具有二阶矩有限噪声的Lasso高维统计分析

研究在非高斯噪声下的Lasso的高维统计分析,给出了在误差噪声满足二阶矩有限条件下,Lasso方法的高维界估计,推广了现有的关于Lasso的主要理论结果.所得结果具有一定的理论及应用价值.     

Ensemble Linear Subspace Analysis of High-Dimensional Data

Regression models provide prediction frameworks for multivariate mutual information analysis that uses information concepts when choosing covariates (also called features) that are important for analysis and prediction. We consider a high dimensional regression framework where the number of covariates (p) exceed the sample size (n). Recent work in high dimensional regression analysis has embraced an ensemble subspace approach that consists of selecting random subsets of covariates with fewer than p covariates, doing statistical analysis on each subset, and then merging the results from the subsets. We examine conditions under which penalty methods such as Lasso perform better when used in the ensemble approach by computing mean squared prediction errors for simulations and a real data example. Linear models with both random and fixed designs are considered. We examine two versions of penalty methods: one where the tuning parameter is selected by cross-validation; and one where the final predictor is a trimmed average of individual predictors corresponding to the members of a set of fixed tuning parameters. We find that the ensemble approach improves on penalty methods for several important real data and model scenarios. The improvement occurs when covariates are strongly associated with the response, when the complexity of the model is high. In such cases, the trimmed average version of ensemble Lasso is often the best predictor.     

Modified Cross-Validation for Penalized High-Dimensional Linear Regression Models

In this article, for Lasso penalized linear regression models in high-dimensional settings, we propose a modified cross-validation (CV) method for selecting the penalty parameter. The methodology is extended to other penalties, such as Elastic Net. We conduct extensive simulation studies and real data analysis to compare the performance of the modified CV method with other methods. It is shown that the popular K-fold CV method includes many noise variables in the selected model, while the modified CV works well in a wide range of coefficient and correlation settings. Supplementary materials containing the computer code are available online.     

A Path Algorithm for the Fused Lasso Signal Approximator

The Lasso is a very well-known penalized regression model, which adds an L₁ penalty with parameter λ₁ on the coefficients to the squared error loss function. The Fused Lasso extends this model by also putting an L₁ penalty with parameter λ₂ on the difference of neighboring coefficients, assuming there is a natural ordering. In this article, we develop a path algorithm for solving the Fused Lasso Signal Approximator that computes the solutions for all values of λ₁ and λ₂. We also present an approximate algorithm that has considerable speed advantages for a moderate trade-off in accuracy. In the Online Supplement for this article, we provide proofs and further details for the methods developed in the article.     

带有组结构的稀疏模型的参数估计和变量选择方法

本文针对带有组结构的广义线性稀疏模型,引入布雷格曼散度作为一般性的损失函数,进行参数估计和变量选择,使得该方法不局限于特定模型或特定的损失函数.本文比较研究了Ridge,SACD,Lasso,自适应Lasso,组Lasso,分层Lasso,自适应分层Lasso和稀疏组Lasso共8种惩罚函数的特点和引入模型后参数估计和...     

试验设计在爆炸网络可靠性研究中的应用

为了设计和评价爆炸网络的可靠性,研究了影响爆炸网络可靠性的主要因素与可靠性特征量之间的定量关系。通过正交试验和均匀试验方法,首先对23个可能的影响因素建立正交试验分析,筛选出7个影响爆速的主要因素;然后基于主要影响因素构造有效的均匀试验,对试验结果进行回归分析,得到主要因素的取值与爆速间的定量模型。     

基于LARS-Lasso的指数跟踪及其在股指期货套利策略中的应用

本文将多元线性回归选择变量的Lasso方法引入到指数跟踪和股指期货套利策略研究,提出运用LARS算法实现非负限制下的Lasso选择现货组合问题,为业界给出了一种选择构造现货组合的股票的新方法。实证表明:采用本文提出的方法得到的现货组合,在组合含有较少数量股票的情况下,得到较文献中已有方法更小的跟踪误差。同时,利用本文的方法对沪深300仿真交易的期现套利进行研究,得到有重要市场价值的结果。     

Signal recovery under mutual incoherence property and oracle inequalities

We consider the signal recovery through an unconstrained minimization in the framework of mutual incoherence property. A sufficient condition is provided to guarantee the stable recovery in the noisy case. Furthermore, oracle inequalities of both sparse signals and non-sparse signals are derived under the mutual incoherence condition in the case of Gaussian noises. Finally, we investigate the relationship between mutual incoherence property and robust null space property and find that robust null space property can be deduced from the mutual incoherence property.     

Lasso算法的油砂钠元素近红外建模

以油砂中钠元素为研究对象,首次应用近红外光谱,结合Lasso(least absolute shrinkage and selection operator)建模方法,建立了油砂金属钠含量的近红外光谱定量校正模型,并与传统的PLS建模方法进行比较。结果表明,两种方法建立的油砂金属钠含量校正模型都具有很高的精度,预测性能方面略有差异。在实验验证集与预测集中,PLS与Lasso算法的相关系数分别是：R_v=0.878 8,R_p=0.857 9和R_v=0.887 4,R_p=0.860 0。实验验证了使用近红外光谱快速测定油砂金属钠含量的有效性,并分析了PLS与Lasso算法的适用范围。