def approx_bound(self, docs, gamma):
"""
Estimates the variational bound over *all documents* using only
the documents passed in as "docs." gamma is the set of parameters
to the variational distribution q(theta) corresponding to the
set of documents passed in.
The output of this function is going to be noisy, but can be
useful for assessing convergence.
"""
(wordids, wordcts) = utils.unzipDocs(docs)
batchD = len(docs)
score = 0
Elogtheta = dirichlet_expectation(gamma)
expElogtheta = n.exp(Elogtheta)
# E[log p(docs | theta, beta)]
for d in range(0, batchD):
gammad = gamma[d, :]
ids = wordids[d]
cts = n.array(wordcts[d])
phinorm = n.zeros(len(ids))
for i in range(0, len(ids)):
temp = Elogtheta[d, :] + self._Elogbeta[:, ids[i]]
tmax = max(temp)
phinorm[i] = n.log(sum(n.exp(temp - tmax))) + tmax
score += n.sum(cts * phinorm)
# oldphinorm = phinorm
# phinorm = n.dot(expElogtheta[d, :], self._expElogbeta[:, ids])
# print oldphinorm
# print n.log(phinorm)
# score += n.sum(cts * n.log(phinorm))
# E[log p(theta | alpha) - log q(theta | gamma)]
score += n.sum((self._alpha - gamma) * Elogtheta)
score += n.sum(gammaln(gamma) - gammaln(self._alpha))
score += sum(gammaln(self._alpha * self._K) - gammaln(n.sum(gamma, 1)))
# Compensate for the subsampling of the population of documents
score = score * self._D / len(docs)
# E[log p(beta | eta) - log q (beta | lambda)]
score = score + n.sum((self._eta - self._lambda) * self._Elogbeta)
score = score + n.sum(gammaln(self._lambda) - gammaln(self._eta))
score = score + n.sum(
gammaln(self._eta * self._W) - gammaln(n.sum(self._lambda, 1)))
return (score)
def approx_bound(self, docs, gamma):
"""
Estimates the variational bound over *all documents* using only
the documents passed in as "docs." gamma is the set of parameters
to the variational distribution q(theta) corresponding to the
set of documents passed in.
The output of this function is going to be noisy, but can be
useful for assessing convergence.
"""
(wordids, wordcts) = utils.unzipDocs(docs)
batchD = len(docs)
score = 0
Elogtheta = dirichlet_expectation(gamma)
expElogtheta = n.exp(Elogtheta)
# E[log p(docs | theta, beta)]
for d in range(0, batchD):
gammad = gamma[d, :]
ids = wordids[d]
cts = n.array(wordcts[d])
phinorm = n.zeros(len(ids))
for i in range(0, len(ids)):
temp = Elogtheta[d, :] + self._Elogbeta[:, ids[i]]
tmax = max(temp)
phinorm[i] = n.log(sum(n.exp(temp - tmax))) + tmax
score += n.sum(cts * phinorm)
# oldphinorm = phinorm
# phinorm = n.dot(expElogtheta[d, :], self._expElogbeta[:, ids])
# print oldphinorm
# print n.log(phinorm)
# score += n.sum(cts * n.log(phinorm))
# E[log p(theta | alpha) - log q(theta | gamma)]
score += n.sum((self._alpha - gamma)*Elogtheta)
score += n.sum(gammaln(gamma) - gammaln(self._alpha))
score += sum(gammaln(self._alpha*self._K) - gammaln(n.sum(gamma, 1)))
# Compensate for the subsampling of the population of documents
score = score * self._D / len(docs)
# E[log p(beta | eta) - log q (beta | lambda)]
score = score + n.sum((self._eta-self._lambda)*self._Elogbeta)
score = score + n.sum(gammaln(self._lambda) - gammaln(self._eta))
score = score + n.sum(gammaln(self._eta*self._W) -
gammaln(n.sum(self._lambda, 1)))
return(score)
def do_e_step(self, docs):
"""
Given a mini-batch of documents, estimates the parameters
gamma controlling the variational distribution over the topic
weights for each document in the mini-batch.
Arguments:
docs: List of D documents. Each document must be represented
as a string. (Word order is unimportant.) Any
words not in the vocabulary will be ignored.
Returns a tuple containing the estimated values of gamma,
as well as sufficient statistics needed to update lambda.
"""
(wordids, wordcts) = utils.unzipDocs(docs)
batchD = len(docs)
# Initialize the variational distribution q(theta|gamma) for
# the mini-batch
gamma = 1 * n.random.gamma(100., 1. / 100., (batchD, self._K))
Elogtheta = dirichlet_expectation(gamma)
expElogtheta = n.exp(Elogtheta)
sstats = n.zeros(self._lambda.shape)
# Now, for each document d update that document's gamma and phi
it = 0
meanchange = 0
for d in range(0, batchD):
# These are mostly just shorthand (but might help cache locality)
ids = wordids[d]
cts = wordcts[d]
gammad = gamma[d, :]
Elogthetad = Elogtheta[d, :]
expElogthetad = expElogtheta[d, :]
expElogbetad = self._expElogbeta[:, ids]
# The optimal phi_{dwk} is proportional to
# expElogthetad_k * expElogbetad_w. phinorm is the normalizer.
phinorm = n.dot(expElogthetad, expElogbetad) + 1e-100
# Iterate between gamma and phi until convergence
for it in range(0, 100):
lastgamma = gammad
# We represent phi implicitly to save memory and time.
# Substituting the value of the optimal phi back into
# the update for gamma gives this update. Cf. Lee&Seung 2001.
gammad = self._alpha + expElogthetad * \
n.dot(cts / phinorm, expElogbetad.T)
Elogthetad = dirichlet_expectation(gammad)
expElogthetad = n.exp(Elogthetad)
phinorm = n.dot(expElogthetad, expElogbetad) + 1e-100
# If gamma hasn't changed much, we're done.
meanchange = n.mean(abs(gammad - lastgamma))
if (meanchange < meanchangethresh):
break
gamma[d, :] = gammad
# Contribution of document d to the expected sufficient
# statistics for the M step.
sstats[:, ids] += n.outer(expElogthetad.T, cts / phinorm)
# This step finishes computing the sufficient statistics for the
# M step, so that
# sstats[k, w] = \sum_d n_{dw} * phi_{dwk}
# = \sum_d n_{dw} * exp{Elogtheta_{dk} + Elogbeta_{kw}} / phinorm_{dw}.
sstats = sstats * self._expElogbeta
return ((gamma, sstats))
def do_e_step(self, docs):
"""
Given a mini-batch of documents, estimates the parameters
gamma controlling the variational distribution over the topic
weights for each document in the mini-batch.
Arguments:
docs: List of D documents. Each document must be represented
as a string. (Word order is unimportant.) Any
words not in the vocabulary will be ignored.
Returns a tuple containing the estimated values of gamma,
as well as sufficient statistics needed to update lambda.
"""
(wordids, wordcts) = utils.unzipDocs(docs)
batchD = len(docs)
# Initialize the variational distribution q(theta|gamma) for
# the mini-batch
gamma = 1*n.random.gamma(100., 1./100., (batchD, self._K))
Elogtheta = dirichlet_expectation(gamma)
expElogtheta = n.exp(Elogtheta)
sstats = n.zeros(self._lambda.shape)
# Now, for each document d update that document's gamma and phi
it = 0
meanchange = 0
for d in range(0, batchD):
# These are mostly just shorthand (but might help cache locality)
ids = wordids[d]
cts = wordcts[d]
gammad = gamma[d, :]
Elogthetad = Elogtheta[d, :]
expElogthetad = expElogtheta[d, :]
expElogbetad = self._expElogbeta[:, ids]
# The optimal phi_{dwk} is proportional to
# expElogthetad_k * expElogbetad_w. phinorm is the normalizer.
phinorm = n.dot(expElogthetad, expElogbetad) + 1e-100
# Iterate between gamma and phi until convergence
for it in range(0, 100):
lastgamma = gammad
# We represent phi implicitly to save memory and time.
# Substituting the value of the optimal phi back into
# the update for gamma gives this update. Cf. Lee&Seung 2001.
gammad = self._alpha + expElogthetad * \
n.dot(cts / phinorm, expElogbetad.T)
Elogthetad = dirichlet_expectation(gammad)
expElogthetad = n.exp(Elogthetad)
phinorm = n.dot(expElogthetad, expElogbetad) + 1e-100
# If gamma hasn't changed much, we're done.
meanchange = n.mean(abs(gammad - lastgamma))
if (meanchange < meanchangethresh):
break
gamma[d, :] = gammad
# Contribution of document d to the expected sufficient
# statistics for the M step.
sstats[:, ids] += n.outer(expElogthetad.T, cts/phinorm)
# This step finishes computing the sufficient statistics for the
# M step, so that
# sstats[k, w] = \sum_d n_{dw} * phi_{dwk}
# = \sum_d n_{dw} * exp{Elogtheta_{dk} + Elogbeta_{kw}} / phinorm_{dw}.
sstats = sstats * self._expElogbeta
return((gamma, sstats))
