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Predicting Multidimensional Data via Tensor Learning

Research output: Contribution to journalArticlepeer-review

Original languageEnglish
Article number101372
Pages (from-to)1-10
Number of pages10
JournalJournal of Computational Science
Issue number101372
Early online date19 Apr 2021
Accepted/In press7 Apr 2021
E-pub ahead of print19 Apr 2021
PublishedJul 2021


King's Authors


The analysis of multidimensional data is becoming a more and more relevant topic in statistical and machine learning research. Given their complexity, such data objects are usually reshaped into matrices or vectors and then analysed. However, this methodology presents several drawbacks. First of all, it destroys the intrinsic interconnections among datapoints in the multidimensional space and, secondly, the number of parameters to be estimated in a model increases exponentially. We develop a model that overcomes such drawbacks. In par- ticular, in this paper, we propose a parsimonious tensor regression model that retains the intrinsic multidimensional structure of the dataset. Tucker structure is employed to achieve parsimony and a shrinkage penalization is introduced to deal with over-fitting and collinearity. To estimate the model parameters, an Al- ternating Least Squares algorithm is developed. In order to validate the model performance and robustness, a simulation exercise is produced. Moreover, we perform an empirical analysis that highlight the forecasting power of the model with respect to benchmark models. This is achieved by implementing an au- toregressive specification on the Foursquares spatio-temporal dataset together with a macroeconomic panel dataset. Overall, the proposed model is able to outperform benchmark models present in the forecasting literature.

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