def sample_from_network_hawkes(C, K, T, dt, dt_max, B):
# Create a true model
p = 0.8 * np.eye(C)
v = 10.0 * np.eye(C) + 20.0 * (1 - np.eye(C))
c = (0.0 * (np.arange(K) < 10) + 1.0 * (np.arange(K) >= 10)).astype(np.int)
true_model = DiscreteTimeNetworkHawkesModelSpikeAndSlab(C=C,
K=K,
dt=dt,
dt_max=dt_max,
B=B,
c=c,
p=p,
v=v)
# Plot the true network
plt.ion()
plot_network(true_model.weight_model.A,
true_model.weight_model.W,
vmax=0.5)
# Sample from the true model
S, R = true_model.generate(T=T)
# Return the spike count matrix
return S, true_model
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 sample_from_network_hawkes(K, T, dt, dt_max, B):
# Create a true model
true_model = DiscreteTimeNetworkHawkesModelSpikeAndSlab(K=K, dt=dt, dt_max=dt_max, B=B,
network_hypers=dict(p=0.1))
# Plot the true network
plt.ion()
true_model.plot_network()
# Sample from the true model
S,R = true_model.generate(T=T)
# Return the spike count matrix
return S, true_model
def test_compute_rate():
K = 1
T = 100
dt = 1.0
true_model = DiscreteTimeNetworkHawkesModelSpikeAndSlab(K=K, dt=dt)
S, R = true_model.generate(T=T)
print "Expected number of events: ", np.trapz(R, dt * np.arange(T), axis=0)
print "Actual number of events: ", S.sum(axis=0)
print "Lambda0: ", true_model.bias_model.lambda0
print "W: ", true_model.weight_model.W
print ""
R_test = true_model.compute_rate()
assert np.allclose(R, R_test)
def test_generate_statistics():
K = 1
T = 100
dt = 1.0
true_model = DiscreteTimeNetworkHawkesModelSpikeAndSlab(K=K, dt=dt)
S, R = true_model.generate(T=T)
E_N = np.trapz(R, dt * np.arange(T), axis=0)
std_N = np.sqrt(E_N)
N = S.sum(axis=0)
assert np.all(N >= E_N - 3 * std_N), "N less than 3std below mean"
assert np.all(N <= E_N + 3 * std_N), "N more than 3std above mean"
print "Expected number of events: ", E_N
print "Actual number of events: ", S.sum(axis=0)
def generate_hawkes(edges):
"""
UNDER CONSTRUCTION. Will need the package pyhawkes. Generates firing times
of N individuals in a given network defined by edges.
"""
from pyhawkes.models import DiscreteTimeNetworkHawkesModelSpikeAndSlab
np.random.seed(1122334455)
# Create a simple random network with K nodes a sparsity level of p
# Each event induces impulse responses of length dt_max on connected nodes
a = set()
for edge in edges:
a.add(edge[0])
a.add(edge[1])
K = len(a)
p = 0.25
dt_max = 20
network_hypers = {"p": p, "allow_self_connections": False}
true_model = DiscreteTimeNetworkHawkesModelSpikeAndSlab(
K=K, dt_max=dt_max, network_hypers=network_hypers)
A2 = np.zeros((K, K))
for edge in edges:
A2[edge[0]][edge[1]] = 1.0
true_model.weight_model.A = A2
A3 = 0.5 * np.ones((K, K))
true_model.weight_model.W = A3
Tmax = 50000
S, R = true_model.generate(T=Tmax)
times = dict()
for idi in range(K):
for it in range(Tmax):
n = S[it][idi]
if n > 0:
if idi not in times.keys():
times[idi] = []
else:
times[idi].append(it)
ids = list(times.keys())
for idn in ids:
times[idn].sort()
return ids, times
def sample_from_network_hawkes(C, K, T, dt, B):
# Create a true model
p = 0.8 * np.eye(C)
v = 10.0 * np.eye(C) + 20.0 * (1-np.eye(C))
c = (0.0 * (np.arange(K) < 10) + 1.0 * (np.arange(K) >= 10)).astype(np.int)
true_model = DiscreteTimeNetworkHawkesModelSpikeAndSlab(C=C, K=K, dt=dt, B=B, c=c, p=p, v=v)
# Plot the true network
plt.ion()
plot_network(true_model.weight_model.A,
true_model.weight_model.W,
vmax=0.5)
# Sample from the true model
S,R = true_model.generate(T=T)
# Return the spike count matrix
return S, R, true_model
def test_compute_rate():
K = 1
T = 100
dt = 1.0
network_hypers = {'c': np.zeros(K, dtype=np.int), 'p': 1.0, 'kappa': 10.0, 'v': 10*5.0}
true_model = DiscreteTimeNetworkHawkesModelSpikeAndSlab(K=K, dt=dt,
network_hypers=network_hypers)
S,R = true_model.generate(T=T)
print "Expected number of events: ", np.trapz(R, dt * np.arange(T), axis=0)
print "Actual number of events: ", S.sum(axis=0)
print "Lambda0: ", true_model.bias_model.lambda0
print "W: ", true_model.weight_model.W
print ""
R_test = true_model.compute_rate()
assert np.allclose(R, R_test)
def test_generate_statistics():
K = 1
T = 100
dt = 1.0
network_hypers = {'c': np.zeros(K, dtype=np.int), 'p': 1.0, 'kappa': 10.0, 'v': 10*5.0}
true_model = DiscreteTimeNetworkHawkesModelSpikeAndSlab(K=K, dt=dt,
network_hypers=network_hypers)
S,R = true_model.generate(T=T)
E_N = np.trapz(R, dt * np.arange(T), axis=0)
std_N = np.sqrt(E_N)
N = S.sum(axis=0)
assert np.all(N >= E_N - 3*std_N), "N less than 3std below mean"
assert np.all(N <= E_N + 3*std_N), "N more than 3std above mean"
print "Expected number of events: ", E_N
print "Actual number of events: ", S.sum(axis=0)
def test_gibbs_sbm(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)
C = 2
K = 100
c = np.arange(C).repeat(np.ceil(K / float(C)))[:K]
T = 1000
dt = 1.0
B = 3
# Generate from a true model
true_p = np.random.rand(C, C) * 0.25
true_network = StochasticBlockModel(K, C, c=c, p=true_p, v=10.0)
true_model = \
DiscreteTimeNetworkHawkesModelSpikeAndSlab(
K=K, dt=dt, B=B, network=true_network)
S, R = true_model.generate(T)
# Plot the true network
plt.ion()
true_im = true_model.plot_adjacency_matrix()
plt.pause(0.001)
# Make a new model for inference
test_network = StochasticBlockModel(K, C, beta=1. / K)
test_model = \
DiscreteTimeNetworkHawkesModelSpikeAndSlab(
K=K, dt=dt, B=B, network=test_network)
test_model.add_data(S)
# Gibbs sample
N_samples = 100
c_samples = []
lps = []
for itr in progprint_xrange(N_samples):
c_samples.append(test_network.c.copy())
lps.append(test_model.log_probability())
# Resample the network only
test_model.network.resample(
(true_model.weight_model.A, true_model.weight_model.W))
c_samples = np.array(c_samples)
plt.ioff()
# Compute sample statistics for second half of samples
print("True c: ", true_model.network.c)
print("Test c: ", c_samples[-10:, :])
# Compute the adjusted mutual info score of the clusterings
amis = []
arss = []
for c in c_samples:
amis.append(adjusted_mutual_info_score(true_model.network.c, c))
arss.append(adjusted_rand_score(true_model.network.c, c))
plt.figure()
plt.plot(np.arange(N_samples), amis, '-r')
plt.plot(np.arange(N_samples), arss, '-b')
plt.xlabel("Iteration")
plt.ylabel("Clustering score")
plt.show()
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()
"""
Create a discrete time Hawkes model and generate from it.
:return:
"""
K = 1
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}
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)
def generate_synthetic_data(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)
# Create a true model
# Larger v (weight scale) implies smaller weights
T_test = 1000
# Debugging network:
# C = 1
# K = 4
# T = 1000
# dt = 1.0
# B = 3
# p = 0.5
# kappa = 3.0
# v = kappa * 5.0
# c = np.zeros(K, dtype=np.int)
# Small network:
# Seed: 1957629166
# C = 4
# K = 20
# T = 10000
# dt = 1.0
# B = 3
# kappa = 3.0
# p = 0.9 * np.eye(C) + 0.05 * (1-np.eye(C))
# v = kappa * (5.0 * np.eye(C) + 25.0 * (1-np.eye(C)))
# c = np.arange(C).repeat((K // C))
# Medium network:
# Seed: 2723361959
# C = 5
# K = 50
# T = 100000
# dt = 1.0
# B = 3
# kappa = 3.0
# p = 0.75 * np.eye(C) + 0.05 * (1-np.eye(C))
# v = kappa * (9 * np.eye(C) + 25.0 * (1-np.eye(C)))
# c = np.arange(C).repeat((K // C))
# Medium netowrk 2:
# Seed = 3848328624
# C = 5
# K = 50
# T = 100000
# dt = 1.0
# B = 3
# kappa = 2.0
# c = np.arange(C).repeat((K // C))
# p = 0.4 * np.eye(C) + 0.01 * (1-np.eye(C))
# v = kappa * (5 * np.eye(C) + 5.0 * (1-np.eye(C)))
# Medium netowrk, one cluster
# Seed: 3848328624
C = 1
K = 50
T = 100000
dt = 1.0
B = 3
p = 0.08
kappa = 3.0
v = kappa * 5.0
c = np.zeros(K, dtype=np.int)
# Large network:
# Seed = 2467634490
# C = 5
# K = 100
# T = 100000
# dt = 1.0
# B = 3
# kappa = 3.0
# p = 0.4 * np.eye(C) + 0.025 * (1-np.eye(C))
# v = kappa * (10 * np.eye(C) + 25.0 * (1-np.eye(C)))
# c = np.arange(C).repeat((K // C))
# Large network 2:
# Seed =
# C = 10
# K = 100
# T = 100000
# dt = 1.0
# B = 3
# kappa = 3.0
# p = 0.75 * np.eye(C) + 0.05 * (1-np.eye(C))
# v = kappa * (9 * np.eye(C) + 25.0 * (1-np.eye(C)))
# c = np.arange(C).repeat((K // C))
# Extra large network:
# Seed: 2327447870
# C = 20
# K = 1000
# T = 100000
# dt = 1.0
# B = 3
# kappa = 3.0
# p = 0.25 * np.eye(C) + 0.0025 * (1-np.eye(C))
# v = kappa * (15 * np.eye(C) + 30.0 * (1-np.eye(C)))
# c = np.arange(C).repeat((K // C))
# Create the model with these parameters
network_hypers = {'C': C, 'kappa': kappa, 'c': c, 'p': p, 'v': v}
# Create a simple network
from pyhawkes.internals.network import ErdosRenyiFixedSparsity
network = ErdosRenyiFixedSparsity(K, p, kappa, v=v)
true_model = DiscreteTimeNetworkHawkesModelSpikeAndSlab(K=K,
dt=dt,
B=B,
network=network)
assert true_model.check_stability()
# Plot the true network
plt.ion()
plot_network(true_model.weight_model.A, true_model.weight_model.W)
plt.pause(0.001)
# Sample from the true model
S, R = true_model.generate(T=T, keep=False, print_interval=50)
# Pickle and save the data
out_dir = os.path.join('data', "synthetic")
out_name = 'synthetic_K%d_C%d_T%d.pkl.gz' % (K, C, T)
out_path = os.path.join(out_dir, out_name)
with gzip.open(out_path, 'w') as f:
print("Saving output to ", out_path)
pickle.dump((S, true_model), f, protocol=-1)
# Sample test data
S_test, _ = true_model.generate(T=T_test, keep=False)
# Pickle and save the data
out_dir = os.path.join('data', "synthetic")
out_name = 'synthetic_test_K%d_C%d_T%d.pkl.gz' % (K, C, T_test)
out_path = os.path.join(out_dir, out_name)
with gzip.open(out_path, 'w') as f:
print("Saving output to ", out_path)
pickle.dump((S_test, true_model), f, protocol=-1)
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 = 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)
def test_gibbs_sbm(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)
C = 2
K = 100
c = np.arange(C).repeat(np.ceil(K/float(C)))[:K]
T = 1000
dt = 1.0
B = 3
# Generate from a true model
true_p = np.random.rand(C,C) * 0.25
true_network = StochasticBlockModel(K, C, c=c, p=true_p, v=10.0)
true_model = \
DiscreteTimeNetworkHawkesModelSpikeAndSlab(
K=K, dt=dt, B=B, network=true_network)
S,R = true_model.generate(T)
# Plot the true network
plt.ion()
true_im = true_model.plot_adjacency_matrix()
plt.pause(0.001)
# Make a new model for inference
test_network = StochasticBlockModel(K, C, beta=1./K)
test_model = \
DiscreteTimeNetworkHawkesModelSpikeAndSlab(
K=K, dt=dt, B=B, network=test_network)
test_model.add_data(S)
# Gibbs sample
N_samples = 100
c_samples = []
lps = []
for itr in progprint_xrange(N_samples):
c_samples.append(test_network.c.copy())
lps.append(test_model.log_probability())
# Resample the network only
test_model.network.resample((true_model.weight_model.A,
true_model.weight_model.W))
c_samples = np.array(c_samples)
plt.ioff()
# Compute sample statistics for second half of samples
print("True c: ", true_model.network.c)
print("Test c: ", c_samples[-10:, :])
# Compute the adjusted mutual info score of the clusterings
amis = []
arss = []
for c in c_samples:
amis.append(adjusted_mutual_info_score(true_model.network.c, c))
arss.append(adjusted_rand_score(true_model.network.c, c))
plt.figure()
plt.plot(np.arange(N_samples), amis, '-r')
plt.plot(np.arange(N_samples), arss, '-b')
plt.xlabel("Iteration")
plt.ylabel("Clustering score")
plt.show()
def demo(seed=None):
"""
Create a discrete time Hawkes model and generate from it.
:return:
"""
raise NotImplementedError("This example needs to be updated.")
if seed is None:
seed = np.random.randint(2**32)
print "Setting seed to ", seed
np.random.seed(seed)
C = 1
K = 10
T = 1000
dt = 1.0
B = 3
# Create a true model
p = 0.8 * np.eye(C)
v = 10.0 * np.eye(C) + 20.0 * (1-np.eye(C))
# m = 0.5 * np.ones(C)
c = (0.0 * (np.arange(K) < 10) + 1.0 * (np.arange(K) >= 10)).astype(np.int)
true_model = DiscreteTimeNetworkHawkesModelSpikeAndSlab(C=C, K=K, dt=dt, B=B, c=c, p=p, v=v)
# Plot the true network
plt.ion()
plot_network(true_model.weight_model.A,
true_model.weight_model.W,
vmax=0.5)
plt.pause(0.001)
# Sample from the true model
S,R = true_model.generate(T=T)
# Make a new model for inference
test_model = DiscreteTimeStandardHawkesModel(K=K, dt=dt, B=B, beta=1.0)
test_model.add_data(S)
# Plot the true and inferred firing rate
kplt = 0
plt.figure()
plt.plot(np.arange(T), R[:,kplt], '-k', lw=2)
plt.ion()
ln = plt.plot(np.arange(T), test_model.compute_rate(ks=kplt), '-r')[0]
plt.show()
# Gradient descent
N_steps = 10000
lls = []
for itr in xrange(N_steps):
W,ll,grad = test_model.gradient_descent_step(stepsz=0.001)
lls.append(ll)
# Update plot
if itr % 5 == 0:
ln.set_data(np.arange(T), test_model.compute_rate(ks=kplt))
plt.title("Iteration %d" % itr)
plt.pause(0.001)
plt.ioff()
print "W true: ", true_model.weight_model.A * true_model.weight_model.W
print "lambda0 true: ", true_model.bias_model.lambda0
print "ll true: ", true_model.log_likelihood()
print ""
print "W test: ", test_model.W
print "lambda0 test ", test_model.bias
print "ll test: ", test_model.log_likelihood()
plt.figure()
plt.plot(np.arange(N_steps), lls)
plt.xlabel("Iteration")
plt.ylabel("Log likelihood")
plot_network(np.ones((K,K)), test_model.W, vmax=0.5)
plt.show()
def generate_synthetic_data(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)
# Create a true model
# Larger v (weight scale) implies smaller weights
T_test=1000
# Debugging network:
# C = 1
# K = 4
# T = 1000
# dt = 1.0
# B = 3
# p = 0.5
# kappa = 3.0
# v = kappa * 5.0
# c = np.zeros(K, dtype=np.int)
# Small network:
# Seed: 1957629166
# C = 4
# K = 20
# T = 10000
# dt = 1.0
# B = 3
# kappa = 3.0
# p = 0.9 * np.eye(C) + 0.05 * (1-np.eye(C))
# v = kappa * (5.0 * np.eye(C) + 25.0 * (1-np.eye(C)))
# c = np.arange(C).repeat((K // C))
# Medium network:
# Seed: 2723361959
# C = 5
# K = 50
# T = 100000
# dt = 1.0
# B = 3
# kappa = 3.0
# p = 0.75 * np.eye(C) + 0.05 * (1-np.eye(C))
# v = kappa * (9 * np.eye(C) + 25.0 * (1-np.eye(C)))
# c = np.arange(C).repeat((K // C))
# Medium netowrk 2:
# Seed = 3848328624
# C = 5
# K = 50
# T = 100000
# dt = 1.0
# B = 3
# kappa = 2.0
# c = np.arange(C).repeat((K // C))
# p = 0.4 * np.eye(C) + 0.01 * (1-np.eye(C))
# v = kappa * (5 * np.eye(C) + 5.0 * (1-np.eye(C)))
# Medium netowrk, one cluster
# Seed: 3848328624
C = 1
K = 50
T = 100000
dt = 1.0
B = 3
p = 0.08
kappa = 3.0
v = kappa * 5.0
c = np.zeros(K, dtype=np.int)
# Large network:
# Seed = 2467634490
# C = 5
# K = 100
# T = 100000
# dt = 1.0
# B = 3
# kappa = 3.0
# p = 0.4 * np.eye(C) + 0.025 * (1-np.eye(C))
# v = kappa * (10 * np.eye(C) + 25.0 * (1-np.eye(C)))
# c = np.arange(C).repeat((K // C))
# Large network 2:
# Seed =
# C = 10
# K = 100
# T = 100000
# dt = 1.0
# B = 3
# kappa = 3.0
# p = 0.75 * np.eye(C) + 0.05 * (1-np.eye(C))
# v = kappa * (9 * np.eye(C) + 25.0 * (1-np.eye(C)))
# c = np.arange(C).repeat((K // C))
# Extra large network:
# Seed: 2327447870
# C = 20
# K = 1000
# T = 100000
# dt = 1.0
# B = 3
# kappa = 3.0
# p = 0.25 * np.eye(C) + 0.0025 * (1-np.eye(C))
# v = kappa * (15 * np.eye(C) + 30.0 * (1-np.eye(C)))
# c = np.arange(C).repeat((K // C))
# Create the model with these parameters
network_hypers = {'C': C, 'kappa': kappa, 'c': c, 'p': p, 'v': v}
# Create a simple network
from pyhawkes.internals.network import ErdosRenyiFixedSparsity
network = ErdosRenyiFixedSparsity(K, p, kappa, v=v)
true_model = DiscreteTimeNetworkHawkesModelSpikeAndSlab(K=K, dt=dt, B=B,
network=network)
assert true_model.check_stability()
# Plot the true network
plt.ion()
plot_network(true_model.weight_model.A,
true_model.weight_model.W)
plt.pause(0.001)
# Sample from the true model
S,R = true_model.generate(T=T, keep=False, print_interval=50)
# Pickle and save the data
out_dir = os.path.join('data', "synthetic")
out_name = 'synthetic_K%d_C%d_T%d.pkl.gz' % (K,C,T)
out_path = os.path.join(out_dir, out_name)
with gzip.open(out_path, 'w') as f:
print "Saving output to ", out_path
cPickle.dump((S, true_model), f, protocol=-1)
# Sample test data
S_test,_ = true_model.generate(T=T_test, keep=False)
# Pickle and save the data
out_dir = os.path.join('data', "synthetic")
out_name = 'synthetic_test_K%d_C%d_T%d.pkl.gz' % (K,C,T_test)
out_path = os.path.join(out_dir, out_name)
with gzip.open(out_path, 'w') as f:
print "Saving output to ", out_path
cPickle.dump((S_test, true_model), f, protocol=-1)
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(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)
C = 1
K = 10
T = 1000
dt = 1.0
B = 3
# Create a true model
p = 0.8 * np.eye(C)
v = 10.0 * np.eye(C) + 20.0 * (1 - np.eye(C))
# m = 0.5 * np.ones(C)
c = (0.0 * (np.arange(K) < 10) + 1.0 * (np.arange(K) >= 10)).astype(np.int)
true_model = DiscreteTimeNetworkHawkesModelSpikeAndSlab(C=C,
K=K,
dt=dt,
B=B,
c=c,
p=p,
v=v)
# Plot the true network
plt.ion()
plot_network(true_model.weight_model.A,
true_model.weight_model.W,
vmax=0.5)
plt.pause(0.001)
# Sample from the true model
S, R = true_model.generate(T=T)
# Make a new model for inference
test_model = DiscreteTimeStandardHawkesModel(K=K, dt=dt, B=B, beta=1.0)
test_model.add_data(S)
# Plot the true and inferred firing rate
kplt = 0
plt.figure()
plt.plot(np.arange(T), R[:, kplt], '-k', lw=2)
plt.ion()
ln = plt.plot(np.arange(T), test_model.compute_rate(ks=kplt), '-r')[0]
plt.show()
# Gradient descent
N_steps = 10000
lls = []
for itr in xrange(N_steps):
W, ll, grad = test_model.gradient_descent_step(stepsz=0.001)
lls.append(ll)
# Update plot
if itr % 5 == 0:
ln.set_data(np.arange(T), test_model.compute_rate(ks=kplt))
plt.title("Iteration %d" % itr)
plt.pause(0.001)
plt.ioff()
print "W true: ", true_model.weight_model.A * true_model.weight_model.W
print "lambda0 true: ", true_model.bias_model.lambda0
print "ll true: ", true_model.log_likelihood()
print ""
print "W test: ", test_model.W
print "lambda0 test ", test_model.bias
print "ll test: ", test_model.log_likelihood()
plt.figure()
plt.plot(np.arange(N_steps), lls)
plt.xlabel("Iteration")
plt.ylabel("Log likelihood")
plot_network(np.ones((K, K)), test_model.W, vmax=0.5)
plt.show()
