摘要翻译：
我们考虑了求解惩罚最小二乘回归问题的最小角回归和前向分段算法。在Efron,Hastie,Johnstone&Tibshirani（2004）中，证明了最小角回归算法只需稍加修改就能解决lasso回归问题。在这里，我们给出了一个类似的结果，增量向前阶段回归，表明它解决了一个版本的套索问题，强制单调性。由此得到的一个结果是：当lasso在降低系数$\beta$的每单位增加$l_1$-范数的残差平方和方面取得最佳进展时，向前阶段是沿着系数路径行进的每单位$l_1$弧长的最佳进展。我们还研究了lasso的系数路径单调的一个条件，从而使不同的算法重合。最后，在一个涉及大量相关预测因子的模拟研究中，我们比较了lasso和前向分段过程。
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英文标题：
《Forward stagewise regression and the monotone lasso》
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作者：
Trevor Hastie, Jonathan Taylor, Robert Tibshirani, Guenther Walther
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最新提交年份：
2007
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分类信息：

一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  We consider the least angle regression and forward stagewise algorithms for solving penalized least squares regression problems. In Efron, Hastie, Johnstone & Tibshirani (2004) it is proved that the least angle regression algorithm, with a small modification, solves the lasso regression problem. Here we give an analogous result for incremental forward stagewise regression, showing that it solves a version of the lasso problem that enforces monotonicity. One consequence of this is as follows: while lasso makes optimal progress in terms of reducing the residual sum-of-squares per unit increase in $L_1$-norm of the coefficient $\beta$, forward stage-wise is optimal per unit $L_1$ arc-length traveled along the coefficient path. We also study a condition under which the coefficient paths of the lasso are monotone, and hence the different algorithms coincide. Finally, we compare the lasso and forward stagewise procedures in a simulation study involving a large number of correlated predictors.
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PDF链接：
https://arxiv.org/pdf/705.0269