论文标题
分类型：普遍有条件独立性
Categoroids: Universal Conditional Independence
论文作者
论文摘要
有条件的独立性已被广泛用于AI，因果推断，机器学习和统计数据。我们介绍分类生物，这是一种代数结构，用于表征条件独立性的通用特性。分类物被定义为两个类别的混合体：一个编码由对象和箭头定义的预定的晶格结构；第二个二元参数化涉及定义条件独立性结构的三角体对象和形态，桥梁形态提供了二元结构和三元结构之间的接口。我们使用公理集的三个众所周知的示例说明了分类生物：绘画，整数值的多组和分离型。 FOUDCOROIDS将一个分类型映射到另一个分类，并保留由共同域中所有三种类型的箭头定义的关系。我们描述了跨官能素的自然转化，该函数是跨常规物体和三角形对象的自然变化，以构建条件独立性的通用表示。我们使用分类型之间的辅助和单子来抽象地表征有条件独立性的图形和非图形表示的忠诚。
Conditional independence has been widely used in AI, causal inference, machine learning, and statistics. We introduce categoroids, an algebraic structure for characterizing universal properties of conditional independence. Categoroids are defined as a hybrid of two categories: one encoding a preordered lattice structure defined by objects and arrows between them; the second dual parameterization involves trigonoidal objects and morphisms defining a conditional independence structure, with bridge morphisms providing the interface between the binary and ternary structures. We illustrate categoroids using three well-known examples of axiom sets: graphoids, integer-valued multisets, and separoids. Functoroids map one categoroid to another, preserving the relationships defined by all three types of arrows in the co-domain categoroid. We describe a natural transformation across functoroids, which is natural across regular objects and trigonoidal objects, to construct universal representations of conditional independence.. We use adjunctions and monads between categoroids to abstractly characterize faithfulness of graphical and non-graphical representations of conditional independence.
