Hardness of Maximum Likelihood Learning of DPPs

Determinantal Point Processes (DPPs) are a widely used probabilistic model for negatively correlated sets. DPPs have been successfully employed in Machine Learning applications to select a diverse, yet representative subset of data. In these applications, a set of parameters that maximize the likelihood of the data is typically desirable. The algorithms used for this task to date either optimize over a limited family of DPPs, or use local improvement heuristics that do not provide theoretical guarantees of optimality.