Query DAGs: A practical paradigm for implementing belief-network inference

We describe a new paradigm for implement­ ing inference in belief networks, which con­ sists of two steps: (1) compiling a belief network into an arithmetic expression called a Query DAG (Q-DAG); and (2) answering queries using a simple evaluation algorithm. Each non-leaf node of a Q-DAG represents a numeric operation, a number, or a symbol for evidence. Each leaf node of a Q-DAG repre­ sents the answer to a network query, that is, the probability of some event of interest. It appears that Q-DAGs can be generated us­ ing any of the standard algorithms for exact inference in belief networks we show how they can be generated using the clustering al­ gorithm. The time and space complexity of a Q-DAG generation algorithm is no worse than the time complexity of the inference al­ gorithm on which it is based. T�e COII_lPI:x­ ity of a Q-DAG evaluatzon algonthm IS !�n­ ear in the size of the Q-DAG, and such In­ ference amounts to a standard evaluation of the arithmetic expression it represents. The main value of Q-DAGs is in reducing the soft­ ware and hardware resources required to uti­ lize belief networks in on-line, real-world ap­ plications. The proposed framework also fa­ cilitates the development of on-line inference on different software and hardware platforms due to the simplicity of the Q-DAG evalua­ tion algorithm.