def test_multinomial():
R = RandomStreams(234)
n = R.multinomial(5, numpy.ones(5,)/5, draw_shape=(2,))
f = theano.function([], n)
assert f().shape == (2, 5)
def test_multinomial():
R = RandomStreams(234)
n = R.multinomial(5, numpy.ones(5, ) / 5, draw_shape=(2, ))
f = theano.function([], n)
assert f().shape == (2, 5)
nr_topics = 2
alpha = 0.8
beta = 1.
# Topic distribution per document
doc_mixture = memoized(lambda doc_id: s_rng.dirichlet([alpha/nr_topics]*nr_topics))
# Word distribution per topic
topic_mixture = memoized(lambda top_id: s_rng.dirichlet([beta/nr_words]*nr_words))
# For each word in the document, draw a topic according to multinomial with document specific prior
# TODO, see comment below: topics = memoized(lambda doc_id, nr: s_rng.multinomial(1, doc_mixture[doc_id], draw_shape=(nr,)))
topics = memoized(lambda doc_id, nr: s_rng.binomial(1, doc_mixture(doc_id)[0], draw_shape=(nr,)))
# Draw words for a specific topic
word_topic = lambda top_id: s_rng.multinomial(1, topic_mixture(top_id))
# TODO: memoized only works on the pre-compiled graph. This makes it fail in the case where we have to map
# a vector of topics to individual multinomials with as priors the different topics. In the case of two topics
# we can hack around this by using a binomial topic distribution and using a switch statement here:
word_topic_mapper = lambda top_id: tensor.switch(top_id, word_topic(0), word_topic(1))
# Maps topics to words
# TODO, see comment above: get_words = memoized(lambda doc_id, nr: theano.map(word_topic, topics(doc_id, nr))[0])
get_words = memoized(lambda doc_id, nr: theano.map(word_topic_mapper, topics(doc_id, nr))[0])
# Define training 'documents'
document_1 = numpy.asarray([[1,0,0,0],
[1,0,0,0],
[0,1,0,0],
[1,0,0,0],
# Topic distribution per document
doc_mixture = memoized(
lambda doc_id: s_rng.dirichlet([alpha / nr_topics] * nr_topics))
# Word distribution per topic
topic_mixture = memoized(
lambda top_id: s_rng.dirichlet([beta / nr_words] * nr_words))
# For each word in the document, draw a topic according to multinomial with document specific prior
# TODO, see comment below: topics = memoized(lambda doc_id, nr: s_rng.multinomial(1, doc_mixture[doc_id], draw_shape=(nr,)))
topics = memoized(lambda doc_id, nr: s_rng.binomial(
1, doc_mixture(doc_id)[0], draw_shape=(nr, )))
# Draw words for a specific topic
word_topic = lambda top_id: s_rng.multinomial(1, topic_mixture(top_id))
# TODO: memoized only works on the pre-compiled graph. This makes it fail in the case where we have to map
# a vector of topics to individual multinomials with as priors the different topics. In the case of two topics
# we can hack around this by using a binomial topic distribution and using a switch statement here:
word_topic_mapper = lambda top_id: tensor.switch(top_id, word_topic(0),
word_topic(1))
# Maps topics to words
# TODO, see comment above: get_words = memoized(lambda doc_id, nr: theano.map(word_topic, topics(doc_id, nr))[0])
get_words = memoized(
lambda doc_id, nr: theano.map(word_topic_mapper, topics(doc_id, nr))[0])
# Define training 'documents'
document_1 = numpy.asarray(
[[1, 0, 0, 0], [1, 0, 0, 0], [0, 1, 0, 0], [1, 0, 0, 0], [0, 1, 0, 0],
import numpy, pylab
import theano
from rstreams import RandomStreams
import distributions
from sample import mh2_sample
from for_theano import memoized
s_rng = RandomStreams(23424)
phi = s_rng.dirichlet(numpy.asarray([1, 1, 1, 1, 1]))
alpha = s_rng.gamma(2., 2.)
prototype = phi*alpha
bag_prototype = memoized(lambda bag: s_rng.dirichlet(prototype))
draw_marbles = lambda bag, nr: s_rng.multinomial(1, bag_prototype(bag), draw_shape=(nr,))
marbles_bag_1 = numpy.asarray([[1,1,1,1,1,1],
[0,0,0,0,0,0],
[0,0,0,0,0,0],
[0,0,0,0,0,0],
[0,0,0,0,0,0]], dtype=theano.config.floatX).T
marbles_bag_2 = numpy.asarray([[0,0,0,0,0,0],
[1,1,1,1,1,1],
[0,0,0,0,0,0],
[0,0,0,0,0,0],
[0,0,0,0,0,0]], dtype=theano.config.floatX).T
marbles_bag_3 = numpy.asarray([[0,0,0,0,0,0],
[0,0,0,0,0,0],
[0,0,0,0,0,0],
[1,1,1,1,1,1],
[0,0,0,0,0,0]], dtype=theano.config.floatX).T
[1,1,1,1,1,1],
[0,0,0,0,0,0],
[0,0,0,0,0,0],
[0,0,0,0,0,0]], dtype=theano.config.floatX).T
marbles_bag_3 = numpy.asarray([[0,0,0,0,0,0],
[0,0,0,0,0,0],
[0,0,0,0,0,0],
[1,1,1,1,1,1],
[0,0,0,0,0,0]], dtype=theano.config.floatX).T
marbles_bag_4 = numpy.asarray([[0],[0],[0],[0],[1]], dtype=theano.config.floatX).T
# Define flat model
bag_prototype = memoized(lambda bag: s_rng.dirichlet(numpy.asarray([1, 1, 1, 1, 1])*5))
draw_marbles = lambda bag, nr: s_rng.multinomial(1, bag_prototype(bag), draw_shape=(nr,))
# Generate samples from the model
givens = {draw_marbles(1,6): marbles_bag_1,
draw_marbles(2,6): marbles_bag_2,
draw_marbles(3,6): marbles_bag_3,
draw_marbles(4,1): marbles_bag_4}
sampler = mh2_sample(s_rng, [draw_marbles(4,1)], givens)
samples = sampler(200, 100, 100)
data = samples[0]
# Show histogram
pylab.subplot(211)
pylab.bar(range(5), data.sum(axis=0))
