Decision-making in distributed sensor networks: a belief-theoretic Bayes-like

A Dempster-Shafer (DS) belief theoretic evidence updating strategy is ideally suited to accommodate the difficulties associated with the availability of only incomplete information at each node of a distributed sensor network (DSN). Such a strategy however must also account for sensor heterogeneity, 'inertia' and 'integrity' of the existing knowledge base and reliability of the data generated at each sensor node. In this paper, we propose a Bayes-like theorem that can conveniently address these issues while allowing one to compute the 'posterior' belief of a 'hypothesis' given an 'observation' when the corresponding 'likelihoods' and 'priors' are available. Unlike previous work on DS belief theoretic generalizations of Bayes' theorem, our work is based on the Fagin-Halpern conditional notions that can be considered more 'natural extensions' of corresponding Bayesian notions

Rule mining and classification in imperfect databases

A rule-based classifier learns rules from a set of training data instances with assigned class labels and then uses those rules to assign a class label for a new incoming data instance. To accommodate data imperfections, a probabilistic relational model would represent the attributes by probabilistic functions. One extension to this model uses belief functions instead. Such an approach can represent a wider range of data imperfections. However, the task of extracting frequent patterns and rules from such a "belief theoretic" relational database has to overcome a potentially enormous computational burden. In this work, we present a data structure that is an alternate representation of a belief theoretic relational database. We then develop efficient algorithms to query for belief of item sets, extract frequent item sets and generate corresponding association rules from this representation. This set of rules is then used as the basis on which an unknown data instance, whose attributes are represented via belief functions, is classified. These algorithms are tested on a data set collected from a test bed that mimics airport threat detection and classification scenario where both data attributes and threat class labels may possess imperfections