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A LASSO FOR HIERARCHICAL INTERACTIONS.

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.

SUBMITTER: Bien J

PROVIDER: S-EPMC4527358 | biostudies-literature | 2013 Jun

REPOSITORIES: biostudies-literature

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A LASSO FOR HIERARCHICAL INTERACTIONS.

Bien Jacob J Taylor Jonathan J Tibshirani Robert R

Annals of statistics 20130601 3

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 hiera ...[more]

PMID: 26257447

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A LASSO FOR HIERARCHICAL INTERACTIONS.

Publications

A LASSO FOR HIERARCHICAL INTERACTIONS.

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