def demo(K=3, T=1000, dt_max=20, p=0.25):
"""
:param K: Number of nodes
:param T: Number of time bins to simulate
:param dt_max: Number of future time bins an event can influence
:param p: Sparsity of network
:return:
"""
###########################################################
# Generate synthetic data
###########################################################
network_hypers = {"p": p, "allow_self_connections": False}
true_model = DiscreteTimeNetworkHawkesModelSpikeAndSlab(
K=K, dt_max=dt_max,
network_hypers=network_hypers)
assert true_model.check_stability()
# Sample from the true model
S,R = true_model.generate(T=T, keep=True, print_interval=50)
plt.ion()
true_figure, _ = true_model.plot(color="#377eb8", T_slice=(0,100))
###########################################################
# Create a test spike and slab model
###########################################################
test_model = DiscreteTimeNetworkHawkesModelSpikeAndSlab(
K=K, dt_max=dt_max,
network_hypers=network_hypers)
test_model.add_data(S)
# Initialize plots
test_figure, test_handles = test_model.plot(color="#e41a1c", T_slice=(0,100))
###########################################################
# Fit the test model with Gibbs sampling
###########################################################
N_samples = 100
samples = []
lps = []
for itr in range(N_samples):
print("Gibbs iteration ", itr)
test_model.resample_model()
lps.append(test_model.log_probability())
samples.append(test_model.copy_sample())
# Update plots
test_model.plot(handles=test_handles)
###########################################################
# Analyze the samples
###########################################################
analyze_samples(true_model, samples, lps)
def demo(K=3, T=1000, dt_max=20, p=0.25):
"""
:param K: Number of nodes
:param T: Number of time bins to simulate
:param dt_max: Number of future time bins an event can influence
:param p: Sparsity of network
:return:
"""
###########################################################
# Generate synthetic data
###########################################################
network_hypers = {"p": p, "allow_self_connections": False}
true_model = DiscreteTimeNetworkHawkesModelSpikeAndSlab(
K=K, dt_max=dt_max,
network_hypers=network_hypers)
assert true_model.check_stability()
# Sample from the true model
S,R = true_model.generate(T=T, keep=True, print_interval=50)
plt.ion()
true_figure, _ = true_model.plot(color="#377eb8", T_slice=(0,100))
###########################################################
# Create a test spike and slab model
###########################################################
test_model = DiscreteTimeNetworkHawkesModelSpikeAndSlab(
K=K, dt_max=dt_max,
network_hypers=network_hypers)
test_model.add_data(S)
# Initialize plots
test_figure, test_handles = test_model.plot(color="#e41a1c", T_slice=(0,100))
###########################################################
# Fit the test model with Gibbs sampling
###########################################################
N_samples = 100
samples = []
lps = []
for itr in xrange(N_samples):
print "Gibbs iteration ", itr
test_model.resample_model()
lps.append(test_model.log_probability())
samples.append(test_model.copy_sample())
# Update plots
test_model.plot(handles=test_handles)
###########################################################
# Analyze the samples
###########################################################
analyze_samples(true_model, samples, lps)
def demo(K=3, T=1000, dt_max=20, p=0.25):
"""
:param K: Number of nodes
:param T: Number of time bins to simulate
:param dt_max: Number of future time bins an event can influence
:param p: Sparsity of network
:return:
"""
###########################################################
# Generate synthetic data
###########################################################
network = ErdosRenyiFixedSparsity(K, p, v=1., allow_self_connections=False)
bkgd_hypers = {"alpha": 1.0, "beta": 20.0}
true_model = DiscreteTimeNetworkHawkesModelSpikeAndSlab(
K=K, dt_max=dt_max, bkgd_hypers=bkgd_hypers, network=network)
A_true = np.zeros((K, K))
A_true[0, 1] = A_true[0, 2] = 1
W_true = np.zeros((K, K))
W_true[0, 1] = W_true[0, 2] = 1.0
true_model.weight_model.A = A_true
true_model.weight_model.W = W_true
true_model.bias_model.lambda0[0] = 0.2
assert true_model.check_stability()
# Sample from the true model
S, R = true_model.generate(T=T, keep=True, print_interval=50)
plt.ion()
true_figure, _ = true_model.plot(color="#377eb8", T_slice=(0, 100))
# Save the true figure
true_figure.savefig("gifs/true.gif")
###########################################################
# Create a test spike and slab model
###########################################################
test_model = DiscreteTimeNetworkHawkesModelSpikeAndSlab(K=K,
dt_max=dt_max,
network=network)
test_model.add_data(S)
# Initialize plots
test_figure, test_handles = test_model.plot(color="#e41a1c",
T_slice=(0, 100))
test_figure.savefig("gifs/test0.gif")
###########################################################
# Fit the test model with Gibbs sampling
###########################################################
N_samples = 100
samples = []
lps = []
for itr in xrange(N_samples):
print "Gibbs iteration ", itr
test_model.resample_model()
lps.append(test_model.log_probability())
samples.append(test_model.copy_sample())
# Update plots
test_model.plot(handles=test_handles)
test_figure.savefig("gifs/test%d.gif" % (itr + 1))
def demo(seed=None):
"""
Create a discrete time Hawkes model and generate from it.
: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 = pickle.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 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_network = StochasticBlockModel(K=K, **network_hypers)
test_model = DiscreteTimeNetworkHawkesModelSpikeAndSlab(
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=test_network)
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 = 50
samples = []
lps = []
# plls = []
for itr in range(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)
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': 1,
'p': 0.5,
'kappa': 3.0,
'alpha': 3.0,
'beta': 1.0 / 20.0
}
model = DiscreteTimeNetworkHawkesModelSpikeAndSlab(
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()
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])
# The marginal distribution of W under a gamma prior on the scale
# is a beta prime distribution
p_W1 = betaprime(model.network.kappa,
model.network.alpha,
scale=model.network.beta)
_, 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)')
# 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)
# Plot the histogram of weight scale
plt.figure()
for c1 in range(model.C):
for c2 in range(model.C):
plt.subplot(model.C, model.C, 1 + c1 * model.C + c2)
p_v = gamma(model.network.alpha, scale=1. / model.network.beta)
_, bins, _ = plt.hist(v_samples[:, c1, c2],
bins=20,
alpha=0.5,
normed=True)
bincenters = 0.5 * (bins[1:] + bins[:-1])
plt.plot(bincenters, p_v.pdf(bincenters), 'r--', linewidth=1)
plt.xlabel('v_{%d,%d}' % (c1, c2))
plt.ylabel('p(v)')
plt.show()
# 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 = DiscreteTimeNetworkHawkesModelSpikeAndSlab(K=K, dt=dt, dt_max=dt_max,
weight_hypers={"parallel_resampling": False},
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()
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])
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)
def demo(seed=None):
"""
Create a discrete time Hawkes model and generate from it.
: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 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_network = StochasticBlockModel(K=K, **network_hypers)
test_model = DiscreteTimeNetworkHawkesModelSpikeAndSlab(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=test_network)
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 = 50
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)
def demo(K=3, T=1000, dt_max=20, p=0.25):
"""
:param K: Number of nodes
:param T: Number of time bins to simulate
:param dt_max: Number of future time bins an event can influence
:param p: Sparsity of network
:return:
"""
###########################################################
# Generate synthetic data
###########################################################
network = ErdosRenyiFixedSparsity(K, p, v=1., allow_self_connections=False)
bkgd_hypers = {"alpha": 1.0, "beta": 20.0}
true_model = DiscreteTimeNetworkHawkesModelSpikeAndSlab(
K=K, dt_max=dt_max, bkgd_hypers=bkgd_hypers, network=network)
A_true = np.zeros((K,K))
A_true[0,1] = A_true[0,2] = 1
W_true = np.zeros((K,K))
W_true[0,1] = W_true[0,2] = 1.0
true_model.weight_model.A = A_true
true_model.weight_model.W = W_true
true_model.bias_model.lambda0[0] = 0.2
assert true_model.check_stability()
# Sample from the true model
S,R = true_model.generate(T=T, keep=True, print_interval=50)
plt.ion()
true_figure, _ = true_model.plot(color="#377eb8", T_slice=(0,100))
# Save the true figure
true_figure.savefig("gifs/true.gif")
###########################################################
# Create a test spike and slab model
###########################################################
test_model = DiscreteTimeNetworkHawkesModelSpikeAndSlab(
K=K, dt_max=dt_max, network=network)
test_model.add_data(S)
# Initialize plots
test_figure, test_handles = test_model.plot(color="#e41a1c", T_slice=(0,100))
test_figure.savefig("gifs/test0.gif")
###########################################################
# Fit the test model with Gibbs sampling
###########################################################
N_samples = 100
samples = []
lps = []
for itr in xrange(N_samples):
print "Gibbs iteration ", itr
test_model.resample_model()
lps.append(test_model.log_probability())
samples.append(test_model.copy_sample())
# Update plots
test_model.plot(handles=test_handles)
test_figure.savefig("gifs/test%d.gif" % (itr+1))
model = DiscreteTimeNetworkHawkesModelSpikeAndSlab(
K=K,
dt=dt,
dt_max=dt_max,
weight_hypers={"parallel_resampling": False},
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()
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])
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 = 0
A_mean = A_samples[offset:, ...].mean(axis=0)