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題名 基於貝氏IRT模型之線上學習演算法
Online Learning Algorithms based on Bayesian IRT models
作者 賴翔偉
貢獻者 翁久幸
賴翔偉
關鍵詞 項目反應理論
潛在變量
貝氏
動差配對法
靜態學習
動態學習
Bayesian
Dynamical learning
Item response theory
Latent trait
Moment-matching method
Statical learning
日期 2018
上傳時間 27-Jul-2018 11:28:29 (UTC+8)
摘要 我們在此篇論文中呈現兩種類型的線上學習演算法─靜態與動態，用以即時的量化網路評分類型資料中，使用者與被評分項的潛在變量。靜態學習演算法是延續Weng and Coad (2018)的結果，在他們所採用Ho and Quinn (2008)的Bayesian ordinal IRT 模型中的截斷點加上常態型先驗分配；動態學習演算法則是試行Graepel et al.(2010)中所採用的動態概念來改進靜態學習演算法下可能產生的缺失。
透過實驗，我們得到以下兩個結論：(1)截斷點加上先驗分配後，經過序列化的修正所得到的結果，會比截斷點沒有設置先驗並固定下所得到的結果來的好；(2)雖然靜態學習演算法的運算時間少於動態學習演算法，但動態學習在某些配置下，可能會表現的比靜態學習好。
在文末，針對 Ho and Quinn的Bayesian ordinal IRT 模型中的潛在變量，我們給出幾個比較合適的先驗參數配置。
In this paper, we present two types of online learning algorithms--statical and dynamical--to capture users’ and items’ latent traits’ information through online product rating data in a real-time manner. The statical one extends Weng and Coad (2018)’s deterministic moment-matching method by adding priors to cutpoints, and the dynamical one extends the statical one with the dynamical ideas adopted in Graepel et al. (2010) for taking users’ and items’ time-dependent latent traits into account. Both learning algorithms are designed for the Bayesian ordinal IRT model proposed by Ho and Quinn (2008).

Through experiments, we have verified two things: First, updating cutpoints sequentially produces better results. Second, statical learning’s computational time is almost twice as less as dynamical learning’s, but dynamical learning can
slightly outperform statical learning under some configurations.

At the end of the paper, we give some useful configurations for setting up the priors of the latent variables of Ho and Quinn’s ordinal IRT model.
參考文獻 Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee’s ability. Statistical theories of mental test scores.
Coelho, F. C., Codeço, C. T., and Gomes, M. G. M. (2011). A bayesian framework for parameter estimation in dynamical models. PloS one, 6(5):e19616.
Graepel, T., Candela, J. Q., Borchert, T., and Herbrich, R. (2010). Web-scale bayesian click-through rate prediction for sponsored search advertising in microsoft’s bing search engine. Omnipress.
Harper, F. M. and Konstan, J. A. (2016). The movielens datasets: History and context. ACM Transactions on Interactive Intelligent Systems (TiiS), 5(4):19.
Ho, D. E. and Quinn, K. M. (2008). Improving the presentation and interpretation of online ratings data with model-based figures. The American Statistician, 62(4):279-288.
McNeish, D. (2016). On using Bayesian methods to address small sample problems. Structural Equation Modeling: A Multidisciplinary Journal, 23(5):750-773.
Moser, J. (2010). The math behind trueskill.
Muraki, E. (1990). Fitting a polytomous item response model to likert-type data. Applied Psychological Measurement, 14(1):59-71.
Rasch, G. (1961). On general laws and the meaning of measurement in psychology. In Proceedings of the fourth Berkeley symposium on mathematical statistics and probability, volume 4, pages 321 333.
Samejima, F. (1970). Estimation of latent ability using a response pattern of graded scores. Psychometrika, 35(1):139-139.
Shane Mac (2016). The pendulum. my attempt at building a diverse company from the start.
Strogatz, S. H. (1994). Nonlinear dynamics and chaos: With applications to physics, biology, chemistry and engineering.
Van De Schoot, R., Broere, J. J., Perryck, K. H., Zondervan-Zwijnenburg, M., and Van Loey, N. E. (2015). Analyzing small data sets using bayesian estimation: the case of post-traumatic stress symptoms following mechanical ventilation in burn survivors. European Journal of Psychotraumatology, 6(1):25216.
van der Linden, W. J. (2010). Item respoinse theory. In International Encyclopedia of Education, pages 81-88.
Weng, R. C.-H. and Coad, D. S. (2018). Real-time bayesian parameter estimation for item response models. Bayesian Analysis, 13(1):115-137.
Weng, R. C.-H. and Lin, C.-J. (2011). A bayesian approximation method for online ranking. Journal of Machine Learning Research, 12(Jan):267-300.
描述 碩士
國立政治大學
統計學系
105354011
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0105354011
資料類型 thesis
dc.contributor.advisor 翁久幸zh_TW
dc.contributor.author (Authors) 賴翔偉zh_TW
dc.creator (作者) 賴翔偉zh_TW
dc.date (日期) 2018en_US
dc.date.accessioned 27-Jul-2018 11:28:29 (UTC+8)-
dc.date.available 27-Jul-2018 11:28:29 (UTC+8)-
dc.date.issued (上傳時間) 27-Jul-2018 11:28:29 (UTC+8)-
dc.identifier (Other Identifiers) G0105354011en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/118932-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 統計學系zh_TW
dc.description (描述) 105354011zh_TW
dc.description.abstract (摘要) 我們在此篇論文中呈現兩種類型的線上學習演算法─靜態與動態，用以即時的量化網路評分類型資料中，使用者與被評分項的潛在變量。靜態學習演算法是延續Weng and Coad (2018)的結果，在他們所採用Ho and Quinn (2008)的Bayesian ordinal IRT 模型中的截斷點加上常態型先驗分配；動態學習演算法則是試行Graepel et al.(2010)中所採用的動態概念來改進靜態學習演算法下可能產生的缺失。
透過實驗，我們得到以下兩個結論：(1)截斷點加上先驗分配後，經過序列化的修正所得到的結果，會比截斷點沒有設置先驗並固定下所得到的結果來的好；(2)雖然靜態學習演算法的運算時間少於動態學習演算法，但動態學習在某些配置下，可能會表現的比靜態學習好。
在文末，針對 Ho and Quinn的Bayesian ordinal IRT 模型中的潛在變量，我們給出幾個比較合適的先驗參數配置。		zh_TW
dc.description.abstract (摘要) In this paper, we present two types of online learning algorithms--statical and dynamical--to capture users’ and items’ latent traits’ information through online product rating data in a real-time manner. The statical one extends Weng and Coad (2018)’s deterministic moment-matching method by adding priors to cutpoints, and the dynamical one extends the statical one with the dynamical ideas adopted in Graepel et al. (2010) for taking users’ and items’ time-dependent latent traits into account. Both learning algorithms are designed for the Bayesian ordinal IRT model proposed by Ho and Quinn (2008).

Through experiments, we have verified two things: First, updating cutpoints sequentially produces better results. Second, statical learning’s computational time is almost twice as less as dynamical learning’s, but dynamical learning can
slightly outperform statical learning under some configurations.

At the end of the paper, we give some useful configurations for setting up the priors of the latent variables of Ho and Quinn’s ordinal IRT model.		en_US
dc.description.tableofcontents 1 Introduction ---1

2 Online Rating Data --- 3

3 Item Response Theory (IRT) --- 5
3.1 Unidimensional Logistic Models for Dichotomous Items --- 6
3.2 Models for Polytomous Items --- 7

4 Online Learning Algorithm --- 10
4.1 Statical Learning --- 10
4.2 Dynamical Learning --- 16

5 Experimental Results --- 22
5.1 Limiting properties of Ω " and Δ " --- 22
5.2 Algorithm Evaluation --- 27
5.2.1 Simulation --- 27
5.2.2 Statical vs. dynamical --- 29
5.3 Configuration searching process --- 31

6 Conclusions --- 36

References --- 37

A Derivations of Statical Learning formulas --- 39
A.1 Preliminaries --- 40
A.2 Posterior expectation and variation of α j --- 41
A.3 Posterior expectation and variation of β j --- 43
A.4 Posterior expectation and variation of θ i --- 45
A.5 Posterior expectation and variation of (γ c−1 , γ c ) --- 45
A.6 Limiting properties of Ω " and Δ " --- 45		zh_TW
dc.format.extent 1019134 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0105354011en_US
dc.subject (關鍵詞) 項目反應理論zh_TW
dc.subject (關鍵詞) 潛在變量zh_TW
dc.subject (關鍵詞) 貝氏zh_TW
dc.subject (關鍵詞) 動差配對法zh_TW
dc.subject (關鍵詞) 靜態學習zh_TW
dc.subject (關鍵詞) 動態學習zh_TW
dc.subject (關鍵詞) Bayesianen_US
dc.subject (關鍵詞) Dynamical learningen_US
dc.subject (關鍵詞) Item response theoryen_US
dc.subject (關鍵詞) Latent traiten_US
dc.subject (關鍵詞) Moment-matching methoden_US
dc.subject (關鍵詞) Statical learningen_US
dc.title (題名) 基於貝氏IRT模型之線上學習演算法zh_TW
dc.title (題名) Online Learning Algorithms based on Bayesian IRT modelsen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee’s ability. Statistical theories of mental test scores.
Coelho, F. C., Codeço, C. T., and Gomes, M. G. M. (2011). A bayesian framework for parameter estimation in dynamical models. PloS one, 6(5):e19616.
Graepel, T., Candela, J. Q., Borchert, T., and Herbrich, R. (2010). Web-scale bayesian click-through rate prediction for sponsored search advertising in microsoft’s bing search engine. Omnipress.
Harper, F. M. and Konstan, J. A. (2016). The movielens datasets: History and context. ACM Transactions on Interactive Intelligent Systems (TiiS), 5(4):19.
Ho, D. E. and Quinn, K. M. (2008). Improving the presentation and interpretation of online ratings data with model-based figures. The American Statistician, 62(4):279-288.
McNeish, D. (2016). On using Bayesian methods to address small sample problems. Structural Equation Modeling: A Multidisciplinary Journal, 23(5):750-773.
Moser, J. (2010). The math behind trueskill.
Muraki, E. (1990). Fitting a polytomous item response model to likert-type data. Applied Psychological Measurement, 14(1):59-71.
Rasch, G. (1961). On general laws and the meaning of measurement in psychology. In Proceedings of the fourth Berkeley symposium on mathematical statistics and probability, volume 4, pages 321 333.
Samejima, F. (1970). Estimation of latent ability using a response pattern of graded scores. Psychometrika, 35(1):139-139.
Shane Mac (2016). The pendulum. my attempt at building a diverse company from the start.
Strogatz, S. H. (1994). Nonlinear dynamics and chaos: With applications to physics, biology, chemistry and engineering.
Van De Schoot, R., Broere, J. J., Perryck, K. H., Zondervan-Zwijnenburg, M., and Van Loey, N. E. (2015). Analyzing small data sets using bayesian estimation: the case of post-traumatic stress symptoms following mechanical ventilation in burn survivors. European Journal of Psychotraumatology, 6(1):25216.
van der Linden, W. J. (2010). Item respoinse theory. In International Encyclopedia of Education, pages 81-88.
Weng, R. C.-H. and Coad, D. S. (2018). Real-time bayesian parameter estimation for item response models. Bayesian Analysis, 13(1):115-137.
Weng, R. C.-H. and Lin, C.-J. (2011). A bayesian approximation method for online ranking. Journal of Machine Learning Research, 12(Jan):267-300.		zh_TW
dc.identifier.doi (DOI) 10.6814/THE.NCCU.STAT.006.2018.B03-