This workshop focuses on the role of random matrices in data science, machine learning, and theoretical computer science.

Playing a significant role in modern data science, random matrices provide an elegant way to represent both (a) the data and (b) the way we process it. To give an example of (a), the classical model of high-dimensional data is a set of points drawn from a certain distribution in a high-dimensional space which can be represented as a random matrix. An even more natural example is that most data in practice is noisy, so it can be represented as a deterministic matrix plus a random noise, which is a random matrix with a non-zero mean. An example of (b) is data compression, which can be realized by applying a random matrix of smaller sizes to the data in (a), thereby reducing its dimensions. Another example is data completion, where we need to reconstruct data (in the form of a matrix) from a random sub-matrix, given that the original matrix satisfies certain structural constraints (such as being low rank).

To deal with these problems, we need to develop techniques beyond the scope of standard random matrix theory. For example, while the sensitivity of matrix spectrum to small random perturbations is extensively studied in the mean field regime, the problem in the setting of structured random matrices, which allows for more adequate modeling of real-world data, is wide open. As another example, the core mechanism of an artificial neural network is a composition of linear and nonlinear transformations, leading to nonlinear generalizations of random matrices. Our understanding of mathematical principles behind examples like this is still in its infancy.

The goal is to discuss a number of hot topics in these areas, focusing on recent theoretical progress and the potential pool of applications, in a manner that is accessible to a wide audience, including researchers in data science, electrical engineering, statistics, and numerical analysis.