-
Notifications
You must be signed in to change notification settings - Fork 1
/
onlineldavb.py
297 lines (257 loc) · 11.6 KB
/
onlineldavb.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
# onlineldavb.py: Package of functions for fitting Latent Dirichlet
# Allocation (LDA) with online variational Bayes (VB).
#
# Copyright (C) 2010 Matthew D. Hoffman
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
import sys, re, time, string
import numpy as n
from scipy.special import gammaln, psi
n.random.seed(100000001)
meanchangethresh = 0.001
def dirichlet_expectation(alpha):
"""
For a vector theta ~ Dir(alpha), computes E[log(theta)] given alpha.
"""
if (len(alpha.shape) == 1):
return(psi(alpha) - psi(n.sum(alpha)))
return(psi(alpha) - psi(n.sum(alpha, 1))[:, n.newaxis])
def parse_doc_list(docs, vocab):
"""
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())
return((wordids, wordcts))
class OnlineLDA:
"""
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, 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)
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(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)
# Estimate held-out likelihood for current values of lambda.
bound = self.approx_bound(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 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.
"""
# 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)))
return(score)