A Lasso for Hierarchical Interactions.

@article{Bien2013ALF,
  title={A Lasso for Hierarchical Interactions.},
  author={Jacob Bien and Jonathan Taylor and Robert Tibshirani},
  journal={Annals of statistics},
  year={2013},
  volume={41 3},
  pages={1111-1141}
}
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… CONTINUE READING
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