Encode a distribution
A VAE commonly models a distribution over latent variables conditioned on an input. Sampling can produce different latent values for the same input.
Two pressures during training
The usual objective combines a reconstruction-related term and a regularization term that relates the latent distribution to a prior. Their balance and exact form depend on the model. Combine the mean and the fixed noise contribution to obtain this one sample.
INTERACTIVE EXPLORATION
Sample a latent value
For z = μ + σϵ, keep σ = 2 and ϵ = 0.5 and change μ.
A scalar illustration
For a normal variable z = μ + σϵ, changing μ or σ changes a sample when ϵ is fixed. This reparameterization illustrates a sampling step; it is not an entire VAE.
Check your understanding
If μ = 1, σ = 2 and ϵ = 0.5, what is z?
2.