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Abstract:
Bayesian belief propagation in graphical models has been
recently shown to have very close ties to inference methods based
in statistical physics. After Yedidia
et al
. demonstrated that belief propagation fixed points correspond
to extrema of the so-called Bethe free energy, Yuille derived a
double loop algorithm that is guaranteed to converge to a local
minimum of the Bethe free energy. Yuille's algorithm is based on
a certain decomposition of the Bethe free energy and he mentions
that other decompositions are possible and may even be fruitful.
In the present work, we begin with the Bethe free energy and show
that it has a principled interpretation as pairwise mutual
information minimization and marginal entropy maximization
(MIME). Next, we construct a family of free energy functions from
a spectrum of decompositions of the original Bethe free energy.
For each free energy in this family, we develop a new algorithm
that is guaranteed to converge to a local minimum. Preliminary
computer simulations are in agreement with this theoretical
development.
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