Uncertainty
Propagating belief functions in qualitative Markov trees
Shafer, G. | Shenoy, P. P. | Mellouli, K.
This article is concerned with the computational aspects of combining evidence within the theory of belief functions. It shows that by taking advantage of logical or categorical relations among the questions we consider, we can sometimes avoid the computational complexity associated with brute-force application of Dempster's rule. The mathematical setting for this article is the lattice of partitions of a fixed overall frame of discernment. Different questions are represented by different partitions of this frame, and the categorical relations among these questions are represented by relations of qualitative conditional independence or dependence among the partitions. Qualitative conditional independence is a categorical rather than a probabilistic concept, but it is analogous to conditional independence for random variables.
A model for reasoning about persistence and causation
Dean, Thomas | Kanazawa., Keiji
In most situations, however, there is not enough information to make accurate predictions.
Simulation approaches to general probabilistic inference on belief networks
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Weighting and integrating evidence for stochastic simulation in Bayesian networks
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Heuristic search as evidential reasoning
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Minkowski-r Back-Propagation: Learning in Connectionist Models with Non-Euclidian Error Signals
Hanson, Stephen Jose, Burr, David J.
It can be shown that neural-like networks containing a single hidden layer of nonlinear activation units can learn to do a piece-wise linear partitioning of a feature space [2]. One result of such a partitioning is a complex gradient surface on which decisions about new input stimuli will be made. The generalization, categorization and clustering propenies of the network are therefore detennined by this mapping of input stimuli to this gradient swface in the output space. This gradient swface is a function of the conditional probability distributions of the output vectors given the input feature vectors as well as a function of the error relating the teacher signal and output.
Minkowski-r Back-Propagation: Learning in Connectionist Models with Non-Euclidian Error Signals
Hanson, Stephen Jose, Burr, David J.
It can be shown that neural-like networks containing a single hidden layer of nonlinear activation units can learn to do a piece-wise linear partitioning of a feature space [2]. One result of such a partitioning is a complex gradient surface on which decisions about new input stimuli will be made. The generalization, categorization and clustering propenies of the network are therefore detennined by this mapping of input stimuli to this gradient swface in the output space. This gradient swface is a function of the conditional probability distributions of the output vectors given the input feature vectors as well as a function of the error relating the teacher signal and output.