支援向量機、邏輯式迴歸和費雪線性判別分析之影響函數與穩健性的比較

Abstract

不管是人為或是非人為所產生的離群值都會對模型造成嚴重的影響，也因此我們利用影響函數去計算支援向量機、邏輯式回歸和費雪線性判別分析之間對離群值的影響，來藉此研究不同模型之間的穩健性。在論文中，我們特別針對在參數估計以及分類錯誤率的影響函數來研究。

In literature there are quite some renowned classical linear methods for discriminant analysis. Their performance may heavily depend on the quality of the training data. However, in practice, the training data might not be clean enough. There might be outliers due to some unexpected error, or heavy-tail distribution, or data contamination, etc. With the contaminated data, the resulting inference might not go well, or might even fail. Thus, the ability to be resistant to outliers becomes an important issue in statistical inference. Linear methods are fundamental for data analysis. In this thesis, we will focus on three types of linear classifiers, namely, logistic regression, support vector machine and Fisher linear discriminant analysis. Their influence functions for parameter estimation and error rate will be discussed and several numerical examples will be presented.