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# Perturbative Corrections to Expectation Consistent Approximate Inference

Published on Dec 31, 20073708 Views

Algorithms for approximate inference usually come without any guarantee for the quality of the approximation. Nevertheless, we often find cases where such algorithms perform extremely well on the comp

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#### Chapter list

Perturbative Corrections for Expectation Propagation00:00

Outline01:31

Expectation Propagation (EP) in a nutshell02:56

Fixed point equations04:40

The partition function05:45

EP is optimal to linear order08:05

Express joint density via q & qn08:46

Corrections for models with pairwise couplings09:46

Correction to marginal likelihood (partition function)11:20

Characteristic function & cumulants13:59

Express the ratio by cumulants15:35

Performing the average16:54

Perturbation expansion to Free energy18:38

Gaussian averages & Feynman graphs - 121:00

Gaussian averages & Feynman graphs - 222:01

Conjecture: EP is fairly accurate if...23:00

Gaussian process classification24:21

The cumulants25:48

Correction to log partition function25:54

Log partition function + correction26:48

Correcting the posterior mean27:26

A toy Ising case31:42

Random Ising networks - 132:53

Random Ising networks - 233:31

Random Ising networks - 334:47

Outlook35:36