Discrete Determinantal Point Processes (DPPs) are a class of probabilistic models that describe repulsive interactions between items. Unlike for most graphical models (e.g., Markov Random Fields, including the ferromagnetic Ising model), many simple yet useful operations, such as conditioning and marginalizing, are tractable with DPPs. This is why they have gained a lot of popularity in numerous applications in the past few years. In this presentation, I will talk about learning the parameter of a DPP, given independent observed copies. The first approach that I will describe is the maximum likelihood estimation. I will mention its asymptotic guarantees and I will explain some computational challenges that it poses. The second approach is based on a method of moments, which relies on a problem called the principal minor assignment problem: Given the list of all principal minors of some matrix, how to recover that matrix in a computationally efficient way?

This talk is based on two joint works with Ankur Moitra, Philippe Rigollet and John Urschell.