Beliefs in Markov Trees - From Local Computations to Local Valuation
This addresses the expressiveness of hypergraphs for belief propagation, offering an incremental improvement in methods for recovering belief networks from data.
The paper tackles the problem of finding the simplest hypergraph structure for uncertainty propagation via local computations, showing that conditional distributions are optimal for hyperedge valuation, which implies that belief network recovery methods cannot find simpler structures. It develops a method for recovering tree-structured belief networks, specialized for Dempster-Shafer belief functions.
This paper is devoted to expressiveness of hypergraphs for which uncertainty propagation by local computations via Shenoy/Shafer method applies. It is demonstrated that for this propagation method for a given joint belief distribution no valuation of hyperedges of a hypergraph may provide with simpler hypergraph structure than valuation of hyperedges by conditional distributions. This has vital implication that methods recovering belief networks from data have no better alternative for finding the simplest hypergraph structure for belief propagation. A method for recovery tree-structured belief networks has been developed and specialized for Dempster-Shafer belief functions