Variational autoencoder in TensorFlow

Variational autoencoders are the modern generative version of autoencoders. Let's build a variational autoencoder for the same preceding problem. We will test the autoencoder by providing images from the original and noisy test set.

We will use a different coding style to build this autoencoder for the purpose of demonstrating the different styles of coding with TensorFlow:

1. Start by defining the hyper-parameters:

learning_rate = 0.001
n_epochs = 20
batch_size = 100
n_batches = int(mnist.train.num_examples/batch_size)
# number of pixels in the MNIST image as number of inputs
n_inputs = 784
n_outputs = n_inputs

2. Next, define a parameter dictionary to hold the weight and bias parameters: 

params={}

3. Define the number of hidden layers in each of the encoder and decoder:

n_layers = 2
# neurons in each hidden layer
n_neurons = [512,256] 

4. The new addition in a variational encoder is that we define the dimensions of the latent variable z:

n_neurons_z = 128 # the dimensions...