An introduction to Variational Auto Encoders (VAEs)

An introduction to Variational Auto Encoders (VAEs)

Understanding Variational Autoencoders (VAEs) from theory to practice using PyTorch

VAE are latent variable models [1,2]. Such models rely on the idea that the data generated by a model can be parametrized by some variables that will generate some specific characteristics of a given data point. These variables are called latent variables.

One of the key ideas behind VAE is that instead of trying to construct a latent space (space of latent variables) explicitly and to sample from it in order to find samples that could actually generate proper outputs (as close as possible to our distribution), we construct an Encoder-Decoder like network which is split in two parts:

• The encoder learns to generate a distribution depending on input samples X from which we can sample a latent variable that is highly likely to generate X samples. In other words we learn a set of parameters θ1 that generate a distribution Q(X,θ1) from which we can sample a latent variable z maximizing P(X|z).
• The decoder part learns to generate an output which belongs to the real data distribution given a latent variable z as an input. In other words, we learn a set of parameters θ2 that generates a function f(z,θ2) that maps the latent distribution that we learned to the real data distribution of the dataset.

In order to understand the mathematics behind Variational Auto Encoders, we will go through the theory and see why these models works better than older approaches.

This article will cover the following

• How to define the construct the latent space
• How to generate data efficiently from latent space sampling.
• The final architecture of VAEs
• Some experiments showing interesting properties of VAEs