A LASSO FOR HIERARCHICAL INTERACTIONS.
A LASSO FOR HIERARCHICAL INTERACTIONS.
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DOI：
10.1214/13-aos1096
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发表时间：
2013-06
影响因子：
4.5
通讯作者：
Tibshirani R
中科院分区：
文献类型：
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作者：
Bien J;Taylor J;Tibshirani R
我们在套索（lasso）方法中添加了一组凸约束，以生成稀疏交互模型，该模型遵循层次结构限制，即只有当一个或两个变量具有边际重要性时，交互项才会被包含在模型中。我们精确地描述了这种层次结构约束的影响，证明了层次结构以概率1成立，并推导出了我们的估计量自由度的无偏估计。这个估计的界限揭示了层次结构约束所“节省”的拟合量。
我们区分了参数稀疏性（非零系数的数量）和实际稀疏性（进行新预测时必须测量的原始变量的数量）。层次结构侧重于后者，它与成本、时间和精力等重要的数据收集问题联系更为紧密。我们开发了一种算法，该算法可在R包hierNet中使用，并对我们的方法进行了实证研究。
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.