一种自适应稀疏Group Lasso分位数回归估计

稀疏惩罚分位数回归是高维数据分析中进行变量选择和稳健估计的重要工具。对于具有分组解释变量的问题,期望达到组内和组间稀疏的理想效果,但是许多现有方法未能实现这一目标。文章将自适应Lasso和自适应Group Lasso相结合,构建了一种自适应稀疏Group Lasso惩罚分位数回归(Q-AdSGL)模型,给出了基于ADMM算法的模型求解方法,并讨论了估计量的Oracle性质。通过Monte Carlo模拟研究和实例分析证明了所提模型和算法的有效性。

基于Group Lasso对数线性回归的智能手环评论数影响因素分析

本文基于Group Lasso对数线性回归构建智能手环评论数的影响因素模型,通过八爪鱼采集器抓取智能手环的详细信息进行实证量化研究。首先,对智能手环详细信息进行描述性分析,初步分析智能手环自身属性、功能属性、所属店铺属性三方面对评论量的影响。在建立虚拟变量的基础上,利用Group Lasso建立对数线性回归模型来探究影响智能手环评论量因素的具体数值关系,并推广应用。研究结果有助于改善智能手环的有关属性,利于商品的推广和销售。

在线Group Lasso学习

对高维流式数据的在线组变量选择问题进行了研究,提出了带Group Lasso惩罚的逻辑斯蒂回归在线估计方法,并给出了GFTPRL(Group Follow the Proximally Regularized Leader)算法。通过给出GFTPRL算法的缺憾界,证明了算法在理论上是有效的。实验结果表明,对于稀疏模型GFTPRL算法的预测分类准确率明显优于其他主流稀疏在线算法。

带Group Lasso正则项的Pi-Sigma神经网络在线梯度算法研究

Pi-Sigma神经网络是隐层带有求和神经元,输出层带有求积神经元的一种前馈神经网络,该网络具有较强的非线性映射能力。在误差函数中添加正则项是神经网络常用的优化方法,和传统的L2、L1/2正则项相比Group Lasso正则项可以在组级别上消除不必要的权值,具有良好的稀疏效果。众所周知,利用梯度法进行权值更新的学习方式有两种:一种是批处理学习算法,另一种是在线学习算法。本文提出带Group Lasso正则项的在线梯度学习算法来训练Pi-Sigma神经网络。最后,数值实验结果表明改进后的算法收敛速度更快并且具有较好的泛化性能。

一类非线性常微分方程参数估计

针对带有交叉项的非线性常微分方程参数估计问题,利用两阶段方法,首先将最小二乘法和样条展开相结合得到基函数展开的估计,为了提高估计效率,文中提出的方法中采用了积分估计,得到了估计基函数展开的积分;其次将积分结果代入Group LASSO模型,得到参数估计值;最后进行数值模拟。结果表明,文中提出的方法在处理非线性常微分方程参数估计问题时效果良好。

一种新颖的深度因果图建模及其故障诊断方法

为了实现复杂工业过程故障检测和诊断一体化建模,提出了一种新颖的深度因果图建模方法.首先,利用循环神经网络建立深度因果图模型,将Group Lasso稀疏惩罚项引入到模型训练中,自动地检测过程变量间的因果关系.其次,利用模型学习到的条件概率预测模型对每个变量建立监测指标,并融合得到综合指标进行整体工业过程故障检测.一旦检测到故障,对故障样本构建变量贡献度指标,隔离故障相关变量,并通过深度因果图模型的局部因果有向图诊断故障根源,辨识故障传播路径.最后,通过田纳西-伊斯曼过程进行仿真验证,实验结果验证了所提方法的有效性.

结合XGBoost算法和Logistic回归的信用评级方法

信用评级模型是金融机构科学评估客户违约风险的重要工具。以提升信用评级模型分类准确性和确保可解释性为目标,提出将XGBoost算法与Logistic Group Lasso模型相结合的信用评级方法,利用XGBoost算法进行特征选择来简化模型结构,构建Logistic Group Lasso模型来确保模型中重要变量的可解释性。基于某商业银行小微企业信贷业务数据的实证研究表明,新方法对贷款客户的分类效果显著优于常规方法,能够有效防控客户的违约风险,为金融机构带来更多收益。

Robust Texture Classification via Group-Collaboratively Representation-Based Strategy

In this paper, we present a simple but powerful ensemble for robust texture classification. The proposed method uses a single type of feature descriptor, i.e. scale-invariant feature transform （SIFT）, and inherits the spirit of the spatial pyramid matching model （SPM）. In a flexible way of partitioning the original texture images, our approach can produce sufficient informative local features and thereby form a reliable feature pond or train a new class-specific dictionary. To take full advantage of this feature pond, we develop a group-collaboratively representation-based strategy （GCRS） for the final classification. It is solved by the well-known group lasso. But we go beyond of this and propose a locality-constraint method to speed up this, named local constraint-GCRS （LC-GCRS）. Experimental results on three public texture datasets demonstrate the proposed approach achieves competitive outcomes and even outperforms the state-of-the-art methods. Particularly, most of methods cannot work well when only a few samples of each category are available for training, but our approach still achieves very high classification accuracy, e.g. an average accuracy of 92.1% for the Brodatz dataset when only one image is used for training, significantly higher than any other methods.

大学生COVID-19认知数据回归分析

基于大学生对于COVID-19认知数据以及影响因素,建立了多类别logistic回归模型。对比Group Lasso惩罚对数似然和逐步回归两种变量选择方法,比较AIC、BIC准则和交叉验证三种模型选择方法的模型效果,得到最优模型来分析影响学生对COVID-19相关知识掌握情况。

静息态人脑功能超网络模型鲁棒性对比分析

鲁棒性作为一种动态行为也是超网络领域的研究热点,对构建鲁棒网络具有重要的现实意义。尽管对超网络的研究越来越多,但对其动态研究相对较少,尤其是在神经影像领域。在现有的脑功能超网络研究中,大多是探究网络的静态拓扑属性,并没有相关研究对脑功能超网络的动力学特性——鲁棒性展开分析。针对这些问题,文中首先引入lasso,group lasso和sparse group lasso方法来求解稀疏线性回归模型以构建超网络;然后基于蓄意攻击中的节点度和节点介数攻击两种实验模型,利用全局效率和最大连通子图相对大小探究脑功能超网络在应对攻击时的节点失效网络的鲁棒性,最后通过实验进行对比分析,以探究更为稳定的网络。实验结果表明,在蓄意攻击模式下,group lasso和sparse group lasso方法构建的超网络的鲁棒性更强一些。同时,综合来看,group lasso方法构建的超网络最稳定。

脱贫地区农户返贫风险与诱发因素分析——基于甘肃省14县1735农户的调查数据

为研究脱贫地区的返贫风险和诱发因素,以甘肃省14县1 735农户为研究对象,利用Group Lasso logistic模型定量分析脱贫地区的返贫诱发因素。结果表明:(1)自然因素是影响返贫的重要因素;(2)物质资本风险抵御作用显著,尤以耐用品折合价值最为明显;(3)不同类型社会资本在谋生中的替代作用存在差异;(4)人力资本的返贫风险防控作用显著。因此,应注重提升农户的自然变现能力,完善技能培训体系,注重人才培养,提高脱贫地区农户人力资本水平,强化农户信息素质。

基于Group LASSO Logistic回归分析模型分析流行性乙型脑炎早期临床症状与预后的关联

目的探索Group LASSO(least absolute shrinkage and selection operator)Logistic回归分析模型在研究流行性乙型脑炎(简称乙脑)早期临床症状与预后之间的关系中的应用。方法收集整理2017—2018年甘肃省乙脑报告发病数据,建立乙脑预后影响因素的Group LASSO Logistic回归分析模型,通过交叉验证法选择惩罚参数,筛选出影响乙脑预后的早期临床症状。结果纳入的866名乙脑患者中,有预后结局的共764名,其中死亡者占22.5%、有后遗症者占12.6%、好转者占17.8%、痊愈者占47.1%。筛选出的变量有意识障碍、呼吸衰竭、呼吸节律改变、肌张力增强及乙脑疫苗接种史。结论通过构建Group LASSO Logistic回归分析模型可以筛选出对预后有影响的早期临床症状。

基于组合稀疏Lasso的投资策略研究

为了利用因子排序组合的信息并保证组合权重具有一定的稀疏性,基于Sparse Group Lasso (SGLasso)和经典的均值-方差(mean-variance,MV)投资组合策略,构建了能够对高维资产数据集进行投资的SGLasso-MV策略.与Lasso和GLasso相比,SGLasso能够同时实现组内和组间的稀疏性,并利用了特征分组信息,因此适用于改进MV策略输出权重的不稳定性和高误差性问题.在实证数据方面,利用A股1997年至2019年所有可用A股股票的日际实证数据集,进行了不固定成分股的滚动投资,以避免样本选择性偏误,并将SGLasso-MV与几种经典的投资组合策略进行了比较.结果显示,相比其他同样包含期望收益率估计量的策略,SGLasso-MV的权重能够在样本外实现显著更低的标准差风险和更低的换手率.

Group LASSO for Change-points in Functional Time Series

Multiple change-points estimation for functional time series is studied in this paper.The change-point problem is first transformed into a high-dimensional sparse estimation problem via basis functions.Group least absolute shrinkage and selection operator(LASSO)is then applied to estimate the number and the locations of possible change points.However,the group LASSO(GLASSO)always overestimate the true points.To circumvent this problem,a further Information Criterion(IC)is applied to eliminate the redundant estimated points.It is shown that the proposed two-step procedure estimates the number and the locations of the change-points consistently.Simulations and two temperature data examples are also provided to illustrate the finite sample performance of the proposed method.

On Globally Q-Linear Convergence of a Splitting Method for Group Lasso

In this paper,we discuss a splitting method for group Lasso.By assuming that the sequence of the step lengths has positive lower bound and positive upper bound(unrelated to the given problem data),we prove its Q-linear rate of convergence of the distance sequence of the iterates to the solution set.Moreover,we make comparisons with convergence of the proximal gradient method analyzed very recently.

Concave group methods for variable selection and estimation in high-dimensional varying coefficient models

The varying-coefficient model is flexible and powerful for modeling the dynamic changes of regression coefficients. We study the problem of variable selection and estimation in this model in the sparse, high- dimensional case. We develop a concave group selection approach for this problem using basis function expansion and study its theoretical and empirical properties. We also apply the group Lasso for variable selection and estimation in this model and study its properties. Under appropriate conditions, we show that the group least absolute shrinkage and selection operator （Lasso） selects a model whose dimension is comparable to the underlying mode], regardless of the large number of unimportant variables. In order to improve the selection results, we show that the group minimax concave penalty （MCP） has the oracle selection property in the sense that it correctly selects important variables with probability converging to one under suitable conditions. By comparison, the group Lasso does not have the oracle selection property. In the simulation parts, we apply the group Lasso and the group MCP. At the same time, the two approaches are evaluated using simulation and demonstrated on a data example.

REDUCED-RANK MODELING FOR HIGH-DIMENSIONAL MODEL-BASED CLUSTERING

Model-based clustering is popularly used in statistical literature, which often models the data with a Gaussian mixture model. As a consequence, it requires estimation of a large amount of parameters, especially when the data dimension is relatively large, in this paper, reduced-rank model and group-sparsity regularization are proposed to equip with the model-based clustering, which substantially reduce the number of parameters and thus facilitate the high-dimensional clustering and variable selection simultaneously. We propose an EM algorithm for this task, in which the M-step is solved using alternating minimization. One of the alternating steps involves both nonsmooth function and nonconvex constraint, and thus we propose a linearized alternating direction method of multipliers （ADMM） for solving it. This leads to an efficient algorithm whose subproblems are all easy to solve. In addition, a model selection criterion based on the concept of clustering stability is developed for tuning the clustering model. The effectiveness of the proposed method is supported in a variety of simulated and real examples, as well as its asymptotic estimation and selection consistencies.