Nonparametric Nonlinear Adaptive Detection and Estimation

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NSF-ECS Proposal 0622239Nonparametric Nonlinear Adaptive Detection and EstimationObjectives and approaches: The objective of this research is to create a unifying nonlinear information processing framework to handle increasingly complex modeling and data analysis problems encountered in science and engineering. The proposed framework exploits and unifies three concepts: reproducing kernel Hilbert spaces, nonparametric kernel density estimation, and information theoretic optimality measures. Developed techniques will be illustrated in a brain interface, in which high dimensional spatiotemporal electroencelaphogram activity will be translated to intended commands for a robot. This interface will be designed to facilitate fusion with myoelectrically controlled neural prostheses.Intellectual merit: Conventional techniques relying on nonlinear programming of semiparametric models with low-order statistical criteria, which is prone to various difficulties including model complexity selection and existence of suboptimal solutions, cannot cope with the challenges of increasingly complex engineering problems. Proposed work facilitates the adaptation of nonlinear models exploiting smooth generalized linear models and principled information processing in a novel unified framework. This will advance the state-of-the-art in nonlinear adaptive signal processing and machine learning. The brain interface testbed will facilitate future collaboration between two currently disconnected neural prostheses communities.Broader impacts: The theoretical framework will impact signal processing and machine learning, thus will have immediate influence on fields that rely heavily on statistical modeling, data analysis, and processing techniques. Specifically, contributions to the emerging neural engineering field will impact the design of future neural prostheses, as well as fundamental brain and cognition research. The project will help educate graduate engineers with mathematical rigor and an interdisciplinary focus.