Approximating probabilistic inference in Bayesian belief networks

Abstract

A belief network comprises a graphical representation of dependencies between variables of a domain and a set of conditional probabilities associated with each dependency. Unless P=NP, an efficient, exact algorithm does not exist to compute probabilistic inference in belief networks. Stochastic simulation methods, which often improve run times, provide an alternative to exact inference algorithms. We present such a stochastic simulation algorithm 2)-BNRAS that is a randomized approximation scheme. To analyze the run time, we parameterize belief networks by the dependence value P E , which is a measure of the cumulative strengths of the belief network dependencies given background evidence E. This parameterization defines the class of f-dependence networks. The run time of 2)-BNRAS is polynomial when f is a polynomial function. Thus, the results of this paper prove the existence of a class of belief networks for which inference approximation is polynomial and, hence, provably faster than any exact algorithm.

The potential of imprecision in intelligent decision making

“…In an intelligent system, this static configuration is a core of the system's "self-belief" capability [13]. This core often requires a third-party (human) intervention to ensure the system is relevant to the current situation, since it has no ability itself to transform its core belief.…”

Decision Support System to Analyze the Cause of Special Equipment Accident

“…Bayesian network is modeled in form of the directed acyclic graph, the nodes represent variables in the system, the edges with the direction represents represent the causal relationship among variables, conditional probability represent the relevancy among variables, it also could be expressed and analyze the multi-source information, which helped it deal with uncertainty problems [25,26] . Both Bayesian network inference and approximate reasoning exist NP problem [27,28] , it could be reasoning efficiently in certain conditions by combining tree algorithm, Gibbs sampling algorithm, importance sampling algorithm and so on [29,30] . Bayesian network models through the following three ways: Artificial modeling method based on expert [31] , Machine learning modeling method based on sample data [32,33] and reasoning modeling method based on knowledge [34] .…”

Intelligent systems:

“…This tool is related to the theory of belief and used for hypothesis evaluation when the evidence is uncertain [171]. A special case of belief evaluation is related to a case when we deal with multilevel preferences, which are typical for RCS value judgement [172], More complex cases of belief evaluation are related to representing degrees of belief for objects or events organized into networks [173]. Updating procedures for the value of belief are described in [174].…”