Predicting multidimensional data via tensor learning

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