集成學習是由多個演算法組成，用於提升預測性能。然而，對於依賴性數據（例如地理數據），這種優越性可能會損失。結合集成學習和變異圖法，提出了一種學習程序來尋找適當的模型。此外，基於選定的模型，應用克立金法於預測問題中。模擬研究證明了所提出的程序在預測問題上的良好表現。通過與現有的PM 2.5 數據方法進行分析和比較，顯示了所提出方法的較好性能。

Ensemble learning consists of multiple algorithms to enhance predictive performance.
However, such superiority may lose for the dependent data such as the geographical data. Combining the ensemble learning with the variogram approach, a learning procedure is proposed to look for the adequate model. Further, kriging based on the selected model is applied in the forecast issue. The simulation study demonstrates that the proposed procedure works well for the forecast issue.
The analysis and comparison with an existing method for PM 2.5 data show better performance of the proposed method.

1 Introduction 1
2 Literature Reviews 3
2.1 Stationary random process 3
2.2 Metric Model 4
2.3 Model Assumptions 5
2.4 Spatio-Temporal Universal Kriging 6
2.4.1 Introduction to the Kriging method 6
2.4.2 Unbiasedness condition 8
2.4.3 The predict variance 8
2.4.4 Minimal Prediction Variance 9
2.5 Neural Network 10
2.5.1 What is neural network 10
2.5.2 How the Neural Network Works 10
2.6 Boosting 14
2.6.1 Introduction to boosting 14
2.6.2 Boosting algorithm 15
2.6.3 The first boosting method - Adaboost 16
2.6.4 XGBoost 17
2.6.5 Catboost 18
2.7 Ensemble Learning 19
3 Methodology 21
3.1 Ensemble method for estimation 21
3.2 Empirical spatio-temporal covariogram 22
3.3 Spatio-Temporal Universal Kriging 22
4 Simulation studies 25
4.1 Experimental assumption 25
5 Real data 31
5.1 Environmental Protection Data 31
5.1.1 Data introduction 31
5.2 Experimental Design 35
5.3 Evaluation Metrics 36
5.4 Experimental Results 36
5.4.1 Taipai 37
5.4.2 Taoyuan 39
5.4.3 Nantou 40
5.4.4 Kaohsiung 41
6 Conclusion 43
References 45

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