Inference for determinantal point processes without spectral knowledge

Determinantal point processes (DPPs) are point process models thatnaturally encode diversity between the points of agiven realization, through a positive definite kernel K . DPPs possess desirable properties, such as exactsampling or analyticity of the moments, but learning the parameters ofkernel K through likelihood-based inference is notstraightforward. First, the kernel that appears in thelikelihood is not K, but another kernel L related to K throughan often intractable spectral decomposition. This issue is typically bypassed in machine learning bydirectly parametrizing the kernel L, at the price of someinterpretability of the model parameters. Second, the likelihood has an intractable normalizingconstant, which takes the form of large determinant in the case of aDPP over a finite set of objects, and the form of a Fredholm determinant in thecase of a DPP over a continuous domain.