自适应弹性网逻辑回归模型的研究

发布时间：2018-03-07 05:11

本文选题：逻辑回归　切入点：正则化　出处：《河北大学》2016年硕士论文　论文类型：学位论文

【摘要】：逻辑回归作为一种重要的数据分析方法,在各个领域应用十分广泛。在实际分类问题的应用中,逻辑回归总是可以收到良好的效果。然而,传统逻辑回归在克服解的复杂性和过拟合问题上存在明显不足。为此,人们提出了众多解决方法,其中,正则化是一种常见方法,并取得了一定的效果。然而,从理论上,人们提出的一些主流的正则化逻辑回归模型由于不具备Oracle性质,使得这些模型并不是“好”正则化方法,使用时存在一定的不确定性。本文基于此,提出了自适应正则化逻辑回归模型,并进行了细致的理论推导,从本质上保证了模型的可靠优性,并利用实验进行了验证。本文主要工作包括:(1)基于弹性网逻辑回归模型,提出了自适应弹性网逻辑回归模型。它可以同时考虑到模型中具有较小和中等相关性的解释变量,从而在一定程度上,提高了预测准确率,有效的改善了传统模型存在的变量选择和计算过拟合问题;(2)讨论了该模型所具有的Oracle性质和群组选择能力,并给出了这些性质的证明过程;(3)为了求解该模型的参数估计值,本文构造了基于坐标下降思想的正则化算法,并在一系列人工数据集和真实数据集上分别进行了实验。实验表明,文中算法具有良好的变量选择能力和预测能力。
[Abstract]:As an important data analysis method, logical regression is widely used in various fields. In the application of practical classification problems, logical regression can always get good results. However, Traditional logic regression has obvious shortcomings in overcoming the complexity of solution and overfitting problem. For this reason, many solutions have been put forward, among which regularization is a common method and has achieved certain results. Some mainstream regularized logical regression models proposed by people do not have Oracle properties, which make these models not "good" regularization methods, and there are some uncertainties in their use. An adaptive regularized logical regression model is proposed, and detailed theoretical derivation is carried out to ensure the reliability and superiority of the model in essence, which is verified by experiments. The main work of this paper includes: 1) based on the elastic network logic regression model. An adaptive elastic network logical regression model is proposed, which can take into account the explanatory variables with small and medium correlation in the model at the same time, thus improving the prediction accuracy to a certain extent. In order to solve the parameter estimation of the model, the Oracle property and group selection ability of the model are discussed, and the process of proving these properties is given. In this paper, a regularization algorithm based on the idea of coordinate descent is constructed, and experiments are carried out on a series of artificial data sets and real data sets. The experiments show that the algorithm has good ability of variable selection and prediction.
【学位授予单位】：河北大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O212.1

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