Reproducibility in Matrix and Tensor Decompositions: Focus on model match, interpretability, and uniqueness

Data-driven solutions are playing an increasingly important role in numerous practical problems across multiple disciplines. The shift from the traditional model-driven approaches to those that are data driven naturally emphasizes the importance of the explainability of solutions, as, in this case, the connection to a physical model is often not obvious. Explainability is a broad umbrella and includes interpretability, but it also implies that the solutions need to be complete, in that one should be able to “audit” them, ask appropriate questions, and hence gain further insight about their inner workings [1] . Thus, interpretability, reproducibility, and, ultimately, our ability to generalize these solutions to unseen scenarios and situations are all strongly tied to the starting point of explainability.