The interactive film is in the book's Companion

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Mean Field: Independent Factors for a Correlated Posterior

Chapter 16 · Mathematics for AI and Machine Learning · Advanced · 1:42

An interactive live film: a correlated Gaussian posterior and its mean-field approximation as two bells in 3D; coordinate ascent zig-zags the means to the true mean, and each factor's variance comes out too small.

Narration

The true posterior over two latent variables, z zero and z one, is a correlated Gaussian: a tilted bell, with an elliptical outline on the floor.

Mean field approximates it by a product of two independent factors, q zero times q one. Its outline can only be an ellipse lined up with the axes.

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 16Preview1:45Posterior Collapse: When Latents Vanish into the PriorChapter 16Preview1:36Expectation Maximization: Coordinate Ascent on the Lower BoundChapter 16Preview1:55Importance-Weighted BoundsChapter 16