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Award ID contains: 2112828

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  1. ; (, Journal of Applied Probability)
    Abstract Gaussian process regression is widely used to model an unknown function on a continuous domain by interpolating a discrete set of observed design points. We develop a theoretical framework for proving new moderate deviations inequalities on different types of error probabilities that arise in GP regression. Two specific examples of broad interest are the probability of falsely ordering pairs of points (incorrectly estimating one point as being better than another) and the tail probability of the estimation error at an arbitrary point. Our inequalities connect these probabilities to the mesh norm, which measures how well the design points fill the space. 
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  2. ; (, Operations Research)
    We derive a new optimal sampling budget allocation for belief models based on linear regression with continuous covariates, where the expected response is interpreted as the value of the covariate vector, and an “error” occurs if a lower-valued vector is falsely identified as being better than a higher-valued one. Our allocation optimizes the rate at which the probability of error converges to zero using a large deviations theoretic characterization. This is the first large deviations-based optimal allocation for continuous decision spaces, and it turns out to be considerably simpler and easier to implement than allocations that use discretization. We give a practicable sequential implementation and illustrate its empirical potential. Funding: This work was supported by the National Science Foundation [Grant CMMI-2112828]. 
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