Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
Network-based heuristics for constraint-satisfaction problems
Artificial Intelligence
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
A valuation-based language for expert systems
International Journal of Approximate Reasoning
Probabilistic inference in multiply connected belief networks using loop cutsets
International Journal of Approximate Reasoning
Finding MAPs for belief networks is NP-hard
Artificial Intelligence
On the hardness of approximate reasoning
Artificial Intelligence
Approximating MAPs for belief networks is NP-hard and other theorems
Artificial Intelligence
Bucket elimination: a unifying framework for reasoning
Artificial Intelligence
Topological parameters for time-space tradeoff
Artificial Intelligence
Artificial Intelligence - special issue on computational tradeoffs under bounded resources
The Challenges of Real-Time AI
Computer
Random Generation of Bayesian Networks
SBIA '02 Proceedings of the 16th Brazilian Symposium on Artificial Intelligence: Advances in Artificial Intelligence
Approximating MAP using Local Search
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
A differential approach to inference in Bayesian networks
Journal of the ACM (JACM)
Accuracy vs. efficiency trade-offs in probabilistic diagnosis
Eighteenth national conference on Artificial intelligence
Understanding belief propagation and its generalizations
Exploring artificial intelligence in the new millennium
Efficient bayesian network inference: genetic algorithms, stochastic local search, and abstraction
Efficient bayesian network inference: genetic algorithms, stochastic local search, and abstraction
Information Theory, Inference & Learning Algorithms
Information Theory, Inference & Learning Algorithms
A differential semantics for jointree algorithms
Artificial Intelligence
The Structure and Dynamics of Networks: (Princeton Studies in Complexity)
The Structure and Dynamics of Networks: (Princeton Studies in Complexity)
Understanding the role of noise in stochastic local search: Analysis and experiments
Artificial Intelligence
Macroscopic models of clique tree growth for Bayesian networks
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 2
Diagnosing faults in electrical power systems of spacecraft and aircraft
IAAI'08 Proceedings of the 20th national conference on Innovative applications of artificial intelligence - Volume 3
Complexity results and approximation strategies for MAP explanations
Journal of Artificial Intelligence Research
Exploiting causal independence in Bayesian network inference
Journal of Artificial Intelligence Research
Variational probabilistic inference and the QMR-DT network
Journal of Artificial Intelligence Research
HUGIN: a shell for building Bayesian belief universes for expert systems
IJCAI'89 Proceedings of the 11th international joint conference on Artificial intelligence - Volume 2
Compiling Bayesian networks using variable elimination
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Efficient stochastic local search for MPE solving
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
IEEE Transactions on Knowledge and Data Engineering
Journal of Automated Reasoning
Extending factor graphs so as to unify directed and undirected graphical models
UAI'03 Proceedings of the Nineteenth conference on Uncertainty in Artificial Intelligence
Factor graphs and the sum-product algorithm
IEEE Transactions on Information Theory
Error bounds for convolutional codes and an asymptotically optimum decoding algorithm
IEEE Transactions on Information Theory
Tree-based reparameterization framework for analysis of sum-product and related algorithms
IEEE Transactions on Information Theory
MAP estimation via agreement on trees: message-passing and linear programming
IEEE Transactions on Information Theory
Turbo decoding as an instance of Pearl's “belief propagation” algorithm
IEEE Journal on Selected Areas in Communications
A search problem in complex diagnostic Bayesian networks
Knowledge-Based Systems
Optimizing parallel belief propagation in junction treesusing regression
Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining
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One of the main approaches to performing computation in Bayesian networks (BNs) is clique tree clustering and propagation. The clique tree approach consists of propagation in a clique tree compiled from a BN, and while it was introduced in the 1980s, there is still a lack of understanding of how clique tree computation time depends on variations in BN size and structure. In this article, we improve this understanding by developing an approach to characterizing clique tree growth as a function of parameters that can be computed in polynomial time from BNs, specifically: (i) the ratio of the number of a BN's non-root nodes to the number of root nodes, and (ii) the expected number of moral edges in their moral graphs. Analytically, we partition the set of cliques in a clique tree into different sets, and introduce a growth curve for the total size of each set. For the special case of bipartite BNs, there are two sets and two growth curves, a mixed clique growth curve and a root clique growth curve. In experiments, where random bipartite BNs generated using the BPART algorithm are studied, we systematically increase the out-degree of the root nodes in bipartite Bayesian networks, by increasing the number of leaf nodes. Surprisingly, root clique growth is well-approximated by Gompertz growth curves, an S-shaped family of curves that has previously been used to describe growth processes in biology, medicine, and neuroscience. We believe that this research improves the understanding of the scaling behavior of clique tree clustering for a certain class of Bayesian networks; presents an aid for trade-off studies of clique tree clustering using growth curves; and ultimately provides a foundation for benchmarking and developing improved BN inference and machine learning algorithms.