隨著可解釋人工智慧興起，了解模型的解釋性對決策者與人工智慧模型間的信任相當關鍵。決策樹作為最具可解釋性的透明模型之一，因此廣受討論。在使用決策樹
模型於不同應用時，會注重不同的特性，使得客觀的比較決策樹是一個具有挑戰的任務。決策樹對微小的資料變化相當敏感，尤其在回歸任務上，使得決策樹的解釋更加不穩定。基於決策樹的多變，比較決策樹的需求逐漸上升。而我們的目標是，針對資料敏感性問題嚴重的回歸問題，透過建立一個僅依賴於預測值以及獨立變數的演算法來比較不同的決策樹模型。以上，我們提出Dynamic Membership Compariosn 動態會籍比較演算法，同時將決策樹的穩定度以及可解釋性納入演算法的考量來客觀比較決策樹。利用一組受測模型都具有高泛化力的資料來衡量決策樹之間的差異性，並且允許一對多的比較決策樹中的葉節點會籍相似度，針對以上問題提出解方。

With the rise of explainable artificial intelligence (XAI), understanding the interpretability of models is critical for building trust between decision-makers and AI models. Decision Trees, one of the most interpretable and transparent models, have been
widely discussed. However, decision trees can be sensitive to minor changes in data, leading to variations in their structure, predictions, and explanations. This sensitivity is particularly pronounced in regression tasks, compared to classification tasks, making decision tree explanations even more unstable. Hence, there is a need to compare decision trees to understand how similar two trees with different structures and predictions are.

Focusing on the stability issue in the regression task, we propose the "Dynamic Membership Comparison" algorithm to objectively compare decision trees. It is a model-agnostic approach that utilizes a set of data with high generalizability for both models
to measure the similarity between decision trees. Simultaneously, the algorithm considers both the stability and interpretability of decision trees, enabling one-to-many comparisons of the membership similarity of leaf nodes in the decision trees.

摘要 3
Abstract 4
Acknowledgements 6
Table of Contents 7
Chapter 1. Introduction 9
Chapter 2. Tree Comparison 11
2.1. Overview of Regression Decision Trees Algorithm 11
2.2. Terminology of Decision Tree 11
2.3. Considerations of using CART 14
2.4 Tree Comparison Scenarios 16
2.5 Prior Work on Tree Comparison 18
Chapter 3. Dynamic Membership Comparison (DMC) 23
3.1 The Importance of Membership Similarity 23
3.2 Membership Similarity Metric 24
3.3 Optimal Similarity Metric: an upper bound for similarity of two trees 26
3.4 DMC Introduction 27
3.4.1 How the distance (cost) is calculated by DTW 29
3.4.2 Similarity Matrix sorted by predictions 32
3.4.3 Near-diagonal path in sorted matrix 35
3.4.4 Algorithm to compute DMC similarity score 36
Chapter 4. Proposed Application of DMC Procedure 41
4.1. General Procedure 41
4.2. Scenario A 44
4.3. Scenario B 46
Chapter 5. Empirical Demonstration 48
5.1. Dataset Description 48
5.2. Scenario Demonstration 49
5.2.1 Preprocessing Techniques before similarity 50
5.2.2 RESULT 1: Membership Similarity Heatmap Visualization 53
5.2.3 RESULT 2: Inherit DTW Two-Way Plot & Three-Way Plot 55
5.2.4 RESULT3: Membership similarity & Decision rules table for optimal pairing leaves 57
5.2.5 RESULT4: Optimal Similarity and Relative Membership Similarity Ratio 58
Chapter 6. Discussion and Future Work 60
References 63
Glossary of Terms 69

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