标题： 概率图模型的复制组合 显示英文标题

标题： Copy-composition for Probabilistic Graphical Models

摘要： 在概率建模中，联合分布通常比边缘分布更受关注，但标准的随机信道组合是通过边缘化定义的。 去年在ACT会议上，引入了“复制组合”的概念，以绕过这个问题并以纤维方式表达相对熵的链式法则，但尽管达到了这一目标，复制组合缺乏一个令人满意的起源故事。 在这里，我们为两种标准的概率工具：有向和无向图模型提供了这样的故事。 我们解释说（有向）贝叶斯网络可以被理解为乘积类型的“随机项”，在这一背景下，复制组合相当于一个拉-推操作。 同样，我们展示了（无向）因子图通过复制组合进行组合。 在每种情况下，我们的构造产生了一个装饰（协）跨度的双重纤维。 在此过程中，我们引入了一个有用的双纤维度量核，以提供对随机项概念的语义，这使我们能够将概率建模从乘积类型推广到依赖类型。 显示英文摘要

摘要： In probabilistic modelling, joint distributions are often of more interest than their marginals, but the standard composition of stochastic channels is defined by marginalization. Last year at ACT, the notion of 'copy-composition' was introduced in order to circumvent this problem and express the chain rule of the relative entropy fibrationally, but while that goal was achieved, copy-composition lacked a satisfactory origin story. Here, we supply such a story for two standard probabilistic tools: directed and undirected graphical models. We explain that (directed) Bayesian networks may be understood as ''stochastic terms'' of product type, in which context copy-composition amounts to a pull-push operation. Likewise, we show that (undirected) factor graphs compose by copy-composition. In each case, our construction yields a double fibration of decorated (co)spans. Along the way, we introduce a useful bifibration of measure kernels, to provide semantics for the notion of stochastic term, which allows us to generalize probabilistic modelling from product to dependent types.