AI 中文总结
本讲义介绍图模型基础与图模型程序实例中的代数隐式化技术，为解决不同数据类型对应图模型的统计推断理论问题提供数学方法基础。
AI 中文摘要
如今日常生活的诸多方面依赖于由多元数据分析先进技术驱动的科技，图模型为这类分析提供了通用框架。但不同数据类型需要不同的图模型，每种都需自身的基础数学理论来指导可靠的统计推断。为一类图模型发展该理论需解决基础问题，新兴数学方法正运用可统称为代数隐式化技术的手段。本讲义介绍图模型的基础，以及当前图模型程序实例中出现的代数隐式化技术。
英文摘要
Many aspects of daily life now rely on technology driven by advanced techniques for analyzing multivariate data. Graphical models provide the general framework within which much of these analyses take place. However, different data types require different graphical models, with each requiring its own basic mathematical theory to guide sound statistical inference. Developing this theory for a family of graphical models requires solutions to fundamental questions, where emerging mathematical approaches are utilizing what can collectively be called algebraic implicitization techniques. These notes provide an introduction to the basics of graphical models and the algebraic implicitization techniques now appearing in instances of the graphical models program.
CommentsThis is a preprint of a chapter intended for publication in a Springer Lecture Notes in Mathematics series based on the lectures given at the 43rd Finnish Summer School on Probability and Statistics in Lammi, Finland. It surveys basic results on graphical models and algebraic techniques, with the intent of being broadly accessible
