Mixtures of Deterministic-Probabilistic Networks and their AND/OR Search Space

TL;DR

This paper presents mixed networks combining probabilistic and deterministic data, introduces an AND/OR search space, and demonstrates how separating constraints can significantly improve search efficiency in graphical models.

Contribution

It proposes a novel mixed network framework and an AND/OR search space, enabling more efficient reasoning by separating constraint processing from probabilistic inference.

Findings

Mixed networks can be exponentially more efficient than pure belief networks.

The AND/OR search space effectively prunes the search process.

Separating constraints improves reasoning efficiency when constraints are tractable.

Abstract

The paper introduces mixed networks, a new framework for expressing and reasoning with probabilistic and deterministic information. The framework combines belief networks with constraint networks, defining the semantics and graphical representation. We also introduce the AND/OR search space for graphical models, and develop a new linear space search algorithm. This provides the basis for understanding the benefits of processing the constraint information separately, resulting in the pruning of the search space. When the constraint part is tractable or has a small number of solutions, using the mixed representation can be exponentially more effective than using pure belief networks which odel constraints as conditional probability tables.