#### Recursive Cavity Modeling

*Jason K. Johnson*

*Recursive cavity modeling* (RCM) is an approximate
inference method for MRFs that blends exact recursive inference with
variational methods that minimize relative entropy. The key idea is
to build *cavity models* of subfields. Each cavity model
provides a tractable, approximate model for statistics on the boundary
of a subfield that is useful for inference outside of the subfield.
Using a nested dissection procedure, these cavity models and a
complementary set of *blanket models* can be built up
recursively. Ultimately, this leads to approximate computation of the
marginal distribution of each variable in the MRF.

*Model thinning* plays an important role in this approach.
This involves selecting a tractable approximation to a given MRF based
on a sub-graph of the MRF (e.g., a cavity or blanket model in RCM),
which requires both selection of a sub-graph and parameter
optimization to minimize relative entropy over the class of MRFs
defined on this sub-graph (an *information projection*). An
efficient information projection method was developed using chordal
graph embedding and exploiting certain tractable representations of
Fisher information for MRFs defined on chordal graphs.