论文标题
扩展MDL在高维问题中的使用：可变选择，健壮的拟合和添加剂建模
Extending the Use of MDL for High-Dimensional Problems: Variable Selection, Robust Fitting, and Additive Modeling
论文作者
论文摘要
在信号处理和统计文献中，最小描述长度（MDL）原理是选择模型复杂性的流行工具。成功的示例包括信号降解和线性回归中的可变选择，相应的MDL溶液通常具有一致的特性并产生非常有希望的经验结果。本文表明，MDL可以自然扩展到高维设置，其中预测因子$ p $的数量大于观测值$ n $的数量。它首先考虑了线性回归的情况，然后允许数据中的异常值，最后扩展到非参数添加模型的可靠拟合。提出了数值实验的结果，以证明MDL方法的效率和有效性。
In the signal processing and statistics literature, the minimum description length (MDL) principle is a popular tool for choosing model complexity. Successful examples include signal denoising and variable selection in linear regression, for which the corresponding MDL solutions often enjoy consistent properties and produce very promising empirical results. This paper demonstrates that MDL can be extended naturally to the high-dimensional setting, where the number of predictors $p$ is larger than the number of observations $n$. It first considers the case of linear regression, then allows for outliers in the data, and lastly extends to the robust fitting of nonparametric additive models. Results from numerical experiments are presented to demonstrate the efficiency and effectiveness of the MDL approach.
