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arXiv · 1205.5050

A lasso for hierarchical interactions

Jacob Bien·Jonathan Taylor·Robert Tibshirani
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Abstract

We add a set of convex constraints to the lasso to produce sparse interaction models that honor the hierarchy restriction that an interaction only be included in a model if one or both variables are marginally important. We give a precise characterization of the effect of this hierarchy constraint, prove that hierarchy holds with probability one and derive an unbiased estimate for the degrees of freedom of our estimator. A bound on this estimate reveals the amount of fitting "saved" by the hierarchy constraint. We distinguish between parameter sparsity - the number of nonzero coefficients - and practical sparsity - the number of raw variables one must measure to make a new prediction. Hierarchy focuses on the latter, which is more closely tied to important data collection concerns such as cost, time and effort. We develop an algorithm, available in the R package hierNet, and perform an empirical study of our method.

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Jacob Bien, Jonathan Taylor, Robert Tibshirani. 2013-06-19. A lasso for hierarchical interactions. https://doi.org/10.1214/13-aos1096

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