def generate_data(V, D, l, alpha, beta):
"""
Generates a synthetic corpus of documents from a Dirichlet process
mixture model with multinomial mixture components (topics). The
mixture components are drawn from a symmetric Dirichlet prior.
Arguments:
V -- vocabulary size
D -- number of documents
l -- average document length
alpha -- concentration parameter for the Dirichlet process
beta -- concentration parameter for the symmetric Dirichlet prior
"""
T = D # maximum number of topics
phi_TV = zeros((T, V))
z_D = zeros(D, dtype=int)
N_DV = zeros((D, V), dtype=int)
for d in xrange(D):
# draw a topic assignment for this document
dist = bincount(z_D).astype(float)
dist[0] = alpha
[t] = sample(dist)
t = len(dist) if t == 0 else t
z_D[d] = t
# if it's a new topic, draw the parameters for that topic
if t == len(dist):
phi_TV[t - 1, :] = dirichlet(beta * ones(V) / V)
# draw the tokens from the topic
for v in sample(phi_TV[t - 1, :], num_samples=poisson(l)):
N_DV[d, v] += 1
z_D = z_D - 1
return phi_TV, z_D, N_DV
def getting_it_right(algorithm, V, D, l, alpha, beta, num_itns, s):
"""
Runs Geweke's "getting it right" test.
"""
seed(s)
# generate forward samples via the generative process
print "Generating forward samples..."
forward_samples = []
for _ in iterview(xrange(num_itns)):
forward_samples.append(generate_data(V, D, l, alpha, beta)[1:])
# generate reverse samples via the inference algorithm
print "Generating reverse samples..."
reverse_samples = []
phi_TV, z_D, _ = generate_data(V, D, l, alpha, beta)
for _ in iterview(xrange(num_itns)):
N_DV = zeros((D, V), dtype=int)
if algorithm.__name__ == "algorithm_8" or algorithm.__name__ == "nonconjugate_split_merge":
for d in xrange(D):
for v in sample(phi_TV[z_D[d], :], num_samples=poisson(l)):
N_DV[d, v] += 1
phi_TV, z_D = algorithm.inference(N_DV, alpha, beta, z_D, 1)
else:
T = D # maximum number of topics
N_TV = zeros((T, V), dtype=int)
N_T = zeros(T, dtype=int)
for d in xrange(D):
t = z_D[d]
for _ in xrange(poisson(l)):
[v] = sample((N_TV[t, :] + beta / V) / (N_T[t] + beta))
N_DV[d, v] += 1
N_TV[t, v] += 1
N_T[t] += 1
z_D = algorithm.inference(N_DV, alpha, beta, z_D, 1)
z_D_copy = empty_like(z_D)
z_D_copy[:] = z_D
reverse_samples.append((z_D_copy, N_DV))
print "Computing test statistics..."
# test statistics: number of topics, maximum topic size, mean
# topic size, standard deviation of topic sizes
# compute test statistics for forward samples
forward_num_topics = []
forward_max_topic_size = []
forward_mean_topic_size = []
forward_std_topic_size = []
for z_D, _ in forward_samples:
forward_num_topics.append(len(unique(z_D)))
topic_sizes = []
for t in unique(z_D):
topic_sizes.append((z_D[:] == t).sum())
topic_sizes = array(topic_sizes)
forward_max_topic_size.append(topic_sizes.max())
forward_mean_topic_size.append(topic_sizes.mean())
forward_std_topic_size.append(topic_sizes.std())
# compute test statistics for reverse samples
reverse_num_topics = []
reverse_max_topic_size = []
reverse_mean_topic_size = []
reverse_std_topic_size = []
for z_D, _ in reverse_samples:
reverse_num_topics.append(len(unique(z_D)))
topic_sizes = []
for t in unique(z_D):
topic_sizes.append((z_D[:] == t).sum())
topic_sizes = array(topic_sizes)
reverse_max_topic_size.append(topic_sizes.max())
reverse_mean_topic_size.append(topic_sizes.mean())
reverse_std_topic_size.append(topic_sizes.std())
# generate P-P plots
pp_plot(array(forward_num_topics), array(reverse_num_topics))
pp_plot(array(forward_max_topic_size), array(reverse_max_topic_size))
pp_plot(array(forward_mean_topic_size), array(reverse_mean_topic_size))
pp_plot(array(forward_std_topic_size), array(reverse_std_topic_size))
def getting_it_right(algorithm, V, D, l, alpha, beta, num_itns, s):
"""
Runs Geweke's "getting it right" test.
"""
seed(s)
# generate forward samples via the generative process
print 'Generating forward samples...'
forward_samples = []
for _ in iterview(xrange(num_itns)):
forward_samples.append(generate_data(V, D, l, alpha, beta)[1:])
# generate reverse samples via the inference algorithm
print 'Generating reverse samples...'
reverse_samples = []
phi_TV, z_D, _ = generate_data(V, D, l, alpha, beta)
for _ in iterview(xrange(num_itns)):
N_DV = zeros((D, V), dtype=int)
if (algorithm.__name__ == 'algorithm_8'
or algorithm.__name__ == 'nonconjugate_split_merge'):
for d in xrange(D):
for v in sample(phi_TV[z_D[d], :], num_samples=poisson(l)):
N_DV[d, v] += 1
phi_TV, z_D = algorithm.inference(N_DV, alpha, beta, z_D, 1)
else:
T = D # maximum number of topics
N_TV = zeros((T, V), dtype=int)
N_T = zeros(T, dtype=int)
for d in xrange(D):
t = z_D[d]
for _ in xrange(poisson(l)):
[v] = sample((N_TV[t, :] + beta / V) / (N_T[t] + beta))
N_DV[d, v] += 1
N_TV[t, v] += 1
N_T[t] += 1
z_D = algorithm.inference(N_DV, alpha, beta, z_D, 1)
z_D_copy = empty_like(z_D)
z_D_copy[:] = z_D
reverse_samples.append((z_D_copy, N_DV))
print 'Computing test statistics...'
# test statistics: number of topics, maximum topic size, mean
# topic size, standard deviation of topic sizes
# compute test statistics for forward samples
forward_num_topics = []
forward_max_topic_size = []
forward_mean_topic_size = []
forward_std_topic_size = []
for z_D, _ in forward_samples:
forward_num_topics.append(len(unique(z_D)))
topic_sizes = []
for t in unique(z_D):
topic_sizes.append((z_D[:] == t).sum())
topic_sizes = array(topic_sizes)
forward_max_topic_size.append(topic_sizes.max())
forward_mean_topic_size.append(topic_sizes.mean())
forward_std_topic_size.append(topic_sizes.std())
# compute test statistics for reverse samples
reverse_num_topics = []
reverse_max_topic_size = []
reverse_mean_topic_size = []
reverse_std_topic_size = []
for z_D, _ in reverse_samples:
reverse_num_topics.append(len(unique(z_D)))
topic_sizes = []
for t in unique(z_D):
topic_sizes.append((z_D[:] == t).sum())
topic_sizes = array(topic_sizes)
reverse_max_topic_size.append(topic_sizes.max())
reverse_mean_topic_size.append(topic_sizes.mean())
reverse_std_topic_size.append(topic_sizes.std())
# generate P-P plots
pp_plot(array(forward_num_topics), array(reverse_num_topics))
pp_plot(array(forward_max_topic_size), array(reverse_max_topic_size))
pp_plot(array(forward_mean_topic_size), array(reverse_mean_topic_size))
pp_plot(array(forward_std_topic_size), array(reverse_std_topic_size))
