# A LASSO FOR HIERARCHICAL INTERACTIONS.

@article{Bien2013ALF, title={A LASSO FOR HIERARCHICAL INTERACTIONS.}, author={Jacob Bien and Jonathan E. 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…

## 393 Citations

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