We propose a new method for computing the lasso path, using the fact that the Manhattan norm of the coefficient vector is linear over every orthant of the parameter space. We use simple calculus and present an algorithm in which the lasso path is series of orthant moves. Our proposal gives the same results as standard literature, with the advantage of neat interpretation of results and explicit lasso formul{\ae}. We extend this proposal to elastic nets and obtain explicit, exact formul{\ae} for the elastic net path, and with a simple change, our lasso algorithm can be used for elastic nets. We present computational examples and provide simple R prototype code.

翻译：我们提出了一种计算Lasso路径的新方法，该方法利用了系数向量的曼哈顿范数在参数空间的每个正交象限上均为线性这一特性。通过使用简单的微积分工具，我们设计了一种算法，其中Lasso路径被表示为一系列正交象限移动的组合。本方法能得到与标准文献一致的结果，且具有结果解释清晰、Lasso公式显式化的优点。我们将此方法扩展至弹性网络，获得了弹性网络路径的显式精确公式，并且通过简单的修改，我们的Lasso算法即可适用于弹性网络。我们给出了计算示例，并提供了简单的R语言原型代码。