Abstract-Random networks of nonlinear functions have a long history of empirical success in function fitting but few theoretical guarantees. In this paper, using techniques from probability on Banach Spaces, we analyze a specific architecture of random nonlinearities, provide L ∞ and L 2 error bounds for approximating functions in Reproducing Kernel Hilbert Spaces, and discuss scenarios when these expansions are dense in the continuous functions. We discuss connections between these random nonlinear networks and popular machine learning algorithms and show experimentally that these networks provide competitive performance at far lower computational cost on large-scale pattern recognition tasks.
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AbstractWe introduce Simultaneous Localization and Tracking (SLAT), the problem of tracking a target in a sensor network while simultaneously localizing and calibrating the nodes of the network. Our proposed solution, LaSLAT, is a Bayesian filter providing on-line probabilistic estimates of sensor locations and target tracks. It does not require globally accessible beacon signals or accurate ranging between the nodes. When applied to a network of 27 sensor nodes, our algorithm can localize the nodes to within one or two centimeters.
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