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 Qingqing Li Journal of Applied Mathematics and Physics (JAMP) , 2019, DOI: 10.4236/jamp.2019.75076 Abstract: There are many factors influencing personal credit. We introduce Lasso technique to personal credit evaluation, and establish Lasso-logistic, Lasso-SVM and Group lasso-logistic models respectively. Variable selection and parameter estimation are also conducted simultaneously. Based on the personal credit data set from a certain lending platform, it can be concluded through experiments that compared with the full-variable Logistic model and the stepwise Logistic model, the variable selection ability of Group lasso-logistic model was the strongest, followed by Lasso-logistic and Lasso-SVM respectively. All three models based on Lasso variable selection have better filtering capability than stepwise selection. In the meantime, the Group lasso-logistic model can eliminate or retain relevant virtual variables as a group to facilitate model interpretation. In terms of prediction accuracy, Lasso-SVM had the highest prediction accuracy for default users in the training set, while in the test set, Group lasso-logistic had the best classification accuracy for default users. Whether in the training set or in the test set, the Lasso-logistic model has the best classification accuracy for non-default users. The model based on Lasso variable selection can also better screen out the key factors influencing personal credit risk.
 吴德辉,李辉,刘青松,戴蓓蒨 模式识别与人工智能 , 2010, Abstract: 针对信道失配和统计模型区分性不足而导致话者确认性能下降问题，文中提出一种将因子分析信道失配补偿与支持向量机模型相结合的文本无关话者确认方法。在SVM话者模型前端采用高斯混合模型-背景模型(GMM-UBM)方法对语音特征参数进行聚类和升维，并利用因子分析(FA)方法，对聚类获得的超矢量进行信道补偿后作为基于SVM话者确认的输入特征，从而有效解决SVM用于文本无关话者确认的大样本、升维问题，以及信道失配对性能影响问题。在NIST06数据库上实验结果表明，文中方法比未做失配补偿的GMM-UBM系统、GMM-SVM系统在等误识率上有50%以上的改善，比做了FA失配补偿的GMM-UBM系统也有15。8%的改善。
 刘明辉,戴蓓,解焱陆 模式识别与人工智能 , 2008, Abstract: 提出一种结合统计模型与区分性模型优点的说话人确认方法:基于GMM多维概率输出的SVM话者模型的说话人确认.以目标说话人的GMM模型对一条语音的不同特征分量的概率输出作为特征参数,建立目标说话人的SVM模型.在NIST’058conv4w1conv4w数据库上的实验表明该方法的有效性.
 Martin Jaggi Computer Science , 2013, Abstract: We investigate the relation of two fundamental tools in machine learning and signal processing, that is the support vector machine (SVM) for classification, and the Lasso technique used in regression. We show that the resulting optimization problems are equivalent, in the following sense. Given any instance of an $\ell_2$-loss soft-margin (or hard-margin) SVM, we construct a Lasso instance having the same optimal solutions, and vice versa. As a consequence, many existing optimization algorithms for both SVMs and Lasso can also be applied to the respective other problem instances. Also, the equivalence allows for many known theoretical insights for SVM and Lasso to be translated between the two settings. One such implication gives a simple kernelized version of the Lasso, analogous to the kernels used in the SVM setting. Another consequence is that the sparsity of a Lasso solution is equal to the number of support vectors for the corresponding SVM instance, and that one can use screening rules to prune the set of support vectors. Furthermore, we can relate sublinear time algorithms for the two problems, and give a new such algorithm variant for the Lasso. We also study the regularization paths for both methods.
 Statistics , 2015, Abstract: We propose an improved LASSO estimation technique based on Stein-rule. We shrink classical LASSO estimator using preliminary test, shrinkage, and positive-rule shrinkage principle. Simulation results have been carried out for various configurations of correlation coefficients ($r$), size of the parameter vector ($\beta$), error variance ($\sigma^2$) and number of non-zero coefficients ($k$) in the model parameter vector. Several real data examples have been used to demonstrate the practical usefulness of the proposed estimators. Our study shows that the risk ordering given by LSE $>$ LASSO $>$ Stein-type LASSO $>$ Stein-type positive rule LASSO, remains the same uniformly in the divergence parameter $\Delta^2$ as in the traditional case.
 Statistics , 2011, DOI: 10.1214/10-AOAS377 Abstract: We propose a computationally intensive method, the random lasso method, for variable selection in linear models. The method consists of two major steps. In step 1, the lasso method is applied to many bootstrap samples, each using a set of randomly selected covariates. A measure of importance is yielded from this step for each covariate. In step 2, a similar procedure to the first step is implemented with the exception that for each bootstrap sample, a subset of covariates is randomly selected with unequal selection probabilities determined by the covariates' importance. Adaptive lasso may be used in the second step with weights determined by the importance measures. The final set of covariates and their coefficients are determined by averaging bootstrap results obtained from step 2. The proposed method alleviates some of the limitations of lasso, elastic-net and related methods noted especially in the context of microarray data analysis: it tends to remove highly correlated variables altogether or select them all, and maintains maximal flexibility in estimating their coefficients, particularly with different signs; the number of selected variables is no longer limited by the sample size; and the resulting prediction accuracy is competitive or superior compared to the alternatives. We illustrate the proposed method by extensive simulation studies. The proposed method is also applied to a Glioblastoma microarray data analysis.
 - , 2015, DOI: 10.7507/1001-5515.20150218 Abstract: 针对肝病分类中存在的特征交互的问题, 我们研究了一种分层交互lasso分类方法。首先对logistic模型添加lasso罚函数和分层凸约束, 其次采用卡罗需-库恩-塔克条件与广义梯度下降法相结合的凸优化方法给出模型求解方法, 最后得到主效应特征系数与交互特征系数的稀疏解, 实现模型分类。本文在两个肝病数据集上进行实验, 证明了特征交互对肝病分类有贡献。实验结果证明了分层交互lasso方法可解释性强, 效果、效率均优于lasso方法、全特征对lasso方法以及支持向量机、最近邻和决策树等传统分类方法。To solve the complex interaction problems of hepatitis disease classification, we proposed a lasso method (least absolute shrinkage and selection operator method) with feature interaction. First, lasso penalized function and hierarchical convex constraint were added to the interactive model which is newly defined. Then the model was solved with the convex optimal method combining Karush-Kuhn-Tucker (KKT) condition with generalized gradient descent. Finally, the sparse solution of the main effect features and interactive features were derived, and the classification model was implemented. The experiments were performed on two liver data sets and proved that features interaction contributed to the classification of liver diseases. The experimental results showed that the feature interaction lasso method was of strong explanatory ability, and its effectiveness and efficiency were superior to those of lasso, of all pair-wise lasso, support vector machine (SVM) method, K nearest neighbor (KNN) method, linear discriminant analysis (LDA) classification method, etc.
 Hamed Haselimashhadi Statistics , 2015, Abstract: Nowadays, l1 penalized likelihood has absorbed a high amount of consideration due to its simplicity and well developed theoretical properties. This method is known as a reliable method in order to apply in a broad range of applications including high-dimensional cases. On the other hand, $L_1$ driven methods, precisely lasso dependent regularizations, suffer the loss of sparsity when the number of observations is too low. In this paper we address a new differentiable approximation of lasso that can produce the same results as lasso and ridge and also can produce smooth results. We prove the theoretical properties of the model as well as its computation complexity. Due to differentiability, proposed method can be implemented by means of the majority of convex optimization methods in literature. That means a higher accuracy in situations where true coefficients are close to zero that is a major issue of LARS. Simulation study as well as flexibility of the method show that the proposed approach is as reliable as lass and ridge and can be used in both situations.
 蔡飞 财会月刊 , 2008, Abstract: 本文首先介绍了市销率指标的有关知识，建立了市销率指标计算的数学模型，然后阐述了市销率指标在股票投资决策中的应用，最后指出了不同市销率之间进行比较时应注意的问题。【关键词】市销率股票市场理论分析选股策略对投资者来说，价值评估在投资方向、投资组合和个股的选择中起了核心作用，而比率又是评价公司或资产价值的最易使用的工具之一。在众多比率中，市销率是评价上市公司投资价值指标中使用不多却是最管用的一个比率。市销率本身所具备的简单、明了的特性使得它成为一种很有效的判断工具。因此，本文试对市销率指标在股票投资决策中的应用作一探讨。　　一、市销率的有关知识　　1.市销率指标的计算及一般原理分析。市销率也称价格营收比，是股票市价与销售收入的比率，是相对估值方法的一种。该指标能够告诉投资者单位销售收入反映的股价水平。其计算公式为：市销率（PSR）=上市公司每股的市价（P）/上市公司每股的销售额（S）。
 Open Journal of Statistics (OJS) , 2016, DOI: 10.4236/ojs.2016.66094 Abstract: When the variable of model is large, the Lasso method and the Adaptive Lasso method can effectively select variables. This paper prediction the rural residents’ consumption expenditure in China, based on respectively using the Lasso method and the Adaptive Lasso method. The results showed that both can effectively and accurately choose the appropriate variable, but the Adaptive Lasso method is better than the Lasso method in prediction accuracy and prediction error. It shows that in variable selection and parameter estimation, Adaptive Lasso method is better than the Lasso method.
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