深度神經網路是一種重要的機器學習工具，在許多領域具有優異的表現。然而， 由於其黑盒性質，讓使用者很難了解輸入數據如何驅動神經網路。新的深度神經網路 技術被開發與應用，解釋深度神經網路決策過程的新方法也逐漸發展成為活躍的研究 領域。Gevrey,Dimopoulos,andLek(2003) 與 Pizarroso, Portela,andMuñoz(2020) 提 供計算敏感度的方法及神經解釋圖說明輸入與輸出的關係，然而這種方法並未得到廣 泛應用。在本論文中，我們從統計的角度探討了通用近似定理。此外，我們提出一種 使用實驗設計技術來解釋深度神經網路輸入與輸出關係的新方法，並透過模擬和真實 例子來展示。

Deep neural networks (DNNs) are an essential machine learning tool with excellent performance in many fields. However, due to its black-box nature, it is difficult for users to understand how the input data drives the neural network. New DNN technologies are developed and applied, and new explainable methods have been an active research field. Gevrey etal.(2003) and Pizarrosoetal.(2020) provide methods for evaluating sensitivity and the neural interpretation diagram to illustrate the relationship between inputs and outputs. However, these methods have not yet been heavily recognized. In this thesis, we tackle the universal approximation theorem based on a statistical perspective, In addition, we propose a new method to explain the relationship between the inputs and outputs of a DNN using the technique of experimental design. We finally illustrate the proposed method through simulations and real examples.

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