UMass LIVING

June 22, 2009

(Jun 25 3-5pm) Pre-meeting Overview: Wainwright / Jordan, ch 4.3

Filed under: Uncategorized — umassliving @ 6:14 pm
Tags: ,

This week’s reading is on expectation propagation (EP), another method for approximating the negative entropy A^\ast and the set of realizable mean parameters \mathcal{M}.

The idea behind EP is to partition the sufficient statistics into a tractable component and an intractable component, such that it is possible to exactly compute marginals in polynomial time for the distribution associated with the tractable component, as well as the distributions associated with the tractable component combined with any one element of the intractable component.

This partitioning leads to an approximation of \mathcal{M} as \mathcal{L} given in Equation 4.67 (how do we know that \mathcal{L} is convex?), and an approximation of the entropy as H_{ep} given in Equation 4.68.  As before, we can apply the Lagrangian method to the resulting constrained optimization problem, and derive the moment matching EP updates (Fig 4.7).

Important things to follow:

  • The running example of the mixture model – Example 4.8, Example 4.12
  • How the Bethe approximation can be seen as a specific case of EP and sum-product as a case of moment matching – Example 4.9, Example 4.10
  • Deriving the EP updates – Section 4.3.2
  • Tree-structured EP – Example 4.11

To think about:

The Bethe approximation is a special case of EP where all the sufficient statistics associated with the nodes are put into the tractable component, and each sufficient statistic associated with an edge is an element of the intractable component.  How would H_{ep} and \mathcal{L} change if, instead, we took the sufficient statistic associated with one particular node, removed it from the tractable component, and made it a separate element of the intractable component?

Advertisements

Leave a Comment »

No comments yet.

RSS feed for comments on this post. TrackBack URI

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

Create a free website or blog at WordPress.com.

%d bloggers like this: