Learning Variational Autoencoders from ELBO

VAE architecture: encoder, latent space, decoder

In a variational autoencoder (VAE), the encoder and decoder form a probabilistic autoencoding pipeline around a latent space. The encoder takes an input data point x (e.g., an image) and maps it into a probability distribution over latent variables z, rather than a single latent vector. This latent distribution is typically parameterized (commonly as a Gaussian) by neural networks that output parameters such as the mean and (optionally) variance. The latent space is the probabilistic bottleneck: sampling from the encoder’s distribution produces a latent sample z. The decoder then maps from this latent space back to the input space, producing a reconstructed output x′ that is probabilistically modeled to be as similar as possible to the original x. Training is done jointly by optimizing an objective that balances (1) reconstruction quality (how close x′ is to x) and (2) regularization that aligns the encoder’s approximate posterior with a chosen prior over latents. This is commonly handled via the evidence lower bound (ELBO), and gradients through sampling are enabled using the reparameterization trick.

0/2 modes complete

Probabilistic modeling: prior, likelihood, posterior

0/2 modes complete