def fit_ct_network_hawkes_gibbs(S,
S_test,
dt,
dt_max,
output_path,
model_args={},
standard_model=None,
N_samples=100,
time_limit=8 * 60 * 60):
K = S.shape[1]
S_ct, C_ct, T = convert_discrete_to_continuous(S, dt)
S_test_ct, C_test_ct, T_test = convert_discrete_to_continuous(S_test, dt)
# Check for existing Gibbs results
if os.path.exists(output_path):
with gzip.open(output_path, 'r') as f:
print("Loading Gibbs results from ", output_path)
results = pickle.load(f)
else:
print(
"Fitting the data with a continuous time network Hawkes model using Gibbs sampling"
)
test_model = \
ContinuousTimeNetworkHawkesModel(K, dt_max=dt_max, **model_args)
test_model.add_data(S_ct, C_ct, T)
# Initialize with the standard model parameters
if standard_model is not None:
test_model.initialize_with_standard_model(standard_model)
# Gibbs sample
samples = []
lps = [test_model.log_probability()]
hlls = [
test_model.heldout_log_likelihood(S_test_ct, C_test_ct, T_test)
]
times = [0]
for _ in progprint_xrange(N_samples, perline=25):
# Update the model
tic = time.time()
test_model.resample_model()
times.append(time.time() - tic)
samples.append(copy.deepcopy(test_model.get_parameters()))
# Compute log probability and heldout log likelihood
# lps.append(test_model.log_probability())
hlls.append(
test_model.heldout_log_likelihood(S_test_ct, C_test_ct,
T_test))
# # Save this sample
# with open(output_path + ".gibbs.itr%04d.pkl" % itr, 'w') as f:
# cPickle.dump(samples[-1], f, protocol=-1)
# Check if time limit has been exceeded
if np.sum(times) > time_limit:
break
# Get cumulative timestamps
timestamps = np.cumsum(times)
lps = np.array(lps)
hlls = np.array(hlls)
# Make results object
results = Results(samples, timestamps, lps, hlls)
# Save the Gibbs samples
with gzip.open(output_path, 'w') as f:
print("Saving Gibbs samples to ", output_path)
pickle.dump(results, f, protocol=-1)
return results
### Fit the models
N_samples = 1000
results = []
results_dir = os.path.join("results", "hippocampus", "run002")
for network, name in zip(networks, names):
results_file = os.path.join(results_dir, "%s.pkl" % name)
if os.path.exists(results_file):
with open(results_file, "r") as f:
result = pickle.load(f)
results.append(result)
continue
print("Fitting model with ", name, " network.")
model = ContinuousTimeNetworkHawkesModel(
K, dt_max=1.,
network=network)
model.add_data(S_train, C_train, T_train)
model.resample_model()
# Add the test data and then remove it. That way we can
# efficiently compute its predictive log likelihood
model.add_data(S_test, C_test, T - T_train)
test_data = model.data_list.pop()
### Fit the model
lls = [model.log_likelihood()]
plls = [model.log_likelihood(test_data)]
Weffs = []
Ps = []
def fit_ct_network_hawkes_gibbs(S,
K,
C,
dt,
dt_max,
output_path,
standard_model=None):
# Check for existing Gibbs results
if os.path.exists(output_path + ".gibbs.pkl"):
with open(output_path + ".gibbs.pkl", 'r') as f:
print "Loading Gibbs results from ", (output_path + ".gibbs.pkl")
(samples, timestamps) = cPickle.load(f)
else:
print "Fitting the data with a network Hawkes model using Gibbs sampling"
S_ct, C_ct, T = convert_discrete_to_continuous(S, dt)
# Set the network prior such that E[W] ~= 0.01
# W ~ Gamma(kappa, v) for kappa = 1.25 => v ~ 125
# v ~ Gamma(alpha, beta) for alpha = 10, beta = 10 / 125
E_W = 0.2
kappa = 10.
E_v = kappa / E_W
alpha = 5.
beta = alpha / E_v
network_hypers = {
'C': 1,
"c": np.zeros(K).astype(np.int),
"p": 0.25,
"v": E_v,
# 'kappa': kappa,
# 'alpha': alpha, 'beta': beta,
# 'p': 0.1,
'allow_self_connections': False
}
test_model = \
ContinuousTimeNetworkHawkesModel(K, dt_max=dt_max,
network_hypers=network_hypers)
test_model.add_data(S_ct, C_ct, T)
# Initialize with the standard model parameters
if standard_model is not None:
test_model.initialize_with_standard_model(standard_model)
plt.ion()
im = plot_network(test_model.weight_model.A,
test_model.weight_model.W,
vmax=0.025)
plt.pause(0.001)
# Gibbs sample
N_samples = 100
samples = []
lps = [test_model.log_probability()]
timestamps = []
for itr in xrange(N_samples):
if itr % 1 == 0:
print "Iteration ", itr, "\tLL: ", lps[-1]
im.set_data(test_model.weight_model.W_effective)
plt.pause(0.001)
# lps.append(test_model.log_probability())
lps.append(test_model.log_probability())
samples.append(test_model.resample_and_copy())
timestamps.append(time.clock())
print test_model.network.p
# Save this sample
with open(output_path + ".gibbs.itr%04d.pkl" % itr, 'w') as f:
cPickle.dump(samples[-1], f, protocol=-1)
# Save the Gibbs samples
with open(output_path + ".gibbs.pkl", 'w') as f:
print "Saving Gibbs samples to ", (output_path + ".gibbs.pkl")
cPickle.dump((samples, timestamps), f, protocol=-1)
return samples, timestamps
def test_geweke():
"""
Create a discrete time Hawkes model and generate from it.
:return:
"""
K = 1
T = 50.0
dt = 1.0
dt_max = 3.0
# network_hypers = {'C': 1, 'p': 0.5, 'kappa': 3.0, 'alpha': 3.0, 'beta': 1.0/20.0}
network_hypers = {'c': np.zeros(K, dtype=np.int), 'p': 0.5, 'kappa': 10.0, 'v': 10*3.0}
bkgd_hypers = {"alpha": 1., "beta": 10.}
model = ContinuousTimeNetworkHawkesModel(K=K, dt_max=dt_max,
network_hypers=network_hypers)
model.generate(T=T)
# Gibbs sample and then generate new data
N_samples = 1000
samples = []
lps = []
for itr in progprint_xrange(N_samples, perline=50):
# Resample the model
model.resample_model()
samples.append(model.copy_sample())
lps.append(model.log_likelihood())
# 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])
mu_samples = np.array([s.impulse_model.mu for s in samples])
tau_samples = np.array([s.impulse_model.tau for s in samples])
lambda0_samples = np.array([s.bias_model.lambda0 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)
mu_mean = mu_samples[offset:, ...].mean(axis=0)
tau_mean = tau_samples[offset:, ...].mean(axis=0)
lambda0_mean = lambda0_samples[offset:, ...].mean(axis=0)
print("A mean: ", A_mean)
print("W mean: ", W_mean)
print("mu mean: ", mu_mean)
print("tau mean: ", tau_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=50, 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])
# p_W1 = betaprime(model.network.kappa, model.network.alpha, scale=model.network.beta)
p_W1 = gamma(model.network.kappa, scale=1./model.network.v[0,0])
if np.sum(Aeq1) > 0:
_, bins, _ = plt.hist(W_samples[Aeq1,0,0], bins=50, 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)')
# Plot the histogram of impulse precisions
plt.figure()
p_tau = gamma(model.impulse_model.alpha_0, scale=1./model.impulse_model.beta_0)
_, bins, _ = plt.hist(tau_samples[:,0,0], bins=50, alpha=0.5, normed=True)
bincenters = 0.5*(bins[1:]+bins[:-1])
plt.plot(bincenters, p_tau.pdf(bincenters), 'r--', linewidth=1)
plt.xlabel('tau')
plt.ylabel('p(tau)')
# Plot the histogram of impulse means
plt.figure()
p_mu = t(df=2*model.impulse_model.alpha_0,
loc=model.impulse_model.mu_0,
scale=np.sqrt(model.impulse_model.beta_0/(model.impulse_model.alpha_0*model.impulse_model.lmbda_0)))
_, bins, _ = plt.hist(mu_samples[:,0,0], bins=50, alpha=0.5, normed=True)
bincenters = 0.5*(bins[1:]+bins[:-1])
plt.plot(bincenters, p_mu.pdf(bincenters), 'r--', linewidth=1)
plt.xlabel('mu')
plt.ylabel('p(mu)')
plt.show()
