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Abstract:
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Optimizing a function using a sequential design is challenging when the function is defined over a high-dimensional design space. Expected improvement algorithms, which balance exploration of the design space with honing in on a global maximum, struggle in high dimensions because estimating the function and its maximum well require a large number of observations. Reducing the dimension of the design space should improve estimation and lead to faster identification of the maximum. However, current variable selection techniques are global; a variable is either in or out of the design matrix. In this paper, we define a measure of local importance to identify which variables are active around regions of local maxima, and we design a method to efficiently search the design space and estimate a global maximum. We present simulation studies involving high-dimensional data and compare the proposed global and local variable selection approach with other methods in terms of their ability to estimate the global maximum. In the simulation study, we show that local variable selection takes fewer steps to estimate a global maximum.
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