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Explicit Link Between Periodic Covariance Functions and State Space Models
"... This paper shows how periodic covariance functions in Gaussian process regression can be reformulated as state space models, which can be solved with classical Kalman filtering theory. This reduces the problematic cubic complexity of Gaussian process regression in the number of time steps into lin ..."
Abstract

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This paper shows how periodic covariance functions in Gaussian process regression can be reformulated as state space models, which can be solved with classical Kalman filtering theory. This reduces the problematic cubic complexity of Gaussian process regression in the number of time steps into linear time complexity. The representation is based on expanding periodic covariance functions into a series of stochastic resonators. The explicit representation of the canonical periodic covariance function is written out and the expansion is shown to uniformly converge to the exact covariance function with a known convergence rate. The framework is generalized to quasiperiodic covariance functions by introducing damping terms in the system and applied to two sets of real data. The approach could be easily extended to nonstationary and spatiotemporal variants. 1
Noname manuscript No. (will be inserted by the editor) HumanAgent Collaboration for Disaster Response
"... Abstract In the aftermath of major disasters, first responders are typically overwhelmed with large numbers of, spatially distributed, search and rescue tasks, each with their own requirements. Moreover, responders have to operate in highly uncertain and dynamic environments where new tasks may app ..."
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Abstract In the aftermath of major disasters, first responders are typically overwhelmed with large numbers of, spatially distributed, search and rescue tasks, each with their own requirements. Moreover, responders have to operate in highly uncertain and dynamic environments where new tasks may appear and hazards may be spreading across the disaster space. Hence, rescue missions may need to be replanned as new information comes in, tasks are completed, or new hazards are discovered. Finding an optimal allocation of resources to complete all the tasks is a major computational challenge. In this paper, we use decision theoretic techniques to solve the task allocation problem posed by emergency response planning and then deploy our solution as part of an agentbased planning tool in realworld field trials. By so doing, we are able to study the interactional issues that arise when humans are guided by an agent. Specifically, we develop an algorithm, based on a MultiAgent Markov Decision Process representation of the task allocation problem and show that it outperforms standard baseline solutions. We then integrate the algorithm into a planning agent that responds to requests for tasks from participants in a mixedreality locationbased game, called AtomicOrchid, that simulates disaster response settings in the realworld. We then run a