Verification of DAG structures in cooperative belief network-based multiagent systems

Abstract

Multiply sectioned Bayesian networks (MSBNs) provide a framework for probabilistic reasoning in a complex single user oriented system as well as in a cooperative multi-agent distributed interpretation system. During the construction or dynamic formation of a MSBN, automatic verification of the acyclicity of the overall structure is desired. Well known algorithms for acyclicity test assume a centralized storage of the structure to be tested. We discuss why a centralized test is undesirable and propose a distributed algorithm that verifies the acyclicity through cooperation among subnets/agents. The algorithm does not require each agent to reveal its internal structure and thus supports construction of a MSBN from subnets built by different vendors.

Constructing the dependency structure of a multiagent probabilistic network

“…Thus, constructing the multiagent dependency structure amounts to finding a method to combine the known conditional independency information supplied by the individual domain experts. We have shown that the method of simply connecting the individual dependency structures in [37] may be too restrictive in some situations.…”

“…Thus, constructing the multiagent dependency structure amounts to finding a method to combine the known conditional independency information supplied by the individual domain experts. One previously proposed method [37] constructs the dependency structure of a multiagent Bayesian network. That method verifies whether the dependency structure formed by connecting the individual agent DAGs is acyclic.…”

“…This set of conflict-free full minimum covers reflects all logically implied conditional independency information for each fixed & x . For the sets q feIYePYeQg and q feIYePYeQYeRg of nonembedded GMVDs in (36) and (37), the respective conflict-free full minimum covers are…”

Building Intelligent Sensor Networks with Multiagent Graphical Models

“…However, as each subnet is private (built by an independent vendor), the global acyclicity cannot be verified by physically merging individual subnets (which requires disclosure of the internal structure of each subnet to a centralizing agent). Despite its seeming impossibility, a verification method has been developed [29] that only requires each agent to pass messages to their hypertree neighbors on whether its subnet contains any parent or child of their shared variables (but not how many and what they are). Nothing else about the internal structure of its subnet is disclosed.…”

Modelling Multiagent Bayesian Networks with Inclusion Dependencies

“…Xiang [8], and Wong and Butz [6], developed methods to ensure the dependency structure is a DAG. Problem (ii) can be sidestepped by assuming that variables common to multiple agents have the same domain.…”