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Abstract:
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We consider a binary classification problem where two different types of predictors, one low-dimensional typically standing for phenotypic characteristics and another high-dimensional, typically standing for genomic information, are present. In such situations, if variable selection is conducted in the usual way, the preponderance of the predictors in the latter category may overwhelm the predictors of the former type. To address this issue, we propose a new selection mechanism, to be called the one-pass method, in which we first apply sparse regression on the low-dimensional predictors with respect to the high-dimensional ones and replace the former by the regression residuals. Then we perform sparse logistic regression with all predictors using a penalized forward selection method to obtain the final classifier. To ensure that the variables from the low dimensional residuals are not overwhelmed by the high dimensional data, the variables in the low dimensional data to enter the sparse logistic regression first. We show that this procedure is numerically effective in simulations as well as computationally efficient. Our applications are chiefly in agronomy.
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