Extended L-ensembles: A new representation for determinantal point processes

Determinantal point processes (DPPs) are a class of repulsive processes, popular for their relative simplicity. They traditionally defined via marginal distributions, but subset DPPs called “L-ensembles” have tractable likelihoods and thus particularly easy to work with. Indeed, in many applications, more naturally based on the L-ensemble formulation rather than through kernel. The fact that not all L-ensembles is unfortunate, there unifying description. We introduce here extended L-ensembles, show (and vice versa). Extended very simple likelihood functions, contain projection as special cases. From theoretical standpoint, they fix some pathologies usual formalism DPPs, instance, L-ensembles. practical extend set kernel functions may be used define DPPs: we conditional positive definite kernels good candidates defining including need no spatial scale parameter. Finally, so-called “saddle-point matrices”, prove an extension Cauchy–Binet theorem such matrices independent interest.