NIPS '07 Workshop on Approximate Bayesian Inference in Continuous/Hybrid Models

A Completed Information Projection Interpretation of Expectation Propagation

author: John MacLaren Walsh, Electrical and Computer Engineering Department, Drexel University

Description

This talk presents an interpretation of expectation propagation (EP) as a hybrid between two different iterated Bregman projections algorithms from the convex analysis and programming literature whose convergence behavior is well studied. It is suggested that convergence results for EP may be developed through this interpretation by adapting relevant convergence proofs for the related projections algorithms. Example convergence results for special cases of EP are derived through this connection, as well as through a connection between EP and the Gauss Seidel iterative solution method.

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*Slides*
0:00	A Completed Information Projection Interpretation of Expectation Propagation
0:06	Exponential Family Densities & Rudimentary Information Geometry
1:11	Expectation Propagation
2:33	Bregman Divergences
4:32	Method of Alternating Bregman Projections
5:02	Dykstra’s Algorithm with Cyclic Bregman Projections
6:45	Two Sets Related to EP
8:32	Actual Sets P & Q for 2 Bits
8:41	EP as a Hybrid Algorithm - 1
9:53	EP as a Hybrid Algorithm - 2
10:21	What Does All This Mean
11:12	Relationship to Prior Work (What Was Innovated)
12:32	So You Don’t Go Home Hungry: Nonlinear Block Gauss Seidel Connection
12:39	- Questions
14:49	So You Don’t Go Home Hungry: Nonlinear Block Gauss Seidel Connection
16:23	Convergence Theorem by Applying NLBGS Theory
17:43	References
17:48	- Questions

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