用于控制正依赖和负依赖的随机子集分布族
A Family of Distributions of Random Subsets for Controlling Positive and Negative Dependence
AI总结：
针对随机子集正/负依赖难以用实用概率模型无缝连接的问题，本研究提出包含行列式点过程和部分玻尔兹曼机的离散核点过程（DKPP）分布族，开发相关计算方法并通过实验验证其依赖可控性与方法有效性。
摘要：
正依赖和负依赖是描述随机子集吸引和排斥行为的基本概念。尽管已知一些概率模型会表现出正依赖或负依赖，但用实用的概率模型无缝连接它们具有挑战性。本研究引入了一个名为离散核点过程（DKPP）的新分布族，该分布族包含行列式点过程和玻尔兹曼机的部分内容。我们还开发了一些用于DKPP概率运算和推理的计算方法，例如计算边际概率和条件概率以及学习参数。我们的数值实验证明了DKPP对正依赖和负依赖的可控性以及计算方法的有效性。
英文摘要：
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.
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