Information Geometry beyond the Exponential Family

ABSTRACT: Information geometry treats families of probability distributions as curves or surfaces in an abstract space of probability distributions. Theoretical results from this field exist in multiple application domains and at least some real systems employ data fusion techniques based on this research. We propose the combination of techniques that have been developed and applied for different applications into a coherent mathematical framework. We will further use the framework to design, analyze, and test a novel data fusion algorithm appropriate for use across potentially heterogeneous sensor networks. Our team includes individuals with expertise in relevant areas of mathematics, science, and engineering. We efficiently model correlations in data by allowing distributions that are not members of the exponential family. This will reduce the number of parameters necessary to characterize sensor measurements. This approach is backed by published results for data fusion problems in different application areas, but we explicitly connect it to published results for the applications described in the solicitation, which will emerge as a special case of our more general mathematical framework.; BENEFIT: Successful completion of our Phase I plan will lay a mathematical framework for a variety of data fusion algorithms that provide efficient characterization of sensor data. This will lead to more accurate fusion on current systems and enable distributed sensors to provide data-rich messages without transmitting large messages. We provide specific transition targets with large and medium sized DOD contractors. We also describe a plan for transitioning elements of the probability modeling to the financial industry.