  Gibbs point processes (GPPs) constitute a large and flexible class of spatial
point processes with explicit dependence between the points. They can model
attractive as well as repulsive point patterns. Feature selection procedures
are an important topic in high-dimensional statistical modeling. In this paper,
composite likelihood approach regularized with convex and non-convex penalty
functions is proposed to handle statistical inference for possibly
high-dimensional inhomogeneous GPPs. The composite likelihood incorporates both
the pseudo-likelihood and the logistic composite likelihood. We particularly
investigate the setting where the number of covariates diverges as the domain
of observation increases. Under some conditions provided on the spatial GPP and
on the penalty functions, we show that the oracle property, the consistency and
the asymptotic normality hold. Our results also cover the low-dimensional case
which fills a large gap in the literature. Through simulation experiments, we
validate our theoretical results and finally, an application to a tropical
forestry dataset illustrates the use of the proposed approach.
