Tensor Algebra and its Applications to Data Science and Statistics

This survey provides an overview of common applications, both implicit and explicit, of "tensors" and "tensor products" in the fields of data science and statistics. One goal is to reconcile seemingly distinct usages of the term "tensor" in the literature, and to explain how these usages are manifestations of a common concept. Not all relevant topics are discussed in detail, but the attempt is made to briefly describe and give references for some of the most important topics not included in the main survey. Particular attention is given to tensor decompositions.