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A new type of dependent thinning for point processes in continuous space isproposed, which leverages the advantages of determinantal point processesdefined on finite spaces and, as such, is particularly amenable to statistical,numerical, and simulation techniques. It gives a new point process that canserve as a network model exhibiting repulsion. The properties and functions ofthe new point process, such as moment measures, the Laplace functional, thevoid probabilities, as well as conditional (Palm) characteristics can beestimated accurately by simulating the underlying (non-thinned) point process,which can be taken, for example, to be Poisson. This is in contrast (andpreference to) finite Gibbs point processes, which, instead of thinning,require weighting the Poisson realizations, involving usually intractablenormalizing constants. Models based on determinantal point processes are alsowell suited for statistical (supervised) learning techniques, allowing themodels to be fitted to observed network patterns with some particular geometricproperties. We illustrate this approach by imitating with determinantalthinning the well-known Mat{\'e}rn~II hard-core thinning, as well as asoft-core thinning depending on nearest-neighbour triangles. These two examplesdemonstrate how the proposed approach can lead to new, statistically optimized,probabilistic transmission scheduling schemes.

Determinantal thinning of point processes with network learning applications