Beyond point forecasts: Uncertainty quantification in tensor extrapolation for relational time series data

References

• Araujo, M., P. Ribeiro, and C. Faloutsos. 2017. “TensorCast: Forecasting with Context Using Coupled Tensors.” In Proceedings of the IEEE International Conference on Data Mining (ICDM), 71–80. IEEE.
   Google Scholar
• Barsbey, M., and T. Cemgil. 2023. “Modeling Hierarchical Seasonality through Low-Rank Tensor Decompositions in Time Series Analysis.” IEEE Access 11 (1):85770–84. https://doi.org/10.1109/ACCESS.2023.3298597.
   Google Scholar
• Bi, X., G. Adomavicius, W. Li, and A. Qu. 2022. “Improving Sales Forecasting Accuracy: A Tensor Factorization Approach with Demand Awareness.” INFORMS Journal on Computing 34 (3):1644–60. https://doi.org/10.1287/ijoc.2021.1147.
   Web of Science ®Google Scholar
• Bi, X., X. Tang, Y. Yuan, Y. Zhang, and A. Qu. 2021. “Tensors in Statistics.” Annual Review of Statistics and Its Applications 8 (1):345–68. https://doi.org/10.1146/annurev-statistics-042720-020816.
   Google Scholar
• Box, G. E. P., and G. M. Jenkins. 1976. Time Series Analysis: Forecasting and Control. San Francisco: Holden-Day.
   Google Scholar
• Carroll, J. D., and J.-J. Chang. 1970. “Analysis of Individual Preferences in Multidimensional Scaling via an N-way Generalization of ‘Eckart-Young’ Decomposition.” Psychometrika 35 (3):283–319. https://doi.org/10.1007/BF02310791.
   Web of Science ®Google Scholar
• Chi, E. C., and T. G. Kolda. 2012. “On Tensors, Sparsity, and Nonnegative Factorizations.” SIAM Journal of Matrix Analysis and Applications 33 (4):1272–99. https://doi.org/10.1137/110859063.
   Web of Science ®Google Scholar
• Cichocki, A., R. Zdunek, A. H. Phan, and S. Amari. 2009. Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multiway Data Analysis and Blind Source Separation. Chichester: Wiley.
   Google Scholar
• Das, A., W. Kong, R. Sen, and Y. Zhou. 2024. “A Decoder-Only Foundation Model for Time-Series Forecasting.” Technical Report, arXiv:2310.10688.
   Google Scholar
• De Stefani, J., and G. Bontempi. 2021. “Factor-Based Framework for Multivariate and Multi-Step-Ahead Forecasting of Large Scale Time Series.” Frontiers in Big Data 4 (1):e690267. https://doi.org/10.3389/fdata.2021.690267.
   PubMedGoogle Scholar
• Deng, J., J. Deng, D. Yin, R. Jiang, and X. Song. 2024. “TTS-Norm: Forecasting Tensor Time Series via Multi-Way Normalization.” ACM Transactions on Knowledge Discovery from Data 18 (1):e3. https://doi.org/10.1145/3605894.
   Web of Science ®Google Scholar
• Donoho, D. 2017. “50 Years of Data Science.” Journal of Computational and Graphical Statistics 26 (4):745–66. https://doi.org/10.1080/10618600.2017.1384734.
   Web of Science ®Google Scholar
• Dunlavy, D. M., T. G. Kolda, and E. Acar. 2011. “Temporal Link Prediction Using Matrix and Tensor Factorizations.” ACM Transactions on Knowledge Discovery from Data 5 (2):e10. https://doi.org/10.1145/1921632.1921636.
   Web of Science ®Google Scholar
• Feuerverger, A., Y. He, and S. Khatri. 2012. “Statistical Significance of the Netflix Challenge.” Statistical Science 27 (2):202–31. https://doi.org/10.1214/11-STS368.
   Web of Science ®Google Scholar
• Fildes, R. 1989. “Evaluation of Aggregate and Individual Forecast Method Selection Rules.” Management Science 35 (9):1056–65. https://doi.org/10.1287/mnsc.35.9.1056.
   Web of Science ®Google Scholar
• Fildes, R., S. Ma, and S. Kolassa. 2022. “Retail Forecasting: Research and Practice.” International Journal of Forecasting 38 (4):1283–318. https://doi.org/10.1016/j.ijforecast.2019.06.004.
   Web of Science ®Google Scholar
• Gastinger, J., S. Nicolas, D. Stepić, M. Schmidt, and A. Schülke. 2021. “A Study on Ensemble Learning for Time Series Forecasting and the Need for Meta-Learning.” Technical Report, arXiv:2104.11475.
   Google Scholar
• George, G., E. C. Osinga, D. Lavie, and B. A. Scott. 2016. “Big Data and Data Science Methods for Management Research.” Academy of Management Journal 59 (5):1493–507. https://doi.org/10.5465/amj.2016.4005.
   Web of Science ®Google Scholar
• Gneiting, T., and A. E. Raftery. 2007. “Strictly Proper Scoring Rules, Prediction, and Estimation.” Journal of the American Statistical Association 102 (477):359–78. https://doi.org/10.1198/016214506000001437.
   Web of Science ®Google Scholar
• Harshman, R. A. 1970. “Foundations of the PARAFAC Procedure: Models and Conditions for an ‘Explanatory’ Multimodal Factor Analysis.” UCLA Working Papers in Phonetics 16:1–84.
   Google Scholar
• Hill, C., J. Li, and M. Schneider. 2021. “The Tensor Auto-Regressive Model.” Journal of Forecasting 40 (4):636–52. https://doi.org/10.1002/for.2735.
   Web of Science ®Google Scholar
• Hitchcock, F. L. 1927. “The Expression of a Tensor or Polyadic as a Sum of Products.” Journal of Mathematics and Physics 6 (1):164–89. https://doi.org/10.1002/sapm192761164.
   Google Scholar
• Hoff, P. D. 2011. “Separable Covariance Arrays via the Tucker Product, with Applications to Multivariate Relational Data.” Bayesian Analysis 6 (2):179–96. https://doi.org/10.1214/11-BA606.
   Web of Science ®Google Scholar
• Hyndman, R. J. 2020. “A Brief History of Forecasting Competitions.” International Journal of Forecasting 36 (1):7–14. https://doi.org/10.1016/j.ijforecast.2019.03.015.
   Web of Science ®Google Scholar
• Hyndman, R. J., and G. Athanasopoulos. 2018. Forecasting: Principles and Practice. Melbourne: OTexts.
   Google Scholar
• Hyndman, R. J., and Y. Khandakar. 2008. “Automatic Time Series Forecasting: The forecast Package for R.” Journal of Statistical Software 27 (3):1–22. https://doi.org/10.18637/jss.v027.i03.
   Web of Science ®Google Scholar
• Hyndman, R. J., and A. B. Koehler. 2006. “Another Look at Measures of Forecast Accuracy.” International Journal of Forecasting 22 (4):679–88. https://doi.org/10.1016/j.ijforecast.2006.03.001.
   Web of Science ®Google Scholar
• Hyndman, R. J., A. B. Koehler, R. D. Snyder, and S. Grose. 2002. “A State Space Framework for Automatic Forecasting Using Exponential Smoothing.” International Journal of Forecasting 18 (3):439–54. https://doi.org/10.1016/S0169-2070(01)00110-8.
   Web of Science ®Google Scholar
• Januschowski, T., J. Gasthaus, Y. Wang, D. Salinas, V. Flunkert, M. Bohlke-Schneider, and L. Callon. 2020. “Criteria for Classifying Forecasting Methods.” International Journal of Forecasting 36 (1):167–77. https://doi.org/10.1016/j.ijforecast.2019.05.008.
   Web of Science ®Google Scholar
• Kang, Y., R. J. Hyndman, and F. Li. 2020, “GRATIS: GeneRAting TIme Series with Diverse and Controllable Characteristics.” Statistical Analysis and Data Mining 13 (4):354–76. https://doi.org/10.1002/sam.11461.
   Web of Science ®Google Scholar
• Karlsson Rosenblad, A. 2021. “Accuracy of Automatic Forecasting Methods for Univariate Time Series Data: A Case Study Predicting the Results of the 2018 Swedish General Election Using Decades-Long Series.” Communications in Statistics: Case Studies, Data Analysis and Applications 7 (3):475–93. https://doi.org/10.1080/23737484.2021.1964407.
   Google Scholar
• Kiers, H. A. L. 2000. “Towards a Standardized Notation and Terminology in Multiway Analysis.” Journal of Chemometrics 14 (3):105–122. https://doi.org/10.1002/1099-128X(200005/06)14:3<105::AID-CEM582>3.0.CO;2-I.
   Web of Science ®Google Scholar
• Kitchin, R. 2014. “Big Data, New Epistemologies and Paradigm Shifts.” Big Data & Society 1 (1):1–12. https://doi.org/10.1177/2053951714528481.
   Google Scholar
• Kolda, T. G., and B. W. Bader. 2009. “Tensor Decompositions and Applications.” SIAM Review 51 (3):455–500. https://doi.org/10.1137/07070111X.
   Web of Science ®Google Scholar
• Kossaifi, J., Y. Panagakis, A. Anandkumar, and M. Pantic. 2019. “TensorLy: Tensor Learning in Python.” Journal of Machine Learning Research 20 (26):1–6.
   Google Scholar
• Landon, J., and N. D. Singpurwalla. 2008. “Choosing a Coverage Probability for Prediction Intervals.” The American Statistician 62 (2):120–24. https://doi.org/10.1198/000313008X304062.
   Web of Science ®Google Scholar
• Liberman, M. 2010. “Obituary: Fred Jelinek.” Computational Linguistics 36 (4):595–99. https://doi.org/10.1162/coli_a_00032.
   Web of Science ®Google Scholar
• Ma, L., S. Qin, and Y. Xia. 2023. “Alteration Detection of Tensor Dependence Structure via Sparsity-Exploited Reranking Algorithm.” Technical Report, arXiv:2310.08798.
   Google Scholar
• Ma, S., and R. Fildes. 2021. “Retail Sales Forecasting with Meta-Learning.” European Journal of Operational Research 288 (1):111–128. https://doi.org/10.1016/j.ejor.2020.05.038.
   Web of Science ®Google Scholar
• Makridakis, S., C. Fry, F. Petropoulos, and E. Spiliotis. 2022a. “The Future of Forecasting Competitions: Design Attributes and Principles.” INFORMS Journal on Data Science 1 (1):96–113. https://doi.org/10.1287/ijds.2021.0003.
   Google Scholar
• Makridakis, S., R. J. Hyndman, and F. Petropoulos. 2020. “Forecasting in Social Settings: The State of the Art.” International Journal of Forecasting 36 (1):15–28. https://doi.org/10.1016/j.ijforecast.2019.05.011.
   Web of Science ®Google Scholar
• Makridakis, S., E. Spiliotis, and V. Assimakopoulos. 2022b. “M5 Accuracy Competition: Results, Findings, and Conclusions.” International Journal of Forecasting 38 (4):1346–64. https://doi.org/10.1016/j.ijforecast.2021.11.013.
   Web of Science ®Google Scholar
• Makridakis, S., E. Spiliotis, V. Assimakopoulos, Z. Chen, A. Gaba, I. Tsetlin, and R. L. Winkler. 2022c. “The M5 Uncertainty Competition: Results, Findings and Conclusions.” International Journal of Forecasting 38 (4):1365–85. https://doi.org/10.1016/j.ijforecast.2021.10.009.
   Web of Science ®Google Scholar
• Müller, O., I. Junglas, J. vom Brocke, and S. Debortoli. 2016. “Utilizing Big Data Analytics for Information Systems Research: Challenges, Promises and Guidelines.” European Journal of Information Systems 25 (4):289–302. https://doi.org/10.1057/ejis.2016.2.
   Web of Science ®Google Scholar
• Nikolopoulos, K., and F. Petropoulos. 2018. “Forecasting Big Data: Does Suboptimality Matter?” Computers & Operations Research 98 (1):322–329. https://doi.org/10.1016/j.cor.2017.05.007.
   Google Scholar
• Papalexakis, E. E., C. Faloutsos, and N. D. Sidiropoulos. 2016. “Tensors for Data Mining and Data Fusion: Models, Applications, and Scalable Algorithms.” ACM Transactions on Intelligent Systems and Technology 8 (2):e16. https://doi.org/10.1145/2915921.
   Web of Science ®Google Scholar
• Petropoulos, F., Y. Grushka-Cockayne, E. Siemsen, and E. Spiliotis. 2022. “Wielding Occam’s Razor: Fast and Frugal Retail Forecasting.” Technical Report, arXiv:2102.13209.
   Google Scholar
• Petropoulos, F., S. Makridakis, V. Assimakopoulos, and K. Nikolopoulos. 2014. “‘Horses for Courses’ in Demand Forecasting.” European Journal of Operational Research 237 (1):152–163. https://doi.org/10.1016/j.ejor.2014.02.036.
   Web of Science ®Google Scholar
• Rabanser, S., O. Shchur, and S. Günnemann. 2017. “Introduction to Tensor Decompositions and their Applications in Machine Learning.” Technical Report, arXiv:1711.10781.
   Google Scholar
• Salinas, D., V. Flunkert, J. Gasthaus, and T. Januschowski. 2020. “DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks.” International Journal of Forecasting 36 (3):1181–91. https://doi.org/10.1016/j.ijforecast.2019.07.001.
   Web of Science ®Google Scholar
• Schosser, J. 2020. “Multivariate Extrapolation: A Tensor-based Approach.” In Operations Research Proceedings 2019, edited by J. S. Neufeld, U. Buscher, R. Lasch, D. Möst, and J. Schönberger, 53–59. Cham: Springer.
   Google Scholar
• Schosser, J. 2022a. “Tensor Extrapolation: An Adaptation to Data Sets with Missing Entries.” Journal of Big Data 9 (1):e26. https://doi.org/10.1186/s40537-022-00574-7.
   Google Scholar
• Schosser, J. 2022b. “Tensor Extrapolation: Forecasting Large-Scale Relational Data.” Journal of the Operational Research Society 73 (5):969–78. https://doi.org/10.1080/01605682.2021.1892460.
   Web of Science ®Google Scholar
• Schwartz, R., J. Dodge, N. A. Smith, and O. Etzioni. 2020. “GreenAI.” Communications of the ACM 63 (12):54–63. https://doi.org/10.1145/3381831.
   Google Scholar
• Seabold, S., and J. Perktold. 2010. “Statsmodels: Econometric and Statistical Modeling with Python.” In Proceedings of the 9th Python in Science Conference (SCIPY 2010), 57–61.
   Google Scholar
• Shah, S. Y., D. Patel, L. Vu, X.-H. Dang, B. Chen, P. Kirchner, H. Samulowitz, D. Wood, G. Bramble, W. M. Gifford, G. Ganapavarapu, R. Vaculin, and P. Zerfos. 2021. “AutoAI-TS: AutoAI for Time Series Forecasting.” In Proceedings of the 2021 International Conference on Management of Data (SIGMOD), 2584–2596. ACM.
   Google Scholar
• Shi, Q., J. Yin, J. Cai, A. Cichocki, T. Yokota, L. Chen, M. Yuan, and J. Zeng. 2020. “Block Hankel Tensor ARIMA for Multiple Short Time Series Forecasting.” In Proceedings of the 34th Conference on Artificial Intelligence (AAAI), 5758–5766. AAAI. https://doi.org/10.1609/aaai.v34i04.6032.
   Google Scholar
• Spiegel, S., J. Clausen, S. Albayrak, and J. Kunegis. 2012. “Link Prediction on Evolving Data Using Tensor Factorization.” In New Frontiers in Applied Data Mining: PAKDD 2011 International Workshops, 100–110. Springer.
   Google Scholar
• Syntetos, A. A., J. E. Boylan, and J. D. Croston. 2005. “On the Categorization of Demand Patterns.” Journal of the Operational Research Society 56 (5):495–503. https://doi.org/10.1057/palgrave.jors.2601841.
   Web of Science ®Google Scholar
• Thompson, N. C., and S. Spanuth. 2021. “The Decline of Computers as a General Purpose Technology.” Communications of the ACM 64 (3):64–72. https://doi.org/10.1145/3430936.
   Web of Science ®Google Scholar
• Wasserman, S., and K. Faust. 1994. Social Network Analysis: Methods and Applications. Cambridge: Cambridge University Press.
   Google Scholar
• Wu, C.-J., R. Raghavendra, U. Gupta, B. Acun, N. Ardalani, K. Maeng, G. Chang, F. A. Behram, J. Huang, C. Bai, M. Gschwind, A. Gupta, M. Ott, A. Melnikov, S. Candido, D. Brooks, G. Chauhan, B. Lee, H.-H. S. Lee, B. Akyildiz, M. Balandat, J. Spisak, R. Jain, M. Rabbat, and K. Hazelwood. 2022. “Sustainable AI: Environmental Implications, Challenges and Opportunities.” In Proceedings of the 5th Conference on Machine Learning and Systems (MLSys), 795–813. Systems and Machine Learning Foundation.
   Google Scholar
• Yu, H.-F., N. Rao, and I. S. Dhillon. 2016. “Temporal Regularized Matrix Factorization for High-Dimensional Time Series Prediction.” In Proceedings of the 29th Annual Conference on Neural Information Processing Systems (NeurIPS), 847–855. NeurIPS Foundation.
   Google Scholar
• Yu, R., S. Zheng, A. Anandkumar, and Y. Yue. 2017. “Long-Term Forecasting Using Tensor-Train RNNs.” Technical report, arXiv:1711.00073.
   Google Scholar