英文标题：
《Generalization error minimization: a new approach to model evaluation
  and selection with an application to penalized regression》
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作者：
Ning Xu, Jian Hong, Timothy C.G. Fisher
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最新提交年份：
2016
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英文摘要：
  We study model evaluation and model selection from the perspective of generalization ability (GA): the ability of a model to predict outcomes in new samples from the same population. We believe that GA is one way formally to address concerns about the external validity of a model. The GA of a model estimated on a sample can be measured by its empirical out-of-sample errors, called the generalization errors (GE). We derive upper bounds for the GE, which depend on sample sizes, model complexity and the distribution of the loss function. The upper bounds can be used to evaluate the GA of a model, ex ante. We propose using generalization error minimization (GEM) as a framework for model selection. Using GEM, we are able to unify a big class of penalized regression estimators, including lasso, ridge and bridge, under the same set of assumptions. We establish finite-sample and asymptotic properties (including $\\mathcal{L}_2$-consistency) of the GEM estimator for both the $n \\geqslant p$ and the $n < p$ cases. We also derive the $\\mathcal{L}_2$-distance between the penalized and corresponding unpenalized regression estimates. In practice, GEM can be implemented by validation or cross-validation. We show that the GE bounds can be used for selecting the optimal number of folds in $K$-fold cross-validation. We propose a variant of $R^2$, the $GR^2$, as a measure of GA, which considers both both in-sample and out-of-sample goodness of fit. Simulations are used to demonstrate our key results.
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中文摘要：
我们从泛化能力（GA）的角度研究模型评估和模型选择：模型在来自相同人群的新样本中预测结果的能力。我们认为，GA是正式解决模型外部有效性问题的一种方法。基于样本估计的模型的GA可以通过其经验样本外误差来衡量，称为泛化误差（GE）。我们推导了GE的上界，它取决于样本大小、模型复杂性和损失函数的分布。上界可用于预先评估模型的GA。我们建议使用泛化误差最小化（GEM）作为模型选择的框架。使用GEM，我们能够在相同的假设集下统一一大类惩罚回归估计量，包括lasso、ridge和bridge。我们建立了$n\\geqslant p$和$n<p$情况下GEM估计量的有限样本和渐近性质（包括$\\数学{L}\\u 2$-一致性）。我们还推导了惩罚回归估计和相应的未赋能回归估计之间的$\\数学{L}\\u 2$-距离。在实践中，GEM可以通过验证或交叉验证来实现。我们表明，GE边界可用于在$K$折叠交叉验证中选择最佳折叠数。我们提出了一个变量$R^2$，即$GR^2$，作为GA的度量，它同时考虑了样本内和样本外的拟合优度。通过仿真验证了我们的主要结果。
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分类信息：

一级分类：Statistics        统计学
二级分类：Machine Learning        机器学习
分类描述：Covers machine learning papers (supervised, unsupervised, semi-supervised learning, graphical models, reinforcement learning, bandits, high dimensional inference, etc.) with a statistical or theoretical grounding
覆盖机器学习论文（监督，无监督，半监督学习，图形模型，强化学习，强盗，高维推理等）与统计或理论基础
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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：Quantitative Finance        数量金融学
二级分类：Economics        经济学
分类描述：q-fin.EC is an alias for econ.GN. Economics, including micro and macro economics, international economics, theory of the firm, labor economics, and other economic topics outside finance
q-fin.ec是econ.gn的别名。经济学，包括微观和宏观经济学、国际经济学、企业理论、劳动经济学和其他金融以外的经济专题
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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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