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Abstract:
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Tuning parameter selection is often a crucial step in variable selection for penalized estimation techniques, particularly in high-dimensional settings. The tendency of many such procedures is to over-select; that is, choose more variables than necessary. Further, many methods for tuning parameter selection in these settings are highly computationally expensive. The purpose of this new approach is to perform tuning parameter selection efficiently while avoiding over-selection. Intended to be a screening process for model selection, this method compares the squared correlations between the observed response and the predicted values of models that have arisen from some tuning parameter or parameters. The objective is to maximize squared correlation until some reasonable threshold is attained, balancing the desire for well-fitting models with a preference for sparsity. This approach is both highly efficient and, in the domain of penalized estimation, competitive with popular tuning parameter selection techniques in its capacity for variable selection. We explore the efficacy of this approach in a project involving optimal EMG placement for a robotic prosthesis controller.
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