The interactive film is in the book's Companion

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Expectation Maximization: Coordinate Ascent on the Lower Bound

Chapter 16 · Mathematics for AI and Machine Learning · Advanced · 1:36

An interactive live film: the expectation step eliminates the KL gap so the ELBO touches the true log-likelihood tangentially, while the maximization step lifts both to higher ground.

Narration

The expectation-maximization algorithm is a classical foundation for learning latent variable models, famously used to fit Gaussian mixture models to clustered data.

This algorithm can be viewed as coordinate ascent on the evidence lower bound, a green surface that never rises above the purple surface of the marginal log-likelihood.

The rest of the narration is in the book's Companion.

More from Chapter 16

Interactive1:46The Reparameterization Trick: Differentiable SamplingChapter 16Preview1:27Monte Carlo: Averages That Close In Like a FunnelChapter 16Preview1:42Mean Field: Independent Factors for a Correlated PosteriorChapter 16Preview1:45Posterior Collapse: When Latents Vanish into the PriorChapter 16Preview1:55Importance-Weighted BoundsChapter 16