"""

For a vector theta ~ Dir(alpha), computes E[log(theta)] given alpha.

"""

if (len(alpha.shape) == 1):

return(psi(alpha) - psi(n.sum(alpha)))

"""

Parse a document into a list of word ids and a list of counts,

or parse a set of documents into two lists of lists of word ids

and counts.

Arguments:

docs: List of D documents. Each document must be represented as

a single string. (Word order is unimportant.) Any

words not in the vocabulary will be ignored.

vocab: Dictionary mapping from words to integer ids.

Returns a pair of lists of lists.

The first, wordids, says what vocabulary tokens are present in

each document. wordids[i][j] gives the jth unique token present in

document i. (Don't count on these tokens being in any particular

order.)

The second, wordcts, says how many times each vocabulary token is

present. wordcts[i][j] is the number of times that the token given

by wordids[i][j] appears in document i.

"""

if (type(docs).__name__ == 'str'):

temp = list()

temp.append(docs)

docs = temp

D = len(docs)

wordids = list()

wordcts = list()

for d in range(0, D):

docs[d] = docs[d].lower()

docs[d] = re.sub(r'-', ' ', docs[d])

docs[d] = re.sub(r'[^a-z ]', '', docs[d])

docs[d] = re.sub(r' +', ' ', docs[d])

words = string.split(docs[d])

ddict = dict()

for word in words:

if (word in vocab):

wordtoken = vocab[word]

if (not wordtoken in ddict):

ddict[wordtoken] = 0

ddict[wordtoken] += 1

wordids.append(ddict.keys())

wordcts.append(ddict.values())

"""

Implements online VB for LDA as described in (Hoffman et al. 2010).

"""

def __init__(self, vocab, K, D, alpha, eta, tau0, kappa):

"""

Arguments:

K: Number of topics

vocab: A set of words to recognize. When analyzing documents, any word

not in this set will be ignored.

D: Total number of documents in the population. For a fixed corpus,

this is the size of the corpus. In the truly online setting, this

can be an estimate of the maximum number of documents that

could ever be seen.

alpha: Hyperparameter for prior on weight vectors theta

eta: Hyperparameter for prior on topics beta

tau0: A (positive) learning parameter that downweights early iterations

kappa: Learning rate: exponential decay rate---should be between

(0.5, 1.0] to guarantee asymptotic convergence.

Note that if you pass the same set of D documents in every time and

set kappa=0 this class can also be used to do batch VB.

"""

self._vocab = dict()

for word in vocab:

word = word.lower()

word = re.sub(r'[^a-z]', '', word)

self._vocab[word] = len(self._vocab)

self._K = K

self._W = len(self._vocab)

self._D = D

self._alpha = alpha

self._eta = eta

self._tau0 = tau0 + 1

self._kappa = kappa

self._updatect = 0

# Initialize the variational distribution q(beta|lambda)

self._lambda = 1*n.random.gamma(100., 1./100., (self._K, self._W))

self._Elogbeta = dirichlet_expectation(self._lambda)

self._expElogbeta = n.exp(self._Elogbeta)

def do_e_step(self, wordids, wordcts):

batchD = len(wordids)

# 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):

print sum(wordcts[d])

# 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)

print gammad[:, n.newaxis]

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_docs(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.

"""

# This is to handle the case where someone just hands us a single

# document, not in a list.

if (type(docs).__name__ == 'string'):

temp = list()

temp.append(docs)

docs = temp

(wordids, wordcts) = parse_doc_list(docs, self._vocab)

return self.do_e_step(wordids, wordcts)

# 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 update_lambda_docs(self, docs):

"""

First does an E step on the mini-batch given in wordids and

wordcts, then uses the result of that E step to update the

variational parameter matrix lambda.

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 gamma, the parameters to the variational distribution

over the topic weights theta for the documents analyzed in this

update.

Also returns an estimate of the variational bound for the

entire corpus for the OLD setting of lambda based on the

documents passed in. This can be used as a (possibly very

noisy) estimate of held-out likelihood.

"""

# rhot will be between 0 and 1, and says how much to weight

# the information we got from this mini-batch.

rhot = pow(self._tau0 + self._updatect, -self._kappa)

self._rhot = rhot

# Do an E step to update gamma, phi | lambda for this

# mini-batch. This also returns the information about phi that

# we need to update lambda.

(gamma, sstats) = self.do_e_step_docs(docs)

# Estimate held-out likelihood for current values of lambda.

bound = self.approx_bound_docs(docs, gamma)

# Update lambda based on documents.

self._lambda = self._lambda * (1-rhot) + \

rhot * (self._eta + self._D * sstats / len(docs))

self._Elogbeta = dirichlet_expectation(self._lambda)

self._expElogbeta = n.exp(self._Elogbeta)

self._updatect += 1

return(gamma, bound)

def update_lambda(self, wordids, wordcts):

"""

First does an E step on the mini-batch given in wordids and

wordcts, then uses the result of that E step to update the

variational parameter matrix lambda.

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 gamma, the parameters to the variational distribution

over the topic weights theta for the documents analyzed in this

update.

Also returns an estimate of the variational bound for the

entire corpus for the OLD setting of lambda based on the

documents passed in. This can be used as a (possibly very

noisy) estimate of held-out likelihood.

"""

# rhot will be between 0 and 1, and says how much to weight

# the information we got from this mini-batch.

rhot = pow(self._tau0 + self._updatect, -self._kappa)

self._rhot = rhot

# Do an E step to update gamma, phi | lambda for this

# mini-batch. This also returns the information about phi that

# we need to update lambda.

(gamma, sstats) = self.do_e_step(wordids, wordcts)

# Estimate held-out likelihood for current values of lambda.

bound = self.approx_bound(wordids, wordcts, gamma)

# Update lambda based on documents.

self._lambda = self._lambda * (1-rhot) + \

rhot * (self._eta + self._D * sstats / len(wordids))

self._Elogbeta = dirichlet_expectation(self._lambda)

self._expElogbeta = n.exp(self._Elogbeta)

self._updatect += 1

return(gamma, bound)

def approx_bound(self, wordids, wordcts, 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.

"""

# This is to handle the case where someone just hands us a single

# document, not in a list.

batchD = len(wordids)

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(wordids)

# 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_docs(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.

"""

# This is to handle the case where someone just hands us a single

# document, not in a list.

if (type(docs).__name__ == 'string'):

temp = list()

temp.append(docs)

docs = temp

(wordids, wordcts) = parse_doc_list(docs, self._vocab)

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)))

infile = sys.argv[1]

K = int(sys.argv[2])

alpha = float(sys.argv[3])

eta = float(sys.argv[4])

kappa = float(sys.argv[5])

S = int(sys.argv[6])

docs = corpus.corpus()

docs.read_data(infile)

vocab = open(sys.argv[7]).readlines()

model = OnlineLDA(vocab, K, 100000,

0.1, 0.01, 1, 0.75)

for i in range(1000):

print i

wordids = [d.words for d in docs.docs[(i*S):((i+1)*S)]]

wordcts = [d.counts for d in docs.docs[(i*S):((i+1)*S)]]

model.update_lambda(wordids, wordcts)