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In a standard regression problem, we have a set of explanatory variableswhose effect on some response vector is modeled. For wide binary data, such asgenetic marker data, we often have two limitations. First, we have moreparameters than observations. Second, main effects are not the main focus;instead the primary aim is to uncover interactions between the binary variablesthat effect the response. Methods such as logic regression are able to findcombinations of the explanatory variables that capture higher-orderrelationships in the response. However, the number of explanatory variablesthese methods can handle is highly limited. To address these two limitations weneed to reduce the number of variables prior to computationally demandinganalyses. In this paper, we demonstrate the usefulness of using so-calledcross-leverage scores as a means of sampling subsets of explanatory variableswhile retaining the valuable interactions.

Cross-Leverage Scores for Selecting Subsets of Explanatory Variables