  Positive and negative dependence are fundamental concepts that characterize
the attractive and repulsive behavior of random subsets. Although some
probabilistic models are known to exhibit positive or negative dependence, it
is challenging to seamlessly bridge them with a practicable probabilistic
model. In this study, we introduce a new family of distributions, named the
discrete kernel point process (DKPP), which includes determinantal point
processes and parts of Boltzmann machines. We also develop some computational
methods for probabilistic operations and inference with DKPPs, such as
calculating marginal and conditional probabilities and learning the parameters.
Our numerical experiments demonstrate the controllability of positive and
negative dependence and the effectiveness of the computational methods for
DKPPs.
