new example: hierarchical logistic regression edward (#509)

* hierarchical logistic regression edward

* pep8

examples/hierarchical_logistic_regression.py

@@ -0,0 +1,87 @@
+#!/usr/bin/env python
+"""Hierarchical logistic regression using variational inference.
+"""
+from __future__ import absolute_import
+from __future__ import division
+from __future__ import print_function
+
+import edward as ed
+import matplotlib.pyplot as plt
+import numpy as np
+import tensorflow as tf
+
+from edward.models import Normal, Bernoulli
+from edward.stats import bernoulli, norm
+
+
+def build_toy_dataset(N, noise_std=0.1):
+    D = 1
+    x = np.linspace(-6, 6, num=N)
+    y = np.tanh(x) + np.random.normal(0, noise_std, size=N)
+    y[y < 0.5] = 0
+    y[y >= 0.5] = 1
+    x = (x - 4.0) / 4.0
+    x = x.reshape((N, D))
+    return x, y
+
+
+ed.set_seed(42)
+
+N = 40  # number of data points
+D = 1  # number of features
+
+x_train, y_train = build_toy_dataset(N)
+
+x = tf.placeholder(tf.float32, [N, D])
+w = Normal(mu=tf.zeros(D), sigma=3.0 * tf.ones(D))
+b = Normal(mu=tf.zeros([]), sigma=3.0 * tf.ones([]))
+y = Bernoulli(logits=ed.dot(x, w) + b)
+
+qw_mu = tf.Variable(tf.random_normal([D]))
+qw_sigma = tf.nn.softplus(tf.Variable(tf.random_normal([D])))
+qb_mu = tf.Variable(tf.random_normal([]) + 10)
+qb_sigma = tf.nn.softplus(tf.Variable(tf.random_normal([])))
+
+qw = Normal(mu=qw_mu, sigma=qw_sigma)
+qb = Normal(mu=qb_mu, sigma=qb_sigma)
+
+sess = ed.get_session()
+data = {x: x_train, y: y_train}
+inference = ed.KLqp({w: qw, b: qb}, data)
+inference.initialize(n_print=10, n_iter=600)
+
+init = tf.global_variables_initializer()
+init.run()
+
+# Set up figure
+fig = plt.figure(figsize=(8, 8), facecolor='white')
+ax = fig.add_subplot(111, frameon=False)
+plt.ion()
+plt.show(block=False)
+
+# draws from approximate posterior
+S = 50
+rs = np.random.RandomState(0)
+inputs = np.linspace(-5, 3, num=400, dtype=np.float32)
+x_in = tf.expand_dims(inputs, 1)
+mus = []
+for s in range(S):
+    mus += [tf.sigmoid(ed.dot(x_in, qw.sample()) + qb.sample())]
+mus = tf.stack(mus)
+
+for t in range(inference.n_iter):
+    info_dict = inference.update()
+    inference.print_progress(info_dict)
+
+    if t % inference.n_print == 0:
+        outputs = mus.eval()
+
+        # Plot data and functions
+        plt.cla()
+        ax.plot(x_train[:], y_train, 'bx')
+        for s in range(S):
+            ax.plot(inputs, outputs[s], alpha=0.2)
+        ax.set_xlim([-5, 3])
+        ax.set_ylim([-0.5, 1.5])
+        plt.draw()
+        plt.pause(1.0 / 60.0)