Tomáš Werner presents Marginal Consistency: Upper-Bounding Partition Functions over Commutative Semirings

Let me invite you to a seminar, where I will explain a theoretically interesting
(though practically perhaps not directly useful) formalism, which unifies
several known algorithms for approximate inference. This was published in a
journal last year. A detailed abstract follows.

Many inference tasks in pattern recognition and artificial intelligence lead to
partition functions in which addition and multiplication are abstract binary
operations forming a commutative semiring. By generalizing max-sum diffusion
(one of convergent message passing algorithms for approximate MAP inference in
graphical models), we propose an iterative algorithm to upper bound such
partition functions over commutative semirings. The iteration of the algorithm
is remarkably simple: change any two factors of the partition function such that
their product remains the same and their overlapping marginals become equal. In
many commutative semirings, repeating this iteration for different pairs of
factors converges to a fixed point when the overlapping marginals of every pair
of factors coincide. We call this state marginal consistency. During that, an
upper bound on the partition function monotonically decreases. This abstract
algorithm unifies several existing algorithms, including max-sum
diffusion and basic costraint propagation (or local consistency) algorithms in
constraint programming.