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| 研究生： |
陳冠廷 Chen, Kuan-Ting |
|---|---|
| 論文名稱： |
隨機梯度下降法對於順序迴歸模型估計之收斂研究及推薦系統應用 Convergence of Stochastic Gradient Descent for Ordinal Regression Model and Applications for Recommender Systems |
| 指導教授： |
翁久幸
Weng, Chiu-Hsing |
| 口試委員: |
黃子銘
Huang, Tzee-Ming 蔡恆修 Tsai, Heng-Hsiu |
| 學位類別： |
碩士
Master |
| 系所名稱： |
商學院 - 統計學系 Department of Statistics |
| 論文出版年： | 2020 |
| 畢業學年度： | 108 |
| 語文別： | 英文 |
| 論文頁數： | 47 |
| 中文關鍵詞： | 矩陣分解 、順序迴歸 、隨機梯度下降法 、批次隨機梯度下降法 、平均估計 |
| 外文關鍵詞： | Matrix Factorization, Ordinal Regression, Stochastic Gradient Descent, Mini-Batch Stochastic Gradient Descent, Average Estimate |
| DOI URL： | http://doi.org/10.6814/NCCU202000780 |
| 相關次數： | 點閱：109 下載：19 |
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矩陣分解是一種普及的協同過濾方法，Koren和Sill在2011年提出了基於順序迴歸的矩陣分解方法。相較於傳統的矩陣分解方法，由於基於順序迴歸的矩陣分解方法能夠輸出用戶對物品各項評分的出現機率，因此在應用方面上具有優勢。雖然他們的實驗在準確性上表現優異，但目前尚沒有開源的程式能夠使用。此次論文我們便應用隨機梯度下降法來實現此矩陣分解模型，並討論遭遇到的數值問題，由於此模型涉及順序迴歸模型，我們也研究了順序迴歸模型在隨機梯度下降法下，其參數估計的收斂。
Matrix factorization is a popular Collaborating Filtering (CF) method. Koren and Sill (2011) proposed an ordinal regression model with a matrix factorization CF method. This approach is advantageous over traditional matrix factorization methods by its ability to output a full probability distribution of the user-item ratings. Though their experiments showed superior results in its accuracy, there is no publicly available software. In this thesis, we implement the algorithms by Stochastic Gradient Descent (SGD) and discuss the numerical issues encountered. As this approach involves ordinal regression models, we will study the convergence of SGD for ordinal regression models as well.
1 INTRODUCTION 5
2 REVIEW 7
2.1 Matrix Factorization Model 7
2.2 Ordinal Regression Model 10
2.3 OrdRec Model 11
2.4 Learning Algorithms 13
3 ORDINAL REGRESSION IMPLEMENTATION 16
3.1 Numerical Problems in Simulation 16
3.2 ASGD for Ordinal Regression Model 20
4 RECOMMENDER SYSTEM IMPLEMENTATION 22
4.1 Optimization Details 22
4.2 Recommender System Update Rule 24
4.3 Simulation for OrdRec Model 27
5 REAL APPLICATION 31
5.1 Experiment Dataset 31
5.2 Evaluation Metrics 33
5.3 Performance Comparison 34
5.4 Check for Convergence 36
6 CONCLUSION 39
A Optimization Detail of Ordinal Regression Models 40
B Assumption Verification 44
References 47
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