The primary goal of this lecture series is to introduce emerging topics in high-dimensional statistical inference. Specifically, I will focus on statistical physics models, such as the Ising model and its disordered variants. Parameterized by the temperature and external field, these models are spin systems, where the spin interactions are described by a structure matrix. While their Gibbs measures belong to the exponential family, understanding their corresponding parameter and structure estimation problems, based on a limited number of given samples, presents intriguing mathematical challenges. Throughout the series, I will highlight recent advancements, explain the approaches, and propose open problems that are particularly well-suited for graduate students and junior researchers to expand their research interests. The prerequisite for the participants is familiarity with at least the first semester of introductory probability at the graduate level.

 

Professor Chen’s research interest generally lies on probability theory with a special focus on the spin glass models originated from the study of some unusual magnetic properties of certain alloys, such as CuMn and AuFe. Mathematically, they are stochastic processes indexed by elements from some metric spaces and known to possess large complexities and rugged landscapes. Professor Chen has been working to study the thermodynamic limits of mean field spin glass models as well as their applications in neural networks, computer science, and high-dimensional statistics.