Open Problem: Tensor Decompositions: Algorithms up to the Uniqueness Threshold?

Abstract

Factor analysis is a basic tool in statistics and machine learning, where the goal is to take many variables and explain them away using fewer unobserved variables, called factors. It was introduced in a pioneering study by psychologist Charles Spearman, who used it to test his theory that there are fundamentally two types of intelligence – verbal and mathematical. This study has had a deep influence on modern psychology, to this day. However there is a serious mathematical limitation to this approach, which we describe next.