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.