處理多重實例學習中標籤歧義的貝氏方法

Abstract

多實例學習 (MIL) 是弱監督學習問題，已被應用於許多領域。多實例（MI）數據包括了袋子和實例的概念，其中每個袋子中都包含了一些實例。另外，袋子的資訊是已知的，而實例的資訊是缺失的。Carbonneau et al. (2018) 提到由於多實例數據中存在缺失值，因此標籤歧義 (label ambiguity) 是在 MIL 中的常見問題。在本論文中，我們了解了某些可能造成標籤歧義的來源，並提出了一個新的袋子模型來解決此問題。我們提出的模型具有幾個優勢：除了放寬現有 MIL 方法中常用的嚴格假設，也能提供更多實例與袋子關聯性的資訊，並且可以與於許多不同的實例分類方法一起合併使用，例如羅吉斯回歸。 本文討論的 MIL 模型是使用貝氏的吉布斯採樣進行模型推論。我們在吉布斯採樣過程中使用變量擴展的方法，具體來說是引入了玻利亞伽瑪的潛變量。我們對提出的袋子模型與現有方法（例如Haußmann et al. (2017) 中提出的方法）進行了比較分析，證明了我們方法的有效性。最後，通過模擬以及實際資料的實驗，驗證了我們方法的性能。

Multiple Instance Learning (MIL) is a weakly supervised learning problem, and it has been used in various fields. Multiple Instance (MI) data includes the concepts of bag and instance, where each bag contains several instances. Also, the bag information is observed, while the instance information is missing. Carbonneau et al. (2018) mentions that label ambiguity is a common issue in MIL due to the missing values in the MI data. In this thesis, we investigate the sources of label ambiguity and propose a novel bag model to address this issue. Our proposed model offers several advantages: (i) It relaxes the strict MIL assumption commonly employed in existing MIL methods. (ii) It provides greater insight into the relationship between instances and their corresponding bags. (iii) It can be integrated with various classifiers at the instance level, such as logistic regression. The MIL models discussed here are inferred by a Gibbs sampling scheme, which is a Bayesian approach. We employ a variable augmentation technique on the Gibbs sampling process, specifically the Pólya­Gamma augmentation. Comparative analysis between our proposed bag model and existing methods, such as the one presented in Haußmann et al. (2017), demonstrate the effectiveness of our approach. Finally, we validate the performance of our model through various simulations and real data.