Large amount of multidimensional data in the form of multilinear arrays, or tensors, arise routinely in modern applications from such diverse fields as chemometrics, genomics, physics, psychology, and signal processing among many others. At the present time, our ability to generate and acquire them has far outpaced our ability to effectively extract useful information from them. There is a clear demand to develop novel statistical methods, efficient computational algorithms, and fundamental mathematical theory to analyze and exploit information in these types of data. Such an endeavor, however, faces unique challenges from both conceptual and computational points of view.
In spite of the challenges, we are at a vantage point to address some of the most pressing and core issues in the statistical analysis of these types of data thanks to recent advances in high dimensional statistics, high dimensional probability, and large scale nonlinear optimization. In this lecture, I will illustrate how we can build upon these advances and develop statistical methods, algorithms and theory to efficiently, both statistically and computationally, analyze large scale data in the form of tensors.