Learning Predictors from Multidimensional Data with Tensor Factorizations

Statistical machine learning algorithms often involve learning a linear relationship between dependent and independent variables. This relationship is modeled as a vector of numerical values, commonly referred to as weights or predictors. These weights allow us to make predictions, and the quality of these weights influence the accuracy of our predictions. However, when the dependent variable inherently possesses a more complex, multidimensional structure, it becomes increasingly difficult to model the relationship with a vector. In this paper, we address this issue by investigating machine learning classification algorithms with multidimensional (tensor) structure. By imposing tensor factorizations on the predictors, we can better model the relationship, as the predictors would take the form of the data in question. We empirically show that our approach works more efficiently than the traditional machine learning method when the data possesses both an exact and an approximate tensor structure. Additionally, we show that estimating predictors with these factorizations also allow us to solve for fewer parameters, making computation more feasible for multidimensional data.