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.

翻译：正依赖与负依赖是刻画随机子集吸引与排斥行为的基本概念。尽管已知某些概率模型表现出正依赖或负依赖特性，但通过实用概率模型实现二者间的无缝衔接仍具挑战性。本研究提出名为离散核点过程的新型分布族，该族包含行列式点过程及部分玻尔兹曼机。我们同时开发了适用于DKPP概率运算与推断的计算方法，包括边际概率与条件概率计算以及参数学习。数值实验验证了正负依赖的可控性及DKPP计算方法的有效性。