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    政大機構典藏 > 商學院 > 統計學系 > 學位論文 >  Item 140.119/152781
    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/152781


    Title: 超高維度圖模型估計以及其對判別分析的應用
    Estimation of Ultrahigh-Dimensional Graphical Models and Its Application to Discriminant Analysis
    Authors: 曹卉姍
    Tsao, Hui-Shan
    Contributors: 陳立榜
    Chen, Li-Pang
    曹卉姍
    Tsao, Hui-Shan
    Keywords: 提升
    變數選取
    測量誤差
    網路結構
    精確矩陣
    超高維度資料
    Boosting
    Feature screening
    Measurement error
    Network structure
    Precision matrix
    Ultrahigh-dimensional data
    Date: 2024
    Issue Date: 2024-08-05 14:00:27 (UTC+8)
    Abstract: 圖模型一直都是統計學習中一個熱門的主題,且其對分析高維度資料的
    網路結構是很有用的。雖然有許多可以處理複雜結構的方法已經被開發出來,
    但是他們大多受限於處理超高維度以及有測量誤差的資料,其中前者反映了變
    數維度大於樣本數,而後者則是眾所周知的測量誤差問題。為了能應對這些挑
    戰並得出可靠的圖形結構的估計結果,我們開發了一個有效的方法來消除測量
    誤差,並應用提升法來同時估計精確矩陣。所提出的方法適用於不同分佈以及
    變數間可能的非線性關係。此外,我們的方法可以避免不可微分的懲罰函數並
    提供簡單的實施方法。在包含模擬以及實際資料分析的數值研究中,我們發現
    所提出的方法可以準確地偵測網路結構,並優於其他現存方法。
    Graphical models have been one of popular topics in statistical learning and are useful
    to analyze the network structure of high-dimensional data. While a large body of
    estimation methods has been developed to address various complex structures, they are
    limited to handle ultrahigh-dimensional and error-prone data, where the former reflects
    that the dimension of variables is larger than the sample size, and the latter is wellknown measurement error problem. To tackle those challenges and derive reliable
    estimation for the graphical structure, we develop a valid method to eliminate the
    measurement error effects and apply the boosting procedure to estimate the precision
    matrix simultaneously. The proposed method is valid to handle various distributions
    and possibly nonlinear relationship among variables. Moreover, our method avoids
    non-differentiable penalty function and provides easy implementation. Throughout the
    numerical studies, including simulation and real data analysis, we find that the proposed
    method can detect network structure accurately, and outperforms the other existing
    methods.
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    Description: 碩士
    國立政治大學
    統計學系
    111354028
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0111354028
    Data Type: thesis
    Appears in Collections:[統計學系] 學位論文

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