Query DAGs: A Practical Paradigm for Implementing Belief Network Inference

TL;DR

This paper introduces Query DAGs, a new method for belief network inference that compiles networks into arithmetic expressions, simplifying evaluation and reducing resource requirements for real-world applications.

Contribution

It presents a novel paradigm for belief network inference using Q-DAGs, which can be generated from existing algorithms and evaluated efficiently.

Findings

Q-DAGs can be generated using clustering and conditioning algorithms.

Q-DAG evaluation is linear in the size of the Q-DAG.

Q-DAGs reduce resource requirements for online belief network inference.

Abstract

We describe a new paradigm for implementing inference in belief networks, which relies on compiling a belief network into an arithmetic expression called a Query DAG (Q-DAG). 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 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 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; that of a Q-DAG on-line 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 main 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, given the simplicity of the Q-DAG evaluation algorithm. This paper describes this new paradigm for probabilistic inference, explaining how it works, its uses, and outlines some of the research directions that it leads to.