DeepAI AI Chat
Log In Sign Up

A Cluster-Cumulant Expansion at the Fixed Points of Belief Propagation

by   Max Welling, et al.

We introduce a new cluster-cumulant expansion (CCE) based on the fixed points of iterative belief propagation (IBP). This expansion is similar in spirit to the loop-series (LS) recently introduced in [1]. However, in contrast to the latter, the CCE enjoys the following important qualities: 1) it is defined for arbitrary state spaces 2) it is easily extended to fixed points of generalized belief propagation (GBP), 3) disconnected groups of variables will not contribute to the CCE and 4) the accuracy of the expansion empirically improves upon that of the LS. The CCE is based on the same Möbius transform as the Kikuchi approximation, but unlike GBP does not require storing the beliefs of the GBP-clusters nor does it suffer from convergence issues during belief updating.


page 1

page 2

page 3

page 4


Local stability of Belief Propagation algorithm with multiple fixed points

A number of problems in statistical physics and computer science can be ...

A Simple Insight into Iterative Belief Propagation's Success

In Non - ergodic belief networks the posterior belief OF many queries gi...

Efficient inference in stochastic block models with vertex labels

We study the stochastic block model with two communities where vertices ...

On the Choice of Regions for Generalized Belief Propagation

Generalized belief propagation (GBP) has proven to be a promising techni...

Empirical Evaluation of Approximation Algorithms for Probabilistic Decoding

It was recently shown that the problem of decoding messages transmitted ...

Probabilistic Belief Change: Expansion, Conditioning and Constraining

The AGM theory of belief revision has become an important paradigm for i...

Choice revision on belief bases

In this contribution we explore choice revision, a sort of belief change...