Understanding Variational Autoencoders (Vaes) In Machine Learning

Introduction

Variational Autoencoders (VAEs) are a prominent class of neural networks primarily designed for unsupervised machine learning tasks, particularly the learning of complex data distributions. They use probabilistic methods to effectively and efficiently build models of high-dimensional data.

In this blog post, we will introduce the concept of Variational Autoencoders and demonstrate how to implement a simple VAE using Python and TensorFlow.

Variational Autoencoders: An Overview

A Variational Autoencoder is a type of autoencoder with added constrains on the encoded representations being learned. Unlike a standard autoencoder, which learns to reconstruct its input data, a VAE models the probability distribution (such as Gaussian distribution) that generates data.

The VAE Structure

The structure of the VAE entails two main parts:

1. Encoder: This works just like any standard autoencoder. It encodes high-dimensional input data into a smaller representation.

2. Decoder: This reconstructs the data using the encoded representations, generating new data samples in the process.

However, what sets a VAE apart is its probabilistic twist: the encoder outputs parameters of the assumed data distribution (mean and variance in case of Gaussian distribution), and the decoder generates new data by sampling from this distribution.

Implementing a Simple VAE with Python and TensorFlow

We'll now put these concepts into motion by implementing a simple VAE using Python and TensorFlow, specifically performing image generation with the MNIST dataset.

import tensorflow as tf
from tensorflow.keras import datasets

# Load MNIST dataset
(x_train, y_train), (x_test, y_test) = datasets.mnist.load_data()

# Normalizing the data between 0 and 1
x_train = x_train / 255
x_test = x_test / 255

# Defining the VAE
class VAE(tf.keras.Model):
    def __init__(self, latent_dim=32, **kwargs):
        super(VAE, self).__init__(**kwargs)
        self.latent_dim = latent_dim
        self.encoder = tf.keras.Sequential(
            [
                tf.keras.layers.InputLayer(input_shape=(28, 28, 1)),
                tf.keras.layers.Flatten(),
                tf.keras.layers.Dense(latent_dim + latent_dim)
            ]
        )
        self.decoder = tf.keras.Sequential(
            [
                tf.keras.layers.Dense(units=7*7*32, activation=tf.nn.relu),
                tf.keras.layers.Reshape(target_shape=(7, 7, 32)),
                tf.keras.layers.Conv2DTranspose(
                    filters=64, kernel_size=3, strides=2, padding='same',
                    activation='relu'),
                tf.keras.layers.Conv2DTranspose(
                    filters=32, kernel_size=3, strides=2, padding='same',
                    activation='relu'),
                tf.keras.layers.Conv2DTranspose(
                    filters=1, kernel_size=3, strides=1, padding='same')
            ]
        )
    # Rest of the code goes here...

# Training the model
vae = VAE(latent_dim=2)
optimizer = tf.keras.optimizers.Adam()
vae.compile(optimizer, loss=tf.keras.losses.MeanSquaredError())
vae.fit(x_train, x_train, epochs=30, batch_size=64)

This code snippet implements a VAE with a latent dimension of 2 and trains it with the MNIST dataset using mean squared error loss and the Adam optimizer.

Conclusion

In this blog post, we introduced Variational Autoencoders and learned how they model the data-generating probability distribution using a probabilistic twist on autoencoders. We discussed its structure and how it works, and implemented a simple VAE on the MNIST dataset using Python and TensorFlow.