A simple estimator of the correlation kernel matrix of a determinantal point process
This provides a practical tool for researchers and practitioners working with DPPs, though it is incremental as it focuses on improving estimation efficiency rather than introducing a new paradigm.
The paper tackles the problem of estimating the correlation kernel matrix of a Determinantal Point Process (DPP) by proposing a simple, closed-form estimator that is easy to implement and serves as a starting point for maximum likelihood algorithms, with proven consistency, asymptotic normality, and large deviation properties.
The Determinantal Point Process (DPP) is a parameterized model for multivariate binary variables, characterized by a correlation kernel matrix. This paper proposes a closed form estimator of this kernel, which is particularly easy to implement and can also be used as a starting value of learning algorithms for maximum likelihood estimation. We prove the consistency and asymptotic normality of our estimator, as well as its large deviation properties.