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題名 高維多變量分布的近似學習
High-Dimensional Multivariate Distributions: Approximation and Learning
作者 林盈盈
Lin, Ying-Ying
貢獻者 周彥君<br>莊皓鈞
Chou, Yen-Chun<br>Chuang, Hao-Chun
林盈盈
Lin, Ying-Ying
關鍵詞 多變量分布
混合密度網路
低秩近似法
高斯 Copula
報童問題
Multivariate Distribution
Mixture Density Network
Low-rank approximation
Gaussian Copula
Newsvendor problem
日期 2024
上傳時間 4-Sep-2024 14:02:43 (UTC+8)
摘要 本研究深入探討高維多變量分布的近似學習問題，並提出兩種創新方法以應對高維度配適的挑戰：結合多變量混合密度網絡（MDN）與低秩近似法，及基於高斯Copula和低秩近似的長短期記憶模型（LSTM）。研究結果表明，這些方法在處理複雜的多變量分布和高維共變異矩陣估計方面均表現出顯著效果。在高維度的模擬實驗中，低秩近似法顯著提升MDN模型在高維數據配適中的準確性與穩定性。此外，本研究模擬高維度的自回歸離散時間序列數據，並針對多品項報童問題進行條件風險價值（CVaR）最佳化，發現使用經典高斯分布作為邊際分布的Copula LSTM模型表現不如預期，因此採用更具彈性的指數修正高斯分布，此方法在時間序列聯合分布學習和風險管理中的利潤優化上展現更優的性能。
This study investigates the approximation of high-dimensional multivariate distributions and introduces two innovative methods to tackle the challenges of high-dimensional distribution fitting: combining Mixture Density Networks (MDN) with low-rank approximation and developing a Copula LSTM model based on Gaussian Copula, Long Short-Term Memory (LSTM), and low-rank approximation. The results indicate that these methods are effective in managing complex multivariate distributions and estimating high-dimensional covariance matrices. In high-dimensional simulation experiments, the low-rank approximation notably enhances the accuracy and stability of the MDN model. Furthermore, this study simulates high-dimensional autoregressive discrete time series data and performs Conditional Value at Risk (CVaR) optimization for multi-item newsvendor problems. It reveals that the Copula LSTM model using classical Gaussian distributions as marginal distributions underperforms. Consequently, an exponentially modified Gaussian distribution is adopted, demonstrating superior performance in time series joint distribution learning and risk-averse profit optimization.
參考文獻 Bishop, C. M. (1994). Mixture density networks. Technical Report. Aston University, Birmingham. (Unpublished). Bishop, C. M. (2006). Pattern Recognition and Machine Learning (Information Science and Statistics). Springer-Verlag. Brando Guillaumes, A. (2017). Mixture density networks for distribution and uncertainty estimation. Universitat Politècnica de Catalunya. Carruthers, J., & Finnie, T. (2023). Using mixture density networks to emulate a stochastic within-host model of Francisella tularensis infection. PLOS Computational Biology, 19(12), e1011266. Charpentier, A., Fermanian, J.-D., & Scaillet, O. (2007). The estimation of copulas: Theory and practice. Copulas: From theory to application in finance, 35. Chen, D., Xue, Y., & Gomes, C. (2018). End-to-end learning for the deep multivariate probit model. International Conference on Machine Learning, Chen, J., & Tan, X. (2009). Inference for multivariate normal mixtures. Journal of Multivariate Analysis, 100(7), 1367-1383. Chen, Y., Xu, M., & Zhang, Z. G. (2009). A risk-averse newsvendor model under the CVaR criterion. Operations research, 57(4), 1040-1044. Danaher, P. J., & Smith, M. S. (2011). Modeling multivariate distributions using copulas: Applications in marketing. Marketing science, 30(1), 4-21. Elidan, G. (2013). Copulas in machine learning. Copulae in Mathematical and Quantitative Finance: Proceedings of the Workshop Held in Cracow, 10-11 July 2012 (pp. 39-60). Berlin, Heidelberg: Springer Berlin Heidelberg. Gonçalves, J. N., Cortez, P., Carvalho, M. S., & Frazao, N. M. (2021). A multivariate approach for multi-step demand forecasting in assembly industries: Empirical evidence from an automotive supply chain. Decision Support Systems, 142, 113452. Haney, S. (2011). Practical applications and properties of the Exponentially Modified Gaussian (EMG) distribution Drexel University]. Huber, J., Müller, S., Fleischmann, M., & Stuckenschmidt, H. (2019). A data-driven newsvendor problem: From data to decision. European Journal of Operational Research, 278(3), 904-915. Jammernegg, W., & Kischka, P. (2012). Newsvendor problems with VaR and CVaR consideration. Handbook of newsvendor problems: models, extensions and applications, 197-216. Kruse, J. (2020). Technical report: Training mixture density networks with full covariance matrices. arXiv preprint arXiv:2003.05739. Liboschik, T., Fokianos, K., & Fried, R. (2017). tscount: An R package for analysis of count time series following generalized linear models. Journal of Statistical Software, 82, 1-51. Madan, D. B. (2020). Multivariate distributions for financial returns. International Journal of Theoretical and Applied Finance, 23(06), 2050041. Makansi, O., Ilg, E., Cicek, O., & Brox, T. (2019). Overcoming limitations of mixture density networks: A sampling and fitting framework for multimodal future prediction. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (pp. 7144-7153). Norwood, B., Roberts, M. C., & Lusk, J. L. (2004). Ranking crop yield models using out‐of‐sample likelihood functions. American Journal of Agricultural Economics, 86(4), 1032-1043. Peerlings, D. E., van den Brakel, J. A., Baştürk, N., & Puts, M. J. (2022). Multivariate density estimation by neural networks. IEEE Transactions on Neural Networks and Learning Systems. Reynolds, D. A. (2009). Gaussian mixture models. Encyclopedia of biometrics, 741(659-663). Salinas, D., Bohlke-Schneider, M., Callot, L., Medico, R., & Gasthaus, J. (2019). High-dimensional multivariate forecasting with low-rank gaussian copula processes. Advances in neural information processing systems, 32. Trentin, E., Lusnig, L., & Cavalli, F. (2018). Parzen neural networks: Fundamentals, properties, and an application to forensic anthropology. Neural Networks, 97, 137-151. Vapnik, V. (1995). The nature of statistical learning theory. Springer. Wang, J., & Taaffe, M. R. (2015). Multivariate mixtures of normal distributions: properties, random vector generation, fitting, and as models of market daily changes. INFORMS Journal on Computing, 27(2), 193-203. Wang, T., Cho, K., & Wen, M. (2019). Attention-based mixture density recurrent networks for history-based recommendation. Proceedings of the 1st International Workshop on Deep Learning Practice for High-Dimensional Sparse Data (pp. 1-9). Wilson, A. G., & Ghahramani, Z. (2010). Copula processes. Advances in neural information processing systems, 23. Xu, J., & Cao, L. (2023). Copula variational LSTM for high-dimensional cross-market multivariate dependence modeling. IEEE Transactions on Neural Networks and Learning Systems. Yu, J.-b., & Xi, L.-f. (2009). A neural network ensemble-based model for on-line monitoring and diagnosis of out-of-control signals in multivariate manufacturing processes. Expert systems with applications, 36(1), 909-921. Zeldes, Y., Theodorakis, S., Solodnik, E., Rotman, A., Chamiel, G., & Friedman, D. (2017). Deep density networks and uncertainty in recommender systems. arXiv preprint arXiv:1711.02487. Zhou, Y., Gao, J., & Asfour, T. (2020). Movement primitive learning and generalization: Using mixture density networks. IEEE Robotics & Automation Magazine, 27(2), 22-32.
描述 碩士
國立政治大學
資訊管理學系
111356005
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0111356005
資料類型 thesis
dc.contributor.advisor 周彥君<br>莊皓鈞zh_TW
dc.contributor.advisor Chou, Yen-Chun<br>Chuang, Hao-Chunen_US
dc.contributor.author (Authors) 林盈盈zh_TW
dc.contributor.author (Authors) Lin, Ying-Yingen_US
dc.creator (作者) 林盈盈zh_TW
dc.creator (作者) Lin, Ying-Yingen_US
dc.date (日期) 2024en_US
dc.date.accessioned 4-Sep-2024 14:02:43 (UTC+8)-
dc.date.available 4-Sep-2024 14:02:43 (UTC+8)-
dc.date.issued (上傳時間) 4-Sep-2024 14:02:43 (UTC+8)-
dc.identifier (Other Identifiers) G0111356005en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/153145-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 資訊管理學系zh_TW
dc.description (描述) 111356005zh_TW
dc.description.abstract (摘要) 本研究深入探討高維多變量分布的近似學習問題，並提出兩種創新方法以應對高維度配適的挑戰：結合多變量混合密度網絡（MDN）與低秩近似法，及基於高斯Copula和低秩近似的長短期記憶模型（LSTM）。研究結果表明，這些方法在處理複雜的多變量分布和高維共變異矩陣估計方面均表現出顯著效果。在高維度的模擬實驗中，低秩近似法顯著提升MDN模型在高維數據配適中的準確性與穩定性。此外，本研究模擬高維度的自回歸離散時間序列數據，並針對多品項報童問題進行條件風險價值（CVaR）最佳化，發現使用經典高斯分布作為邊際分布的Copula LSTM模型表現不如預期，因此採用更具彈性的指數修正高斯分布，此方法在時間序列聯合分布學習和風險管理中的利潤優化上展現更優的性能。zh_TW
dc.description.abstract (摘要) This study investigates the approximation of high-dimensional multivariate distributions and introduces two innovative methods to tackle the challenges of high-dimensional distribution fitting: combining Mixture Density Networks (MDN) with low-rank approximation and developing a Copula LSTM model based on Gaussian Copula, Long Short-Term Memory (LSTM), and low-rank approximation. The results indicate that these methods are effective in managing complex multivariate distributions and estimating high-dimensional covariance matrices. In high-dimensional simulation experiments, the low-rank approximation notably enhances the accuracy and stability of the MDN model. Furthermore, this study simulates high-dimensional autoregressive discrete time series data and performs Conditional Value at Risk (CVaR) optimization for multi-item newsvendor problems. It reveals that the Copula LSTM model using classical Gaussian distributions as marginal distributions underperforms. Consequently, an exponentially modified Gaussian distribution is adopted, demonstrating superior performance in time series joint distribution learning and risk-averse profit optimization.en_US
dc.description.tableofcontents 第一章 緒論 1 第二章 文獻探討 4 第三章 多變量混合密度網路與低秩近似法 6 第一節 模型設計 6 第二節 模擬實驗 12 第四章 高斯Copula、LSTM與低秩近似法 14 第一節 模型設計 14 第二節 模擬實驗 19 第三節 條件風險價值最佳化 23 第五章 結論 30 參考文獻 31zh_TW
dc.format.extent 2808062 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0111356005en_US
dc.subject (關鍵詞) 多變量分布zh_TW
dc.subject (關鍵詞) 混合密度網路zh_TW
dc.subject (關鍵詞) 低秩近似法zh_TW
dc.subject (關鍵詞) 高斯 Copulazh_TW
dc.subject (關鍵詞) 報童問題zh_TW
dc.subject (關鍵詞) Multivariate Distributionen_US
dc.subject (關鍵詞) Mixture Density Networken_US
dc.subject (關鍵詞) Low-rank approximationen_US
dc.subject (關鍵詞) Gaussian Copulaen_US
dc.subject (關鍵詞) Newsvendor problemen_US
dc.title (題名) 高維多變量分布的近似學習zh_TW
dc.title (題名) High-Dimensional Multivariate Distributions: Approximation and Learningen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) Bishop, C. M. (1994). Mixture density networks. Technical Report. Aston University, Birmingham. (Unpublished). Bishop, C. M. (2006). Pattern Recognition and Machine Learning (Information Science and Statistics). Springer-Verlag. Brando Guillaumes, A. (2017). Mixture density networks for distribution and uncertainty estimation. Universitat Politècnica de Catalunya. Carruthers, J., & Finnie, T. (2023). Using mixture density networks to emulate a stochastic within-host model of Francisella tularensis infection. PLOS Computational Biology, 19(12), e1011266. Charpentier, A., Fermanian, J.-D., & Scaillet, O. (2007). The estimation of copulas: Theory and practice. Copulas: From theory to application in finance, 35. Chen, D., Xue, Y., & Gomes, C. (2018). End-to-end learning for the deep multivariate probit model. International Conference on Machine Learning, Chen, J., & Tan, X. (2009). Inference for multivariate normal mixtures. Journal of Multivariate Analysis, 100(7), 1367-1383. Chen, Y., Xu, M., & Zhang, Z. G. (2009). A risk-averse newsvendor model under the CVaR criterion. Operations research, 57(4), 1040-1044. Danaher, P. J., & Smith, M. S. (2011). Modeling multivariate distributions using copulas: Applications in marketing. Marketing science, 30(1), 4-21. Elidan, G. (2013). Copulas in machine learning. Copulae in Mathematical and Quantitative Finance: Proceedings of the Workshop Held in Cracow, 10-11 July 2012 (pp. 39-60). Berlin, Heidelberg: Springer Berlin Heidelberg. Gonçalves, J. N., Cortez, P., Carvalho, M. S., & Frazao, N. M. (2021). A multivariate approach for multi-step demand forecasting in assembly industries: Empirical evidence from an automotive supply chain. Decision Support Systems, 142, 113452. Haney, S. (2011). Practical applications and properties of the Exponentially Modified Gaussian (EMG) distribution Drexel University]. Huber, J., Müller, S., Fleischmann, M., & Stuckenschmidt, H. (2019). A data-driven newsvendor problem: From data to decision. European Journal of Operational Research, 278(3), 904-915. Jammernegg, W., & Kischka, P. (2012). Newsvendor problems with VaR and CVaR consideration. Handbook of newsvendor problems: models, extensions and applications, 197-216. Kruse, J. (2020). Technical report: Training mixture density networks with full covariance matrices. arXiv preprint arXiv:2003.05739. Liboschik, T., Fokianos, K., & Fried, R. (2017). tscount: An R package for analysis of count time series following generalized linear models. Journal of Statistical Software, 82, 1-51. Madan, D. B. (2020). Multivariate distributions for financial returns. International Journal of Theoretical and Applied Finance, 23(06), 2050041. Makansi, O., Ilg, E., Cicek, O., & Brox, T. (2019). Overcoming limitations of mixture density networks: A sampling and fitting framework for multimodal future prediction. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (pp. 7144-7153). Norwood, B., Roberts, M. C., & Lusk, J. L. (2004). Ranking crop yield models using out‐of‐sample likelihood functions. American Journal of Agricultural Economics, 86(4), 1032-1043. Peerlings, D. E., van den Brakel, J. A., Baştürk, N., & Puts, M. J. (2022). Multivariate density estimation by neural networks. IEEE Transactions on Neural Networks and Learning Systems. Reynolds, D. A. (2009). Gaussian mixture models. Encyclopedia of biometrics, 741(659-663). Salinas, D., Bohlke-Schneider, M., Callot, L., Medico, R., & Gasthaus, J. (2019). High-dimensional multivariate forecasting with low-rank gaussian copula processes. Advances in neural information processing systems, 32. Trentin, E., Lusnig, L., & Cavalli, F. (2018). Parzen neural networks: Fundamentals, properties, and an application to forensic anthropology. Neural Networks, 97, 137-151. Vapnik, V. (1995). The nature of statistical learning theory. Springer. Wang, J., & Taaffe, M. R. (2015). Multivariate mixtures of normal distributions: properties, random vector generation, fitting, and as models of market daily changes. INFORMS Journal on Computing, 27(2), 193-203. Wang, T., Cho, K., & Wen, M. (2019). Attention-based mixture density recurrent networks for history-based recommendation. Proceedings of the 1st International Workshop on Deep Learning Practice for High-Dimensional Sparse Data (pp. 1-9). Wilson, A. G., & Ghahramani, Z. (2010). Copula processes. Advances in neural information processing systems, 23. Xu, J., & Cao, L. (2023). Copula variational LSTM for high-dimensional cross-market multivariate dependence modeling. IEEE Transactions on Neural Networks and Learning Systems. Yu, J.-b., & Xi, L.-f. (2009). A neural network ensemble-based model for on-line monitoring and diagnosis of out-of-control signals in multivariate manufacturing processes. Expert systems with applications, 36(1), 909-921. Zeldes, Y., Theodorakis, S., Solodnik, E., Rotman, A., Chamiel, G., & Friedman, D. (2017). Deep density networks and uncertainty in recommender systems. arXiv preprint arXiv:1711.02487. Zhou, Y., Gao, J., & Asfour, T. (2020). Movement primitive learning and generalization: Using mixture density networks. IEEE Robotics & Automation Magazine, 27(2), 22-32.zh_TW