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摘要翻译：
我们考虑了一个高维二元分类问题，并构造了一个分类过程，该过程通过对选择特征数的惩罚来最小化经验误分类风险。我们得到了估计稀疏性和超额误分类风险的非渐近概率界。特别地，我们证明了我们的方法得到了一个稀疏解，该解的L0范数可以任意接近于真稀疏的概率很高，并且得到了对于超额误分类风险的收敛速度。所提出的程序是通过混合整数线性规划的方法实现的。蒙特卡罗实验表明了它的数值性能。
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英文标题：
《High Dimensional Classification through $\ell_0$-Penalized Empirical
Risk Minimization》
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作者：
Le-Yu Chen and Sokbae Lee
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最新提交年份：
2018
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分类信息：
一级分类：Statistics 统计学
二级分类：Methodology 方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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一级分类：Economics 经济学
二级分类：Econometrics 计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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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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英文摘要：
We consider a high dimensional binary classification problem and construct a classification procedure by minimizing the empirical misclassification risk with a penalty on the number of selected features. We derive non-asymptotic probability bounds on the estimated sparsity as well as on the excess misclassification risk. In particular, we show that our method yields a sparse solution whose l0-norm can be arbitrarily close to true sparsity with high probability and obtain the rates of convergence for the excess misclassification risk. The proposed procedure is implemented via the method of mixed integer linear programming. Its numerical performance is illustrated in Monte Carlo experiments.
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PDF链接：
https://arxiv.org/pdf/1811.09540
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