Predicting multidimensional data via tensor learning

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 particular, 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 Alternating 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 autoregressive 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.

Automated summary

This paper proposes a parsimonious tensor regression model that retains the intrinsic multidimensional structure of the dataset using Tucker structure and shrinkage penalization to address overfitting and collinearity, as well as developing an Alternating Least Squares algorithm. The model's performance and robustness are validated through simulation exercises and empirical analysis, demonstrating its superiority over benchmark models in forecasting literature.