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
|
################################################################################
# Copyright (C) 2015 Jaakko Luttinen
#
# This file is licensed under the MIT License.
################################################################################
import numpy as np
from bayespy import nodes
from bayespy.inference import VB
from bayespy.inference.vmp.nodes.constant import Constant
from bayespy.inference.vmp.nodes.categorical import CategoricalMoments
import bayespy.plot as bpplt
def model(n_documents, n_topics, n_vocabulary, corpus, word_documents, plates_multiplier=1):
'''
Construct Latent Dirichlet Allocation model.
Parameters
----------
documents : int
The number of documents
topics : int
The number of topics
vocabulary : int
The number of words in the vocabulary
corpus : integer array
The vocabulary index of each word in the corpus
word_documents : integer array
The document index of each word in the corpus
'''
# Topic distributions for each document
p_topic = nodes.Dirichlet(np.ones(n_topics),
plates=(n_documents,),
name='p_topic')
# Word distributions for each topic
p_word = nodes.Dirichlet(np.ones(n_vocabulary),
plates=(n_topics,),
name='p_word')
# Use a simple wrapper node so that the value of this can be changed if one
# uses stocahstic variational inference
word_documents = Constant(CategoricalMoments(n_documents), word_documents,
name='word_documents')
# Choose a topic for each word in the corpus
topics = nodes.Categorical(nodes.Gate(word_documents, p_topic),
plates=(len(corpus),),
plates_multiplier=(plates_multiplier,),
name='topics')
# Choose each word in the corpus from the vocabulary
words = nodes.Categorical(nodes.Gate(topics, p_word),
name='words')
# Observe the corpus
words.observe(corpus)
# Break symmetry by random initialization
p_topic.initialize_from_random()
p_word.initialize_from_random()
return VB(words, topics, p_word, p_topic, word_documents)
def generate_data(n_documents, n_topics, n_vocabulary, n_words):
# Generate random data from the generative model
# Generate document assignments for the words
word_documents = nodes.Categorical(np.ones(n_documents)/n_documents,
plates=(n_words,)).random()
# Topic distribution for each document
p_topic = nodes.Dirichlet(1e-1*np.ones(n_topics),
plates=(n_documents,)).random()
# Word distribution for each topic
p_word = nodes.Dirichlet(1e-1*np.ones(n_vocabulary),
plates=(n_topics,)).random()
# Topic for each word in each document
topic = nodes.Categorical(p_topic[word_documents],
plates=(n_words,)).random()
# Each word in each document
corpus = nodes.Categorical(p_word[topic],
plates=(n_words,)).random()
bpplt.pyplot.figure()
bpplt.hinton(p_topic)
bpplt.pyplot.title("True topic distribution for each document")
bpplt.pyplot.xlabel("Topics")
bpplt.pyplot.ylabel("Documents")
bpplt.pyplot.figure()
bpplt.hinton(p_word)
bpplt.pyplot.title("True word distributions for each topic")
bpplt.pyplot.xlabel("Words")
bpplt.pyplot.ylabel("Topics")
return (corpus, word_documents)
def run(n_documents=30, n_topics=5, n_vocabulary=10, n_words=50000, stochastic=False, maxiter=1000, seed=None):
if seed is not None:
np.random.seed(seed)
(corpus, word_documents) = generate_data(n_documents, n_topics, n_vocabulary, n_words)
if not stochastic:
Q = model(n_documents=n_documents, n_topics=n_topics, n_vocabulary=n_vocabulary,
corpus=corpus, word_documents=word_documents)
Q.update(repeat=maxiter)
else:
subset_size = 1000
Q = model(n_documents=n_documents, n_topics=n_topics, n_vocabulary=n_vocabulary,
corpus=corpus[:subset_size], word_documents=word_documents[:subset_size],
plates_multiplier=n_words/subset_size)
Q.ignore_bound_checks = True
delay = 1
forgetting_rate = 0.7
for n in range(maxiter):
# Observe a mini-batch
subset = np.random.choice(n_words, subset_size)
Q['words'].observe(corpus[subset])
Q['word_documents'].set_value(word_documents[subset])
# Learn intermediate variables
Q.update('topics')
# Set step length
step = (n + delay) ** (-forgetting_rate)
# Stochastic gradient for the global variables
Q.gradient_step('p_topic', 'p_word', scale=step)
bpplt.pyplot.figure()
bpplt.pyplot.plot(Q.L)
bpplt.pyplot.figure()
bpplt.hinton(Q['p_topic'])
bpplt.pyplot.title("Posterior topic distribution for each document")
bpplt.pyplot.xlabel("Topics")
bpplt.pyplot.ylabel("Documents")
bpplt.pyplot.figure()
bpplt.hinton(Q['p_word'])
bpplt.pyplot.title("Posterior word distributions for each topic")
bpplt.pyplot.xlabel("Words")
bpplt.pyplot.ylabel("Topics")
return
if __name__ == '__main__':
import sys, getopt, os
try:
opts, args = getopt.getopt(sys.argv[1:],
"",
["documents=",
"topics=",
"vocabulary=",
"words=",
"stochastic",
"seed=",
"maxiter="])
except getopt.GetoptError:
print('python lda.py <options>')
print('--documents=<INT> The number of documents')
print('--topics=<INT> The number of topics')
print('--vocabulary=<INT> The size of the vocabulary')
print('--words=<INT> The size of the corpus')
print('--maxiter=<INT> Maximum number of VB iterations')
print('--seed=<INT> Seed (integer) for the RNG')
print('--stochastic Use stochastic variational inference')
sys.exit(2)
kwargs = {}
for opt, arg in opts:
if opt == "--maxiter":
kwargs["maxiter"] = int(arg)
elif opt == "--seed":
kwargs["seed"] = int(arg)
elif opt == "--documents":
kwargs["n_documents"] = int(arg)
elif opt == "--topics":
kwargs["n_topics"] = int(arg)
elif opt == "--vocabulary":
kwargs["n_vocabulary"] = int(arg)
elif opt == "--words":
kwargs["n_words"] = int(arg)
elif opt == "--stochastic":
kwargs["stochastic"] = True
#raise NotImplementedError("Work in progress.. This demo is not yet finished")
run(**kwargs)
bpplt.pyplot.show()
|
