Multiply sectioned Bayesian networks (MSBNs) support multiagent probabilistic inference in distributed large problem domains. Inference with MSBNs can be performed using their compiled representations. The compilation involves moralization and triangulation of a set of local graphical structures. Privacy of agents may prevent us from compiling MSBNs at a central location. In earlier work, agents performed compilation sequentially via a depth-first traversal of the hypertree that organizes local subnets, where communication failure between any two agents would crush the whole work. In this paper, we present an asynchronous compilation method by which multiple agents compile MSBNs in full parallel. Compared with the traversal compilation, the asynchronous one is robust, self-adaptive, and fault-tolerant. Experiments show that both methods provide similar quality compilation to simple MSBNs, but the asynchronous one provides much higher quality compilation to complex MSBNs. Empirical study also indicates that the asynchronous one is consistently faster than the traversal one. Proposition 6. If T f t is properly set, Requirements 1 and 2 would be satisfied by the compiled hypertree MSDAG when PCoCompilation halts.Proof. Similar to the proof to Proposition 4.With a similar analysis as for the parallel cooperative moralization process, we have Proposition 7 for PCoCompilation regarding the termination time. 1 and 2 satisfied. ‡ Similarly for the parallel moralization, the input needs to be consistent hypertree MSDAGs. Figure 10. Standard deviation of the amount of fill-ins produced from the parallel triangulation with or without moralization fill-ins distributed in advance.
Proposition 7. Let T m be the maximum time two agents on the hypertree need to exchange a set of fill-ins properly with each other. Let T c be the maximum time an agent needs to finish a while loop cycle. Then if T f t ≥ T m , and no fill-in is observed within T f t + (0 ≤ ≤ T c ), PCoCompilation would halt safely with RequirementsFigure 11. Triangulation time by the traversal and the parallel compilations on MSBNs b − j.of triangulation, and in particular, at the end of each pass of triangulation, extra examination is needed to determine the completion of triangulation and such examination has similar computational complexity as one pass triangulation, whereas the parallel method examines the completion of triangulation in triangulating.