AND/OR Multi-Valued Decision Diagrams (AOMDDs) for Weighted Graphical Models

Robert Mateescu; Rina Dechter

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arXiv · 1206.5266

AND/OR Multi-Valued Decision Diagrams (AOMDDs) for Weighted Graphical Models

Robert Mateescu·Rina Dechter

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Abstract

Compiling graphical models has recently been under intense investigation, especially for probabilistic modeling and processing. We present here a novel data structure for compiling weighted graphical models (in particular, probabilistic models), called AND/OR Multi-Valued Decision Diagram (AOMDD). This is a generalization of our previous work on constraint networks, to weighted models. The AOMDD is based on the frameworks of AND/OR search spaces for graphical models, and Ordered Binary Decision Diagrams (OBDD). The AOMDD is a canonical representation of a graphical model, and its size and compilation time are bounded exponentially by the treewidth of the graph, rather than pathwidth as is known for OBDDs. We discuss a Variable Elimination schedule for compilation, and present the general APPLY algorithm that combines two weighted AOMDDs, and also present a search based method for compilation method. The preliminary experimental evaluation is quite encouraging, showing the potential of the AOMDD data structure.

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Robert Mateescu, Rina Dechter. 2012-06-20. AND/OR Multi-Valued Decision Diagrams (AOMDDs) for Weighted Graphical Models. https://arxiv.org/abs/1206.5266

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