint(2**32)
print "Setting seed to ", seed
np.random.seed(seed)
###########################################################
# Load some example data.
# See data/synthetic/generate.py to create more.
###########################################################
data_path = os.path.join("data", "synthetic",
"synthetic_K20_C4_T10000.pkl.gz")
with gzip.open(data_path, 'r') as f:
S, true_model = cPickle.load(f)
T = S.shape[0]
K = true_model.K
B = true_model.B
dt = true_model.dt
dt_max = true_model.dt_max
###########################################################
# Initialize with MAP estimation on a standard Hawkes model
###########################################################
init_with_map = True
if init_with_map:
init_len = T
print "Initializing with BFGS on first ", init_len, " time bins."
init_model = DiscreteTimeStandardHawkesModel(K=K,
dt=dt,
dt_max=dt_max,
B=B,
alpha=1.0,
beta=1.0)
init_model.add_data(S[:init_len, :])
init_model.initialize_to_background_rate()
init_model.fit_with_bfgs()
else:
init_model = None
###########################################################
# Create a test weak spike-and-slab model
###########################################################
# Copy the network hypers.
# Give the test model p, but not c, v, or m
network_hypers = true_model.network_hypers.copy()
network_hypers['v'] = None
test_model = DiscreteTimeNetworkHawkesModelGammaMixture(
K=K,
dt=dt,
dt_max=dt_max,
B=B,
basis_hypers=true_model.basis_hypers,
bkgd_hypers=true_model.bkgd_hypers,
impulse_hypers=true_model.impulse_hypers,
weight_hypers=true_model.weight_hypers,
network_hypers=network_hypers)
test_model.add_data(S)
# Initialize with the standard model parameters
if init_model is not None:
test_model.initialize_with_standard_model(init_model)
###########################################################
# Fit the test model with Gibbs sampling
###########################################################
N_samples = 500
samples = []
lps = []
# plls = []
for itr in xrange(N_samples):
lps.append(test_model.log_probability())
# plls.append(test_model.heldout_log_likelihood(S_test, F=F_test))
samples.append(test_model.copy_sample())
print ""
print "Gibbs iteration ", itr
print "LP: ", lps[-1]
test_model.resample_model()
###########################################################
# Analyze the samples
###########################################################
N_samples = len(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])
lps = np.array(lps)
offset = N_samples // 2
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)
plt.figure()
plt.plot(np.arange(N_samples), lps, 'k')
plt.xlabel("Iteration")
plt.ylabel("Log probability")
plt.show()
# Compute the link prediction accuracy curves
auc_init = roc_auc_score(true_model.weight_model.A.ravel(),
init_model.W.ravel())
auc_A_mean = roc_auc_score(true_model.weight_model.A.ravel(),
A_mean.ravel())
auc_W_mean = roc_auc_score(true_model.weight_model.A.ravel(),
W_mean.ravel())
aucs = []
for A in A_samples:
aucs.append(roc_auc_score(true_model.weight_model.A.ravel(),
A.ravel()))
plt.figure()
plt.plot(aucs, '-r')
plt.plot(auc_A_mean * np.ones_like(aucs), '--r')
plt.plot(auc_W_mean * np.ones_like(aucs), '--b')
plt.plot(auc_init * np.ones_like(aucs), '--k')
plt.xlabel("Iteration")
plt.ylabel("Link prediction AUC")
plt.show()
plt.ioff()
plt.show()
test_model.add_data(S)
# Initialize with the standard model parameters
if init_model is not None:
test_model.initialize_with_standard_model(init_model)
###########################################################
# Fit the test model with Gibbs sampling
###########################################################
N_samples = 500
samples = []
lps = []
for itr in progprint_xrange(N_samples):
lps.append(test_model.log_probability())
samples.append(test_model.copy_sample())
test_model.resample_model()
###########################################################
# Analyze the samples
###########################################################
N_samples = len(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])
lps = np.array(lps)
offset = N_samples // 2
A_mean = A_samples[offset:, ...].mean(axis=0)
W_mean = W_samples[offset:, ...].mean(axis=0)
g_mean = g_samples[offset:, ...].mean(axis=0)
def demo(seed=None):
"""
Fit a weakly sparse
:return:
"""
if seed is None:
seed = np.random.randint(2**32)
print "Setting seed to ", seed
np.random.seed(seed)
###########################################################
# Load some example data.
# See data/synthetic/generate.py to create more.
###########################################################
data_path = os.path.join("data", "synthetic", "synthetic_K20_C4_T10000.pkl.gz")
with gzip.open(data_path, 'r') as f:
S, true_model = cPickle.load(f)
T = S.shape[0]
K = true_model.K
B = true_model.B
dt = true_model.dt
dt_max = true_model.dt_max
###########################################################
# Initialize with MAP estimation on a standard Hawkes model
###########################################################
init_with_map = True
if init_with_map:
init_len = T
print "Initializing with BFGS on first ", init_len, " time bins."
init_model = DiscreteTimeStandardHawkesModel(K=K, dt=dt, dt_max=dt_max, B=B,
alpha=1.0, beta=1.0)
init_model.add_data(S[:init_len, :])
init_model.initialize_to_background_rate()
init_model.fit_with_bfgs()
else:
init_model = None
###########################################################
# Create a test weak spike-and-slab model
###########################################################
# Copy the network hypers.
# Give the test model p, but not c, v, or m
network_hypers = true_model.network_hypers.copy()
network_hypers['v'] = None
test_model = DiscreteTimeNetworkHawkesModelGammaMixture(K=K, dt=dt, dt_max=dt_max, B=B,
basis_hypers=true_model.basis_hypers,
bkgd_hypers=true_model.bkgd_hypers,
impulse_hypers=true_model.impulse_hypers,
weight_hypers=true_model.weight_hypers,
network_hypers=network_hypers)
test_model.add_data(S)
# Initialize with the standard model parameters
if init_model is not None:
test_model.initialize_with_standard_model(init_model)
###########################################################
# Fit the test model with Gibbs sampling
###########################################################
N_samples = 500
samples = []
lps = []
# plls = []
for itr in xrange(N_samples):
lps.append(test_model.log_probability())
# plls.append(test_model.heldout_log_likelihood(S_test, F=F_test))
samples.append(test_model.copy_sample())
print ""
print "Gibbs iteration ", itr
print "LP: ", lps[-1]
test_model.resample_model()
###########################################################
# Analyze the samples
###########################################################
N_samples = len(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])
lps = np.array(lps)
offset = N_samples // 2
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)
plt.figure()
plt.plot(np.arange(N_samples), lps, 'k')
plt.xlabel("Iteration")
plt.ylabel("Log probability")
plt.show()
# Compute the link prediction accuracy curves
auc_init = roc_auc_score(true_model.weight_model.A.ravel(),
init_model.W.ravel())
auc_A_mean = roc_auc_score(true_model.weight_model.A.ravel(),
A_mean.ravel())
auc_W_mean = roc_auc_score(true_model.weight_model.A.ravel(),
W_mean.ravel())
aucs = []
for A in A_samples:
aucs.append(roc_auc_score(true_model.weight_model.A.ravel(), A.ravel()))
plt.figure()
plt.plot(aucs, '-r')
plt.plot(auc_A_mean * np.ones_like(aucs), '--r')
plt.plot(auc_W_mean * np.ones_like(aucs), '--b')
plt.plot(auc_init * np.ones_like(aucs), '--k')
plt.xlabel("Iteration")
plt.ylabel("Link prediction AUC")
plt.show()
plt.ioff()
plt.show()
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)
# 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])
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()
# Initialize with the standard model parameters
if init_model is not None:
test_model.initialize_with_standard_model(init_model)
###########################################################
# Fit the test model with Gibbs sampling
###########################################################
N_samples = 500
samples = []
lps = []
for itr in progprint_xrange(N_samples):
lps.append(test_model.log_probability())
samples.append(test_model.copy_sample())
test_model.resample_model()
###########################################################
# Analyze the samples
###########################################################
N_samples = len(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])
lps = np.array(lps)
offset = N_samples // 2
A_mean = A_samples[offset:, ...].mean(axis=0)
W_mean = W_samples[offset:, ...].mean(axis=0)
g_mean = g_samples[offset:, ...].mean(axis=0)
def demo(seed=None):
"""
Fit a weakly sparse
:return:
"""
if seed is None:
seed = np.random.randint(2**32)
print "Setting seed to ", seed
np.random.seed(seed)
###########################################################
# Load some example data.
# See data/synthetic/generate.py to create more.
###########################################################
data_path = os.path.join("data", "synthetic",
"synthetic_K20_C4_T10000.pkl.gz")
with gzip.open(data_path, 'r') as f:
S, true_model = cPickle.load(f)
T = S.shape[0]
K = true_model.K
B = true_model.B
dt = true_model.dt
dt_max = true_model.dt_max
###########################################################
# Initialize with MAP estimation on a standard Hawkes model
###########################################################
init_with_map = True
if init_with_map:
init_len = T
print "Initializing with BFGS on first ", init_len, " time bins."
init_model = DiscreteTimeStandardHawkesModel(K=K,
dt=dt,
dt_max=dt_max,
B=B,
alpha=1.0,
beta=1.0)
init_model.add_data(S[:init_len, :])
init_model.initialize_to_background_rate()
init_model.fit_with_bfgs()
else:
init_model = None
###########################################################
# Create a test weak spike-and-slab model
###########################################################
# Copy the network hypers.
# Give the test model p, but not c, v, or m
network_hypers = true_model.network_hypers.copy()
network_hypers['c'] = None
network_hypers['v'] = None
network_hypers['m'] = None
test_model = DiscreteTimeNetworkHawkesModelGammaMixture(
K=K,
dt=dt,
dt_max=dt_max,
B=B,
basis_hypers=true_model.basis_hypers,
bkgd_hypers=true_model.bkgd_hypers,
impulse_hypers=true_model.impulse_hypers,
weight_hypers=true_model.weight_hypers,
network_hypers=network_hypers)
test_model.add_data(S)
# F_test = test_model.basis.convolve_with_basis(S_test)
# Initialize with the standard model parameters
if init_model is not None:
test_model.initialize_with_standard_model(init_model)
# Initialize plots
ln, im_net, im_clus = initialize_plots(true_model, test_model, S)
###########################################################
# Fit the test model with Gibbs sampling
###########################################################
N_samples = 500
samples = []
lps = []
# plls = []
for itr in xrange(N_samples):
lps.append(test_model.log_probability())
# plls.append(test_model.heldout_log_likelihood(S_test, F=F_test))
samples.append(test_model.copy_sample())
print ""
print "Gibbs iteration ", itr
print "LP: ", lps[-1]
test_model.resample_model()
# Update plot
if itr % 1 == 0:
update_plots(itr, test_model, S, ln, im_clus, im_net)
###########################################################
# Analyze the samples
###########################################################
analyze_samples(true_model, init_model, samples, lps)
