A powerful statistical interpolating concept, which we call \emph{fully lifted} (fl), is introduced and presented while establishing a connection between bilinearly indexed random processes and their corresponding fully decoupled (linearly indexed) comparative alternatives. Despite on occasion very involved technical considerations, the final interpolating forms and their underlying relations admit rather elegant expressions that provide conceivably highly desirable and useful tool for further studying various different aspects of random processes and their applications. We also discuss the generality of the considered models and show that they encompass many well known random structures and optimization problems to which then the obtained results automatically apply.

翻译：本文引入并阐述了一种强大的统计插值概念——我们称之为“完全提升”（fully lifted, fl），同时建立了双线性索引随机过程与其对应的完全解耦（线性索引）比较替代方案之间的联系。尽管有时涉及非常复杂的技术考量，最终的插值形式及其内在关系却呈现出相当简洁的表达式，这为深入研究随机过程及其应用的各个方面提供了极为理想且实用的工具。我们还讨论了所考虑模型的普适性，并表明它们涵盖了许多众所周知的随机结构和优化问题，从而使所得结果可自动应用于这些领域。