本文選題：邏輯回歸　切入點：正則化　出處：《河北大學》2016年碩士論文　論文類型：學位論文

【摘要】：邏輯回歸作為一種重要的數(shù)據(jù)分析方法,在各個領(lǐng)域應(yīng)用十分廣泛。在實際分類問題的應(yīng)用中,邏輯回歸總是可以收到良好的效果。然而,傳統(tǒng)邏輯回歸在克服解的復雜性和過擬合問題上存在明顯不足。為此,人們提出了眾多解決方法,其中,正則化是一種常見方法,并取得了一定的效果。然而,從理論上,人們提出的一些主流的正則化邏輯回歸模型由于不具備Oracle性質(zhì),使得這些模型并不是“好”正則化方法,使用時存在一定的不確定性。本文基于此,提出了自適應(yīng)正則化邏輯回歸模型,并進行了細致的理論推導,從本質(zhì)上保證了模型的可靠優(yōu)性,并利用實驗進行了驗證。本文主要工作包括:(1)基于彈性網(wǎng)邏輯回歸模型,提出了自適應(yīng)彈性網(wǎng)邏輯回歸模型。它可以同時考慮到模型中具有較小和中等相關(guān)性的解釋變量,從而在一定程度上,提高了預(yù)測準確率,有效的改善了傳統(tǒng)模型存在的變量選擇和計算過擬合問題;(2)討論了該模型所具有的Oracle性質(zhì)和群組選擇能力,并給出了這些性質(zhì)的證明過程;(3)為了求解該模型的參數(shù)估計值,本文構(gòu)造了基于坐標下降思想的正則化算法,并在一系列人工數(shù)據(jù)集和真實數(shù)據(jù)集上分別進行了實驗。實驗表明,文中算法具有良好的變量選擇能力和預(yù)測能力。
[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.
【學位授予單位】：河北大學
【學位級別】：碩士
【學位授予年份】：2016
【分類號】：O212.1

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相關(guān)碩士學位論文 前2條

1 王愷樂;基于彈性網(wǎng)技術(shù)下的加速失效時間模型的規(guī)范化估計[D];西南交通大學;2016年

2 連少靜;自適應(yīng)彈性網(wǎng)邏輯回歸模型的研究[D];河北大學;2016年

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本文編號：1578057