高維度模型在近年來成為統計學界的熱門主題，無論在預測還是模型選擇的各方面，都引起了廣泛關注與研究。本論文探討與高維度模型相關的議題，主要應用貪婪演算法來處理不同的高維度問題。文章包含以下三個主題：
1. 高維度問題中貪婪演算法的拓展：此部分著重於當模型存在錯誤時，使統計方法和機器學習方法仍能發揮相當的效果。我們研究在高維度模型中，即使模型有誤，貪婪演算法仍能有效選出重要的特徵。
2. 貪婪演算法在高維度因果推論中的應用 : 我們將貪婪演算法應用於高維度因果推論的方法，並提出平均因果效應的估計量，證明此估計量具備良好的統計性質。
3. 工具變數假設的拓展：目前許多涉及工具變數的研究假設模型為平方可加，而多數高維度研究僅假設模型為絕對可加。本論文將貪婪演算法的理論假設從絕對可加拓展至平方可加的情境，以應用於高維度線性模型中。

High-dimensional models have become a popular topic in the field of statistics in recent
years, attracting extensive attention and research in both prediction and model selection. This
paper explores topics related to high-dimensional models, focusing on the application of greedy
algorithms to address various high-dimensional problems. The paper consists of the following
three themes:
1. Extension of Greedy Algorithms in High-Dimensional Problems: This section
focuses on enabling statistical and machine learning methods to perform effectively even
when models are misspecified. We investigate scenarios in high-dimensional models where,
despite model misspecification, the greedy algorithm can still effectively select important
features.
2. Application of Greedy Algorithms in High-Dimensional Causal Inference: We
apply the greedy algorithm to high-dimensional causal inference, proposing an estimator
for the average causal effect and proving that this estimator possesses desirable statistical
properties.
3. Extension of Instrumental Variable Assumptions: Many studies involving instru-
mental variables assume a squared additivity condition, while most high-dimensional re-
search assumes only absolute additivity. This paper extends the theoretical assumptions
of the greedy algorithm in high-dimensional linear models to include squared additivity.

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