def stochastic_lda(corpus, batches=None, lambda_=None,
ordering=False, S=1, num_topics=10, max_iter=300, tau=1,
kappa=0.5, alpha=0.5, eta=0.001, threshold=0.000001):
'''
Stochastic Variational Inference EM algorithm for LDA.
(from algorithm 2 in Blei 2010)
corpus is a list of lists of [word_index, count] for each document
corpus is a matrix of count: (docs, voca)
Args:
lambda_: to set a specific lambda for the initialization
batches: to set an order on the use of the corpus
S: size of the mini-batches
'''
C, V = corpus.shape
# Initialisation
if not np.any(lambda_):
lambda_ = np.random.gamma(100, 1./100, size=(num_topics, V))
else:
lambda_ = lambda_.copy()
gamma_d_k = np.ones((C, num_topics))
# Sampling
if not np.any(batches):
batches = get_samples(C, S, max_iter)
for t in xrange(len(batches)):
# #### E-step
lambda_int = np.zeros((num_topics, V))
for d in batches[t]:
gamma_d_k, lambda_int = e_step(d, corpus, gamma_d_k, lambda_, lambda_int, alpha, threshold)
# #### M-step
rho = (tau + t)**(-kappa)
indices = np.unique(np.nonzero(corpus[batches[t], :])[1])
lambda_int = eta + C / (1. * S) * lambda_int
lambda_[:, indices] = (1 - rho)*lambda_[:, indices] + rho*lambda_int[:, indices]
return lambda_, gamma_d_k
def batch_lda(corpus, lambda_=None, num_topics=10, num_iter=10, alpha=0.5, eta=0.001, threshold=0.000001):
'''
Batch Variational Inference EM algorithm for LDA, goes over all the data at each iteration.
(from algorithm 1 in Blei 2010)
corpus is a list of lists of [word_index, count] for each document
corpus is a matrix of count: (docs, voca)
Args:
lambda_: to set a specific lambda for the initialization
'''
C, V = corpus.shape
# Initialisation
if not np.any(lambda_):
lambda_ = np.random.gamma(100, 1./100, size=(num_topics, V))
else:
lambda_ = lambda_.copy()
gamma_d_k = np.ones((C, num_topics))
sample = range(C)
np.random.shuffle(sample)
for t in xrange(num_iter):
old_lambda_ = lambda_
# #### E-step
lambda_int = np.zeros((num_topics, V))
for d in sample:
gamma_d_k, lambda_int = e_step(d, corpus, gamma_d_k, lambda_,
lambda_int, alpha, threshold)
# #### M-step
lambda_ = eta + lambda_int
# Check if convergence
if (np.mean(np.abs((lambda_ - old_lambda_) / old_lambda_)) < threshold):
break
return lambda_, gamma_d_k
