Temporal Bayes Net Information & Knowledge Entropy

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1 December 2018
Kenneth J. Hintz, Steve Darcy

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Various information measures have been defined on Bayes Nets (BN) with the assumption that the Bayes Net is stationary. Our interest is in the utilization of a BN as a component of a real-time, information-based sensor management system wherein the dynamics of the situation cause changes both in the structure and underlying probabilities of the nodes in the BN. If a BN is used to represent the situation assessment (SA) of an environment as a result of our observations of that environment, we can say that the BN represents our knowledge about the situation in the form of a temporal Bayes net (TBN). If one were to not observe the processes in an environment with additional sensor observations, then the underlying probabilities of at least some of the BN nodes diffuse at a rate dependent on the dynamics of the process whose uncertainty is represented by that node, hence the use of the modifier temporal. This loss of knowledge in the form of increasing uncertainty results in information flow from the TBN, or, as we refer to it here, temporal information loss. In order to compensate for this temporal information loss and maintain or improve our knowledge of an environment, the environment needs to be observed by obtaining data. We focus in this paper on choosing a global TBN information measure In doing so, we differentiate between aleatory nodes with stationary uncertainties and epistemic nodes with temporal uncertainties, as well as formulate a dynamic representation of these temporal uncertainties. We provide several examples of temporal information loss under different dynamic assumptions.