Implement a stochastic block model example (#715)

* Implement a stochastic block model example

* Joint originally separated MAP and follow PEP8

* Test the model using Zachary’s Karate Club graph

* Follow PEP8

* Put graph and label data in data/

* Delete unnecessary file and fix indent

examples/data/karate_edgelist.txt

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examples/data/karate_labels.txt

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examples/stochastic_block_model.py

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+#!/usr/bin/env python
+"""Stochastic Block Model
+
+"""
+from __future__ import absolute_import
+from __future__ import division
+from __future__ import print_function
+
+import edward as ed
+import numpy as np
+import tensorflow as tf
+
+from sklearn.metrics.cluster import adjusted_rand_score
+from edward.models import Bernoulli, Multinomial, Beta, Dirichlet, PointMass
+
+ed.set_seed(42)
+
+
+def build_dataset(label_filepath, graph_filepath):
+  Z = np.loadtxt(label_filepath, dtype=np.int)
+  N = Z.shape[0]
+
+  X = np.zeros((N, N))
+  for line in open(graph_filepath, 'r'):
+    src, dst = map(int, line.strip().split(' '))
+    X[src, dst] = 1
+
+  return X, Z
+
+
+# DATA
+label_filepath = 'data/karate_labels.txt'
+graph_filepath = 'data/karate_edgelist.txt'
+X_data, Z_true = build_dataset(label_filepath, graph_filepath)
+N = X_data.shape[0]  # number of vertices
+K = 2  # number of clusters
+
+# MODEL
+gamma = Dirichlet(concentration=tf.ones([K]))
+Pi = Beta(concentration0=tf.ones([K, K]), concentration1=tf.ones([K, K]))
+Z = Multinomial(total_count=1., probs=gamma, sample_shape=N)
+X = Bernoulli(probs=tf.matmul(Z, tf.matmul(Pi, tf.transpose(Z))))
+
+# INFERENCE (EM algorithm)
+qgamma = PointMass(params=tf.nn.softmax(tf.Variable(tf.random_normal([K]))))
+qPi = PointMass(params=tf.nn.sigmoid(tf.Variable(tf.random_normal([K, K]))))
+qZ = PointMass(params=tf.nn.softmax(tf.Variable(tf.random_normal([N, K]))))
+
+inference = ed.MAP({gamma: qgamma, Pi: qPi, Z: qZ}, data={X: X_data})
+
+n_iter = 100
+inference.initialize(n_iter=n_iter)
+
+tf.global_variables_initializer().run()
+
+for _ in range(inference.n_iter):
+  info_dict = inference.update()
+  inference.print_progress(info_dict)
+inference.finalize()
+
+# CRITICISM
+Z_pred = qZ.mean().eval().argmax(axis=1)
+print("Result (label filp can happen):")
+print("Predicted")
+print(Z_pred)
+print("True")
+print(Z_true)
+print("Adjusted Rand Index =", adjusted_rand_score(Z_pred, Z_true))