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摘要翻译：
我们提出了二次损失回归估计的一般算法族。我们的算法能够在一个大字典中选择相关的函数。我们证明了许多已经研究过的算法（LASSO和Group LASSO、Dantzig选择器、迭代特征选择器等）都属于我们的家族，并展示了这个家族中的另一个特殊成员，本文称之为相关选择器。利用算法族的一般性质，我们证明了IFS、LASSO和相关选择器的oracle不等式，并在一个toy算例上比较了这些估计器的数值性能。
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英文标题：
《LASSO, Iterative Feature Selection and the Correlation Selector: Oracle
Inequalities and Numerical Performances》
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作者：
Pierre Alquier (PMA, Crest)
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最新提交年份：
2008
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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 propose a general family of algorithms for regression estimation with quadratic loss. Our algorithms are able to select relevant functions into a large dictionary. We prove that a lot of algorithms that have already been studied for this task (LASSO and Group LASSO, Dantzig selector, Iterative Feature Selection, among others) belong to our family, and exhibit another particular member of this family that we call Correlation Selector in this paper. Using general properties of our family of algorithm we prove oracle inequalities for IFS, for the LASSO and for the Correlation Selector, and compare numerical performances of these estimators on a toy example.
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PDF链接：
https://arxiv.org/pdf/710.4466
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