Abstract We propose a generalization of the lasso that allows the model coefficients to vary as a function of a general set of some prespecified modifying variables. These modifiers might be variables such as gender, age, or time. The paradigm is quite general, with each lasso coefficient modified by a sparse linear function of the modifying variables Z. The model is estimated in a hierarchical fashion to control the degrees of freedom and avoid overfitting. The modifying variables may be observed, observed only in the training set, or unobserved overall. There are connections of our proposal to varying coefficient models and high-dimensional interaction models. We present a computationally efficient algorithm for its optimization, with exact screening rules to facilitate application to large numbers of predictors. The method is illustrated on a number of different simulated and real examples. Supplementary materials for this article are available online.

中文翻译：

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柔韧的套索

摘要我们提出了套索的泛化，它允许模型系数作为一组一般的一些预先指定的修改变量的函数而变化。这些修饰符可能是诸如性别、年龄或时间之类的变量。该范式非常通用，每个套索系数由修改变量 Z 的稀疏线性函数修改。模型以分层方式估计，以控制自由度并避免过度拟合。可以观察到修改变量，仅在训练集中观察到，或整体未观察到。我们的提议与不同的系数模型和高维交互模型有联系。我们提出了一种计算效率高的优化算法，具有精确的筛选规则，便于应用于大量预测变量。该方法在许多不同的模拟和真实示例中进行了说明。本文的补充材料可在线获取。