7 · Latent variables, VAEs, GANs, and flows

7 · Latent variables, VAEs, GANs, and flows#

Chapter status: outline

This is the planned scope of Chapter 7. The complete lesson, executable examples, and solutions will be developed later. Chapter 1 is available now.

Question. What alternatives to sequential factorization can represent a complex distribution?

Learn: the encoder/decoder view of a VAE, the evidence lower bound (ELBO), reparameterization, and a conceptual comparison with adversarial learning and invertible flows.
Statistical lens: latent-variable models, variational inference, density-ratio ideas, and change of variables. Compare objectives, sampling, and access to likelihoods.
Python practice: derive the ELBO and implement a small VAE on synthetic two-dimensional data. Treat GANs and flows as comparison topics on the first pass.
Self-check: separate the latent prior, approximate posterior, and observation model; explain why matching a few summary statistics cannot establish distributional equivalence.
Reading: Auto-Encoding Variational Bayes.