#!/usr/bin/env python
# coding: utf-8

# This notebook is an interactive version of the [companion webpage](http://edwardlib.org/iclr2017) for the article, Deep Probabilistic Programming [(Tran et al., 2017)](https://arxiv.org/abs/1701.03757). See Edward's [API](http://edwardlib.org/api/) for details on how to interact with data, models, inference, and criticism.
# 
# The code snippets assume the following versions.
# ```bash
# pip install edward==1.3.1
# pip install tensorflow==1.1.0  # alternatively, tensorflow-gpu==1.1.0
# pip install keras==2.0.0
# ```

# ## Section 3. Compositional Representations for Probabilistic Models
# 
# __Figure 1__. Beta-Bernoulli program.

# In[ ]:


import tensorflow as tf
from edward.models import Bernoulli, Beta

theta = Beta(1.0, 1.0)
x = Bernoulli(tf.ones(50) * theta)


# For an example of it in use, see
# [`examples/beta_bernoulli.py`](https://github.com/blei-lab/edward/blob/master/examples/beta_bernoulli.py)
# in the Github repository.
# 
# __Figure 2__. Variational auto-encoder for a data set of 28 x 28 pixel images
# (Kingma & Welling, 2014; Rezende, Mohamed, & Wierstra, 2014).

# In[ ]:


import tensorflow as tf
from edward.models import Bernoulli, Normal
from keras.layers import Dense

N = 55000  # number of data points
d = 50  # latent dimension

# Probabilistic model
z = Normal(loc=tf.zeros([N, d]), scale=tf.ones([N, d]))
h = Dense(256, activation='relu')(z)
x = Bernoulli(logits=Dense(28 * 28, activation=None)(h))

# Variational model
qx = tf.placeholder(tf.float32, [N, 28 * 28])
qh = Dense(256, activation='relu')(qx)
qz = Normal(loc=Dense(d, activation=None)(qh),
            scale=Dense(d, activation='softplus')(qh))


# For an example of it in use, see
# [`examples/vae.py`](https://github.com/blei-lab/edward/blob/master/examples/vae.py)
# in the Github repository.
# 
# __Figure 3__. Bayesian recurrent neural network (Radford M Neal, 2012).
# The program has an unspecified number of time steps; it uses a
# symbolic for loop (`tf.scan`).

# In[ ]:


import edward as ed
import tensorflow as tf
from edward.models import Normal

H = 50  # number of hidden units
D = 10  # number of features

def rnn_cell(hprev, xt):
  return tf.tanh(ed.dot(hprev, Wh) + ed.dot(xt, Wx) + bh)

Wh = Normal(loc=tf.zeros([H, H]), scale=tf.ones([H, H]))
Wx = Normal(loc=tf.zeros([D, H]), scale=tf.ones([D, H]))
Wy = Normal(loc=tf.zeros([H, 1]), scale=tf.ones([H, 1]))
bh = Normal(loc=tf.zeros(H), scale=tf.ones(H))
by = Normal(loc=tf.zeros(1), scale=tf.ones(1))

x = tf.placeholder(tf.float32, [None, D])
h = tf.scan(rnn_cell, x, initializer=tf.zeros(H))
y = Normal(loc=tf.matmul(h, Wy) + by, scale=1.0)


# ## Section 4. Compositional Representations for Inference
# 
# __Figure 5__. Hierarchical model (Gelman & Hill, 2006).
#   It is a mixture of Gaussians over
#   $D$-dimensional data $\{x_n\}\in\mathbb{R}^{N\times D}$. There are
#   $K$ latent cluster means $\beta\in\mathbb{R}^{K\times D}$.

# In[ ]:


import tensorflow as tf
from edward.models import Categorical, Normal

N = 10000  # number of data points
D = 2  # data dimension
K = 5  # number of clusters

beta = Normal(loc=tf.zeros([K, D]), scale=tf.ones([K, D]))
z = Categorical(logits=tf.zeros([N, K]))
x = Normal(loc=tf.gather(beta, z), scale=tf.ones([N, D]))


# It is used below in Figure 6 (left/right) and Figure * (variational EM).
# 
# __Figure 6__ __(left)__. Variational inference
# (Jordan, Ghahramani, Jaakkola, & Saul, 1999).
# It performs inference on the model defined in Figure 5.

# In[ ]:


import edward as ed
import numpy as np
import tensorflow as tf
from edward.models import Categorical, Normal

x_train = np.zeros([N, D])

qbeta = Normal(loc=tf.Variable(tf.zeros([K, D])),
               scale=tf.exp(tf.Variable(tf.zeros([K, D]))))
qz = Categorical(logits=tf.Variable(tf.zeros([N, K])))

inference = ed.VariationalInference({beta: qbeta, z: qz}, data={x: x_train})


# __Figure 6__ __(right)__. Monte Carlo (Robert & Casella, 1999).
# It performs inference on the model defined in Figure 5.

# In[ ]:


import edward as ed
import numpy as np
import tensorflow as tf
from edward.models import Empirical

x_train = np.zeros([N, D])

T = 10000  # number of samples
qbeta = Empirical(params=tf.Variable(tf.zeros([T, K, D])))
qz = Empirical(params=tf.Variable(tf.zeros([T, N])))


# __Figure 7__. Generative adversarial network
# (Goodfellow et al., 2014).

# In[ ]:


import edward as ed
import numpy as np
import tensorflow as tf
from edward.models import Normal
from keras.layers import Dense

N = 55000  # number of data points
d = 50  # latent dimension

def generative_network(eps):
  h = Dense(256, activation='relu')(eps)
  return Dense(28 * 28, activation=None)(h)

def discriminative_network(x):
  h = Dense(28 * 28, activation='relu')(x)
  return Dense(1, activation=None)(h)

# DATA
x_train = np.zeros([N, 28 * 28])

# MODEL
eps = Normal(loc=tf.zeros([N, d]), scale=tf.ones([N, d]))
x = generative_network(eps)

# INFERENCE
inference = ed.GANInference(data={x: x_train},
                            discriminator=discriminative_network)


# For an example of it in use, see the
# [generative adversarial networks](http://edwardlib.org/tutorials/gan) tutorial.
# 
# __Figure *__. Variational EM (Radford M. Neal & Hinton, 1993).
# It performs inference on the model defined in Figure 5.

# In[ ]:


import edward as ed
import numpy as np
import tensorflow as tf
from edward.models import Categorical, PointMass

# DATA
x_train = np.zeros([N, D])

# INFERENCE
qbeta = PointMass(params=tf.Variable(tf.zeros([K, D])))
qz = Categorical(logits=tf.Variable(tf.zeros([N, K])))

inference_e = ed.VariationalInference({z: qz}, data={x: x_train, beta: qbeta})
inference_m = ed.MAP({beta: qbeta}, data={x: x_train, z: qz})

inference_e.initialize()
inference_m.initialize()

tf.initialize_all_variables().run()

for _ in range(10000):
  inference_e.update()
  inference_m.update()


# For more details, see the
# [inference compositionality](http://edwardlib.org/api/inference-compositionality) webpage.
# See
# [`examples/factor_analysis.py`](https://github.com/blei-lab/edward/blob/master/examples/factor_analysis.py) for
# a version performing Monte Carlo EM for logistic factor analysis
# in the Github repository.
# It leverages Hamiltonian Monte Carlo for the E-step to perform maximum
# marginal a posteriori.
# 
# __Figure *__. Data subsampling.

# In[ ]:


import edward as ed
import tensorflow as tf
from edward.models import Categorical, Normal

N = 10000  # number of data points
M = 128  # batch size during training
D = 2  # data dimension
K = 5  # number of clusters

# DATA
x_batch = tf.placeholder(tf.float32, [M, D])

# MODEL
beta = Normal(loc=tf.zeros([K, D]), scale=tf.ones([K, D]))
z = Categorical(logits=tf.zeros([M, K]))
x = Normal(loc=tf.gather(beta, z), scale=tf.ones([M, D]))

# INFERENCE
qbeta = Normal(loc=tf.Variable(tf.zeros([K, D])),
               scale=tf.nn.softplus(tf.Variable(tf.zeros([K, D]))))
qz = Categorical(logits=tf.Variable(tf.zeros([M, D])))

inference = ed.VariationalInference({beta: qbeta, z: qz}, data={x: x_batch})
inference.initialize(scale={x: float(N) / M, z: float(N) / M})


# For more details, see the
# [data subsampling](http://edwardlib.org/api/inference-data-subsampling) webpage.
# 
# ## Section 5. Experiments
# 
# __Figure 9__. Bayesian logistic regression with Hamiltonian Monte Carlo.

# In[ ]:


import edward as ed
import numpy as np
import tensorflow as tf
from edward.models import Bernoulli, Empirical, Normal

N = 581012  # number of data points
D = 54  # number of features
T = 100  # number of empirical samples

# DATA
x_data = np.zeros([N, D])
y_data = np.zeros([N])

# MODEL
x = tf.Variable(x_data, trainable=False)
beta = Normal(loc=tf.zeros(D), scale=tf.ones(D))
y = Bernoulli(logits=ed.dot(x, beta))

# INFERENCE
qbeta = Empirical(params=tf.Variable(tf.zeros([T, D])))
inference = ed.HMC({beta: qbeta}, data={y: y_data})
inference.run(step_size=0.5 / N, n_steps=10)


# For an example of it in use, see
# [`examples/bayesian_logistic_regression.py`](https://github.com/blei-lab/edward/blob/master/examples/bayesian_logistic_regression.py)
# in the Github repository.
# 
# ## Appendix A. Model Examples
# 
# __Figure 10__. Bayesian neural network for classification (Denker, Schwartz, Wittner, & Solla, 1987).

# In[ ]:


import tensorflow as tf
from edward.models import Bernoulli, Normal

N = 1000  # number of data points
D = 528  # number of features
H = 256  # hidden layer size

W_0 = Normal(loc=tf.zeros([D, H]), scale=tf.ones([D, H]))
W_1 = Normal(loc=tf.zeros([H, 1]), scale=tf.ones([H, 1]))
b_0 = Normal(loc=tf.zeros(H), scale=tf.ones(H))
b_1 = Normal(loc=tf.zeros(1), scale=tf.ones(1))

x = tf.placeholder(tf.float32, [N, D])
y = Bernoulli(logits=tf.matmul(tf.nn.tanh(tf.matmul(x, W_0) + b_0), W_1) + b_1)


# For an example of it in use, see
# [`examples/getting_started_example.py`](https://github.com/blei-lab/edward/blob/master/examples/getting_started_example.py)
# in the Github repository.
# 
# __Figure 11__. Latent Dirichlet allocation (D. M. Blei, Ng, & Jordan, 2003).

# In[ ]:


import tensorflow as tf
from edward.models import Categorical, Dirichlet

D = 4  # number of documents
N = [11502, 213, 1523, 1351]  # words per doc
K = 10  # number of topics
V = 100000  # vocabulary size

theta = Dirichlet(tf.zeros([D, K]) + 0.1)
phi = Dirichlet(tf.zeros([K, V]) + 0.05)
z = [[0] * N] * D
w = [[0] * N] * D
for d in range(D):
  for n in range(N[d]):
    z[d][n] = Categorical(theta[d, :])
    w[d][n] = Categorical(phi[z[d][n], :])


# __Figure 12__. Gaussian matrix factorization
# (Salakhutdinov & Mnih, 2011).

# In[ ]:


import tensorflow as tf
from edward.models import Normal

N = 10
M = 10
K = 5  # latent dimension

U = Normal(loc=tf.zeros([M, K]), scale=tf.ones([M, K]))
V = Normal(loc=tf.zeros([N, K]), scale=tf.ones([N, K]))
Y = Normal(loc=tf.matmul(U, V, transpose_b=True), scale=tf.ones([N, M]))


# __Figure 13__. Dirichlet process mixture model (Antoniak, 1974).

# In[ ]:


import tensorflow as tf
from edward.models import DirichletProcess, Normal

N = 1000  # number of data points
D = 5  # data dimensionality

dp = DirichletProcess(alpha=1.0, base=Normal(loc=tf.zeros(D), scale=tf.ones(D)))
mu = dp.sample(N)
x = Normal(loc=loc, scale=tf.ones([N, D]))


# To see the essential component defining the `DirichletProcess`, see
# [`examples/pp_dirichlet_process.py`](https://github.com/blei-lab/edward/blob/master/examples/pp_dirichlet_process.py)
# in the Github repository. Its source implementation can be found at
# [`edward/models/dirichlet_process.py`](https://github.com/blei-lab/edward/blob/master/edward/models/dirichlet_process.py).
# 
# ## Appendix B. Inference Examples
# 
# __Figure *__. Stochastic variational inference (M. D. Hoffman, Blei, Wang, & Paisley, 2013). 
# For more details, see the
# [data subsampling](http://edwardlib.org/api/inference-data-subsampling) webpage.
# 
# ## Appendix C. Complete Examples
# 
# __Figure 15__. Variational auto-encoder
# (Kingma & Welling, 2014; Rezende et al., 2014).
# See the script
# \href{https://github.com/blei-lab/edward/blob/master/examples/vae.py}{\texttt{examples/vae.py}}
# in the Github repository.
# 
# __Figure 16__. Exponential family embedding (Rudolph, Ruiz, Mandt, & Blei, 2016).
# A Github repository with comprehensive features is available at
# [mariru/exponential_family_embeddings](https://github.com/mariru/exponential_family_embeddings).