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研究生： 李泓緯
Li, Hung-Wei
論文名稱： 資料縮減方法在不平衡分類及節點部署之應用
Applications of Data Reduction Methods on Classification for Imbalanced Data and Knot Placement for Prediction Problems
指導教授： 徐南蓉
Hsu, Nan-Jung
口試委員: 黃信誠
Huang, Hsin-Cheng
陳春樹
Chen, Chun-Shu
學位類別： 碩士
Master
系所名稱： 理學院 - 統計學研究所
Institute of Statistics
論文出版年： 2022
畢業學年度： 110
語文別： 英文
論文頁數： 49
中文關鍵詞： 子抽樣 、薄板樣條 、空間隨機效應模型 、不平衡資料 、節點部署
外文關鍵詞： subsampling, thin-plate spline, spatial random effect model, imbalanced data, knot placement
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    • 在配適統計模型或訓練機器學習模型時, 大數據會帶來高昂的計算成本。為了克服這個議 題，可在執行配適及訓練的過程僅利用數據的子樣本來降低計算成本。本論文探討兩種子採 樣方法 SPlit (Joseph and Vakayil, 2021) 和 Supercompress (Joseph and Mak, 2021)，在不平 衡數據分類問題、平滑預測問題中的節點(knot)放置、及空間預測問題等三個應用問題上 的有效性。經由模擬試驗，得到以下結論:(1)在不平衡數據分類問題上，SPlit 方法能取 出更具代表性的子樣本確實能提升 minority class 分類的正確率，其分類成效明顯優於簡單 隨機抽樣。(2)在節點放置的兩個應用上，不論是 spatial smoothing 或空間隨機效應模型的 預測問題，當資料散佈及數值的變動非常不均勻時，Supercompress 方法的整體空間預測表 現都優於傳統的均勻佈節點的方法。

    Large data typically bring high computation costs when fitting statistical or machine learn- ing models. To overcome this issue, model fitting can be done based on a subsample of data instead of using the entire data set. There are several ways of taking representative subsamples in the literature. This thesis emphasizes two new subsampling methods, SPlit (Joseph and Vakayil, 2021) and Supercompress (Joseph and Mak, 2021), to study their usefulness in the applications of the classification problem with imbalanced data and knot placement for predic- tion problems. Their performance on prediction accuracy is studied via numerical simulations, compared with the traditional approaches. In the application to imbalanced data classification problems, the SPlit method is found to perform generally better than a simple random sampling in terms of classification accuracy for the minority class. In the applications to knot placement, the Supercompress method performs better than the uniform placement when data patterns are inhomogeneous in the spatial domain for both the thin-plate spline fitting and the fixed rank kriging in the spatial random effects model framework.

    摘要 i Abstract ii List of Figures iv List of Tables vi 1 Introduction . . . . . . . . . . . . . . . . . . . . 1 2 Data Reduction Methods . . . . . . . . . . . . . . . . . . . . 4 2.1 Data Sub-sampling Methods . . . . . . . . . . . . . . . . . . . . 4 2.1.1 Simple Random Sampling(SRS) . . . . . . . . . . . . . . . . . . . . 4 2.1.2 SPlit . . . . . . . . . . . . . . . . . . . . 5 2.2 Data Compression Methods . . . . . . . . . . . . . . . . . . . . 8 2.2.1 Equal-space and Equal-quantile . . . . . . . . . . . . . . . . . . . . 8 2.2.2 Supercompress . . . . . . . . . . . . . . . . . . . . 8 2.3 Methods Summary . . . . . . . . . . . . . . . . . . . . 11 3 Application on Classification for Imbalanced Data . . . . . . . . . . . . . . . . . . . . 12 3.1 Simulation Setting . . . . . . . . . . . . . . . . . . . . 12 3.2 Performance Measure . . . . . . . . . . . . . . . . . . . . 14 3.3 The Impact of Each Factor on AUC . . . . . . . . . . . . . . . . . . . . 14 3.4 Summary Result . . . . . . . . . . . . . . . . . . . . 17 4 Application on Knots Selection in Thin Plate Spline Fitting . . . . . . . . . . . . . . . . . . . . 18 4.1 Simulation Setting . . . . . . . . . . . . . . . . . . . . 19 4.2 The Impact of Each Factor in MSE . . . . . . . . . . . . . . . . . . . . 21 4.3 Summary. Result . . . . . . . . . . . . . . . . . . . . 21 5 Application on Basis Selection in Spatial Random Effect Model . . . . . . . . . . . . . . . . . . . . 30 5.1 Simulation Setting . . . . . . . . . . . . . . . . . . . . 31 5.2 The Impact of Each Factor on PE . . . . . . . . . . . . . . . . . . . . 36 6 Conclusion . . . . . . . . . . . . . . . . . . . . 38 Reference . . . . . . . . . . . . . . . . . . . . 39 A Appendix A . . . . . . . . . . . . . . . . . . . . 41

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