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Abstract:
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Many statistical problems involve learning importance/effect of a variable for predicting an outcome of interest based on observing a sample of n independent and identically distributed observations on a list of input variables and an outcome. For example, though prediction/machine learning is, in principle, concerned with learning the optimal unknown mapping from input variables to an outcome from the data, the typical reported output is a list of importance measures for each input variable. The typical approach in prediction has been to learn the unknown optimal predictor from the data and derive, for each of the input variables, the variable importance from the obtained fit. In this article, we propose a new approach that involves for each variable separately defining the wished variable importance as a parameter and deriving the efficient influence curve.
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