不平衡問題 (data imbalance)是目前資料探勘領域中所面臨的重要挑戰之一。至今為止的研究主要聚焦在結果變數 (outcome variable) 的類別不平衡問題 (class imbalance)，而本研究旨在探討另一類型的不平衡問題：預測變數之不平衡問題 (predictor imbalance)，此問題可能導致資料探勘結果對少數族群的不利決策。就研究者目前所知，此一議題尚未在研究文獻中被提及探討。

本研究運用實驗設計來檢驗不平衡預測變數在分類樹 (classification trees) 及邏輯迴歸 (logistic regression) 上的影響。研究結果發現，即使某一不平衡預測變數對於樣本中的某些少數族群（如，某特定人種、疾病等）擁有絕佳的分類能力，但在以不純度為分類基礎的分類樹 (impurity based trees) 及以統計方法為分類基礎的分類樹 (statistic-based trees) 中，該預測變數的重要性極可能被忽略。若忽略此預測變數，在自動化決策蓬勃發展的今日，資料探勘結果很可能導致決策的偏誤，使得決策對於少數族群不利。本研究並提出針對不平衡預測變數之檢測、處理做法。

One key challenge for the data mining community is the problem of data imbalance. While the vast majority of research focuses on the outcome class imbalance problem, this research investigates another type of data imbalance: the predictor imbalance, a problem that would lead to discrimination against minority groups in an automated decision making process.

In this research, we examine the effects of predictor imbalance on classification trees and logistic regression. We posit that unbalanced predictors are likely to be ignored in impurity based trees and some statistic-based trees even when they can perfectly classify the observations in rare subgroups (e.g., rare human races, diseases, etc.). Ignoring such an unbalanced predictor may lead to unjust decision making. This is particularly an issue nowadays as many managerial decisions are driven by AI and data analytical outputs. Guidelines to detect and address discrimination based on unbalanced predictors are also provided.

1. Introduction 2
2. Literature Review 3
2.1 The Data Imbalance Problem 3
2.1.1 Class Imbalance 3
2.1.2 Within-Class Imbalance 3
2.1.3 Unbalanced Predictors and Rare Cases 3
2.2 Classification Tree 5
2.2.1 Classification Tree 5
2.2.2 Splitting Criteria 6
2.2.3 Impurity-based Criteria 6
2.2.4 Statistics-based Criteria 7
2.2.5 Problems of Trees 8
2.3 Logistic Regression 8
2.3.1 Logistic Regression 8
2.3.2 Separation 9
3. Effect of An Unbalanced Predictor on Trees and Logistic Regression 10
3.1 Impurity-based Trees 10
3.2 Statistics-based Trees and Logistic Regression 11
3.3 A Relevant Issue: Separation 11
4. Experimental Design 12
4.1 Data Example: Survival on the Titanic 12
4.2 Modified Titanic Dataset 12
4.3 Study 1: Classification Tree 13
4.4 Study 2: Logistic Regression 14
5. Experimental Results 14
5.1 Study 1: Classification Tree 14
5.1.1 Effect of Under/over-sampling the Unbalanced Predictor 15
5.1.2 Effect of Unbalanced Predictor: Ratio vs. Number of Observations 18
5.1.3 Effect of Discriminatory Power of Unbalanced Predictor 21
5.1.4 Effect of Strength of Other Predictors 26
5.2 Study 2: Logistic Regression 28
5.2.1 Separation Effect 28
5.2.2 Effect of under/over-sampling the unbalanced predictor 30
6. Guidelines, Conclusions, and Future Directions 32
6.1 Guidelines 32
6.2 Conclusions 33
6.3 Future Directions 33
References 35

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