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

We describe a new paradigm for implementing inference in belief networks, which consists 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 node of a Q-DAG represents a numeric operation, a number, or a symbol for evidence. Each leaf node of a Q-DAG represents the answer to a network query, that is, the probability of some event of interest. It appears that Q-DAGs can be generated using any of the standard algorithms for exact inference in belief networks - we show how they can be generated using clustering and conditioning algorithms. The time and space complexity of a Q-DAG generation algorithm is no worse than the time complexity of the inference algorithm on which it is based. The complexity of a Q-DAG evaluation algorithm is linear in the size of the Q-DAG, and such inference amounts to a standard evaluation of the arithmetic expression it represents. The intended value of Q-DAGs is in reducing the software and hardware resources required to utilize belief networks in on-line, real-world applications. The proposed framework also facilitates the development of on-line inference on different software and hardware platforms due to the simplicity of the Q-DAG evaluation algorithm. Interestingly enough, Q-DAGs were found to serve other purposes: simple techniques for reducing Q-DAGs tend to subsume relatively complex optimization techniques for belief-network inference, such as network-pruning and computation-caching.