DeepAI AI Chat
Log In Sign Up

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

by   Robert Mateescu, et al.

Inspired by the recently introduced framework of AND/OR search spaces for graphical models, we propose to augment Multi-Valued Decision Diagrams (MDD) with AND nodes, in order to capture function decomposition structure and to extend these compiled data structures to general weighted graphical models (e.g., probabilistic models). We present the AND/OR Multi-Valued Decision Diagram (AOMDD) which compiles a graphical model into a canonical form that supports polynomial (e.g., solution counting, belief updating) or constant time (e.g. equivalence of graphical models) queries. We provide two algorithms for compiling the AOMDD of a graphical model. The first is search-based, and works by applying reduction rules to the trace of the memory intensive AND/OR search algorithm. The second is inference-based and uses a Bucket Elimination schedule to combine the AOMDDs of the input functions via the the APPLY operator. For both algorithms, the compilation time and the size of the AOMDD are, in the worst case, exponential in the treewidth of the graphical model, rather than pathwidth as is known for ordered binary decision diagrams (OBDDs). We introduce the concept of semantic treewidth, which helps explain why the size of a decision diagram is often much smaller than the worst case bound. We provide an experimental evaluation that demonstrates the potential of AOMDDs.


page 1

page 2

page 3

page 4


Complexity of Inference in Graphical Models

It is well-known that inference in graphical models is hard in the worst...

Solving the Brachistochrone Problem by an Influence Diagram

Influence diagrams are a decision-theoretic extension of probabilistic g...

Coresets for Dependency Networks

Many applications infer the structure of a probabilistic graphical model...

Ordered AND, OR-Decomposition and Binary-Decision Diagram

In the context of knowledge compilation (KC), we study the effect of aug...

An Algebraic Graphical Model for Decision with Uncertainties, Feasibilities, and Utilities

Numerous formalisms and dedicated algorithms have been designed in the l...

Exploiting Model Equivalences for Solving Interactive Dynamic Influence Diagrams

We focus on the problem of sequential decision making in partially obser...