Incremental Dynamic Construction of Layered Polytree Networks

Certain classes of problems, including perceptual data understanding, robotics, discovery, and learning, can be represented as incremental, dynamically constructed belief networks. These automatically constructed networks can be dynamically extended and modified as evidence of new individuals becomes available. The main result of this paper is the incremental extension of the singly connected polytree network in such a way that the network retains its singly connected polytree structure after the changes. The algorithm is deterministic and is guaranteed to have a complexity of single node addition that is at most of order proportional to the number of nodes (or size) of the network. Additional speed-up can be achieved by maintaining the path information. Despite its incremental and dynamic nature, the algorithm can also be used for probabilistic inference in belief networks in a fashion similar to other exact inference algorithms.

[1]  Kuo-Chu Chang,et al.  Node Aggregation for Distributed Inference in Bayesian Networks , 1989, IJCAI.

[2]  Ross D. Shachter,et al.  Symbolic Probabilistic Inference in Belief Networks , 1990, AAAI.

[3]  Richard E. Neapolitan,et al.  Probabilistic reasoning in expert systems - theory and algorithms , 2012 .

[4]  Michael Luby,et al.  Approximating Probabilistic Inference in Bayesian Belief Networks is NP-Hard , 1993, Artif. Intell..

[5]  Kristian G. Olesen,et al.  An algebra of bayesian belief universes for knowledge-based systems , 1990, Networks.

[6]  Ross D. Shachter,et al.  Simulation Approaches to General Probabilistic Inference on Belief Networks , 2013, UAI.

[7]  Alfred V. Aho,et al.  The Design and Analysis of Computer Algorithms , 1974 .

[8]  Ronald L. Rivest,et al.  The Design and Analysis of Computer Algorithms , 1990 .

[9]  Gregory F. Cooper,et al.  Stochastic simulation of Bayesian belief networks , 1987, Int. J. Approx. Reason..

[10]  Tod S. Levitt,et al.  Model-Based Influence Diagrams for Machine Vision , 1989, UAI.

[11]  Dan Geiger,et al.  Identifying independence in bayesian networks , 1990, Networks.

[12]  Ross D. Shachter,et al.  Fusion and Propagation with Multiple Observations in Belief Networks , 1991, Artif. Intell..

[13]  Judea Pearl,et al.  Evidential Reasoning Using Stochastic Simulation of Causal Models , 1987, Artif. Intell..

[14]  Gregory F. Cooper,et al.  A combination of exact algorithms for inference on Bayesian belief networks , 1991, Int. J. Approx. Reason..

[15]  Kuo-Chu Chang,et al.  Weighing and Integrating Evidence for Stochastic Simulation in Bayesian Networks , 2013, UAI.

[16]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[17]  Gregory F. Cooper,et al.  The Computational Complexity of Probabilistic Inference Using Bayesian Belief Networks , 1990, Artif. Intell..

[18]  Gregory F. Cooper,et al.  A randomized approximation algorithm for probabilistic inference on bayesian belief networks , 1990, Networks.

[19]  Judea Pearl,et al.  A Computational Model for Causal and Diagnostic Reasoning in Inference Systems , 1983, IJCAI.

[20]  Judea Pearl,et al.  Fusion, Propagation, and Structuring in Belief Networks , 1986, Artif. Intell..

[21]  John Mark Agosta.  Probabilistic recognition networks: an application of influence diagrams to visual recognition , 1992 .

[22]  Richard E. Neapolitan,et al.  Probabilistic reasoning in expert systems - theory and algorithms , 2012 .

[23]  David J. Spiegelhalter,et al.  Local computations with probabilities on graphical structures and their application to expert systems , 1990 .

[24]  Ross D. Shachter.  Evaluating Influence Diagrams , 1986, Oper. Res..