Nested Junction Trees

The efficiency of inference in both the Hugin and, most notably, the Shafer-Shenoy archi­ tectures can be improved by exploiting the independence relations induced by the incom­ ing messages of a clique. That is, the mes­ sage to be sent from a clique can be com­ puted via a factorization of the clique poten­ tial in the form of a junction tree. In this pa­ per we show that by exploiting such nested junction trees in the computation of messages both space and time costs of the conventional propagation methods may be reduced. The paper presents a structured way of exploit­ ing the nested junction trees technique to achieve such reductions. The usefulness of the method is emphasized through a thor­ ough empirical evaluation involving ten large real-world Bayesian networks and the Hugin inference algorithm.