In the process of building (structural learning) a probabilistic graphical
model from a set of observed data, the directional, cyclic dependencies between
the random variables of the model are often found. Existing graphical models
such as Bayesian and Markov networks can reflect such dependencies. However,
this requires complicating those models, such as adding additional variables or
dividing the model graph into separate subgraphs. Herein, we describe a
probabilistic graphical model - probabilistic relation network - that allows
the direct capture of directional cyclic dependencies during structural
learning. This model is based on the simple idea that each sample of the
observed data can be represented by an arbitrary graph (structured outcome),
which reflects the structure of the dependencies of the variables included in
the sample. Each of the outcomes contains only a part of the graphical model
structure; however, a complete graph of the probabilistic model is obtained by
combining different outcomes. Such a graph, unlike Bayesian and Markov
networks, can be directed and can have cycles. We explored the full joint
distribution and conditional distribution and conditional independence
properties of variables in the proposed model. We defined the algorithms for
constructing of the model from the dataset and for calculating the conditional
and full joint distributions. We also performed a numerical comparison with
Bayesian and Markov networks. This model does not violate the probability
axioms, and it supports learning from observed data. Notably, it supports
probabilistic inference, making it a prospective tool in data analysis and in
expert and design-making applications.

建立概率图模型从观测数据中学习结构时，会发现模型中的随机变量之间存在方向性的循环依赖关系。我们描述了一种概率图模型 - 概率关系网络，它允许直接捕捉结构学习过程中的方向性循环依赖关系。该模型基于一个简单的思想，即观测数据的每个样本都可以通过任意图来表示，这个图反映了样本中包含的变量间的依赖关系结构。我们探索了该模型中的完全联合分布和条件分布以及变量之间的条件独立性质。我们定义了从数据集构建模型和计算条件分布和完全联合分布的算法，并与贝叶斯网络和马尔可夫网络进行了数值比较。该模型不违背概率公理，支持从观测数据中学习，并支持概率推断，因此在数据分析、专家决策和设计应用中具有潜在的用途。