In [1]:
# This notebook is used to decide on a tolerable level of corruptableness.
%matplotlib inline
import numpy as np
from scipy.stats import entropy as KL_divergence
import pandas as pd
from itertools import product
from sklearn.cross_validation import StratifiedKFold
import matplotlib.pyplot as plt
from slda.topic_models import GRTM
from modules.helpers import plot_images
In [23]:
# Generate topics
# We assume a vocabulary of 'rows'^2 terms, and create 'rows'*2 "topics",
# where each topic assigns exactly 'rows' consecutive terms equal probability.
rows = 3
V = rows * rows
K = rows * 2
N = K * K
D = 1000
seed = 42
topics = []
topic_base = np.concatenate((np.ones((1, rows)) * (1/rows),
np.zeros((rows-1, rows))), axis=0).ravel()
for i in range(rows):
topics.append(np.roll(topic_base, i * rows))
topic_base = np.concatenate((np.ones((rows, 1)) * (1/rows),
np.zeros((rows, rows-1))), axis=1).ravel()
for i in range(rows):
topics.append(np.roll(topic_base, i))
topics = np.array(topics)
# Generate documents from topics
# We generate D documents from these V topics by sampling D topic
# distributions, one for each document, from a Dirichlet distribution with
# parameter α=(1,…,1)
alpha = np.ones(K)
np.random.seed(seed)
thetas = np.random.dirichlet(alpha, size=D)
topic_assignments = np.array([np.random.choice(range(K), size=N, p=theta)
for theta in thetas])
word_assignments = np.array([[np.random.choice(range(V), size=1,
p=topics[topic_assignments[d, n]])[0]
for n in range(N)] for d in range(D)])
doc_term_matrix = np.array([np.histogram(word_assignments[d], bins=V,
range=(0, V - 1))[0] for d in range(D)])
# choose parameter values
mu = 0.
nu2 = 1.
np.random.seed(14)
H = np.random.normal(loc=mu, scale=nu2, size=(K, K))
zeta = pd.DataFrame([(i, j, np.dot(np.dot(thetas[i], H), thetas[j])) for i, j in product(range(D), repeat=2)],
columns=('tail', 'head', 'zeta'))
_ = zeta.zeta.hist(bins=50)
# choose parameter values
zeta['y'] = (zeta.zeta >= 0).astype(int)
y = zeta[['tail', 'head', 'y']].values
skf = StratifiedKFold(y[:, 2], n_folds=100)
_, train_idx = next(iter(skf))
# Estimate parameters
_K = K
_alpha = alpha[:_K]
_beta = np.repeat(0.01, V)
_mu = mu
_nu2 = nu2
_b = 1.
n_iter = 1000
grtm = GRTM(_K, _alpha, _beta, _mu, _nu2, _b, n_iter, seed=42, n_report_iter=1)
grtm.fit(doc_term_matrix, y[train_idx])
results = grtm.phi
2016-06-16 15:52:02.851924 start iterations
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In [24]:
for res in results:
minimized_KL = 1
for topic in topics:
KL = KL_divergence(topic, res)
if KL < minimized_KL:
minimized_KL = KL
print(minimized_KL)
0.0360687572607
0.0201122685326
0.0812316413996
0.0236193602784
0.108897505098
0.175199332381
In [25]:
plot_images(plt, results, (rows, rows), (2, rows))
plt.figure()
plt.plot(grtm.loglikelihoods)
plt.figure()
plt.plot(np.diff(grtm.loglikelihoods)[-100:])
Out[25]:
[<matplotlib.lines.Line2D at 0x11360bef0>]
In [ ]:
Content source: Savvysherpa/slda
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