诱导因式分解概率分布的可比性
Inducing Comparability of Factorised Probability Distributions
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中文总结 AI 辅助
研究如何对定义在不同变量集上的概率图模型进行比较，提出用条件均匀扩展方案，建立形式基础，实现将因子图扩展到共同可测空间及共同图形结构，还讨论相关性质与比较标准。
中文摘要 AI 辅助
为了对定义在不同变量集上的两个概率图模型进行有原则的比较，必须将它们提升到一个共同的可测空间。为此，我们提出了一种针对任意两个给定模型的扩展方案并建立了形式基础：使用条件均匀（拉普拉斯）扩展来完成不匹配的组件，使得得到的联合分布与原始分布仅相差乘法常数且在投影下重合。这保留了概率语义，同时允许应用定义良好的分布差异度量。我们建立了诱导联合在投影下的不变性，并使用扩展通过确定性算法将两个因子图最小结构扩展到最小的共同可测空间以及共同的图形结构。此外，我们讨论了结构和测度理论性质，并确定了比较方法的有前景标准。
英文摘要
To allow for principled comparison between two probabilistic graphical models defined over non-identical variable sets, they have to be lifted to a common measurable space. To this end, we propose an extension scheme for any two given models and establish the formal foundation: Unmatched components are completed using conditionally uniform (Laplace) extensions such that the resulting joint distributions differ from the original ones only by multiplicative constants and coincide under projection. This preserves the probabilistic semantics while enabling the application of well-defined distributional discrepancy measures. We establish the invariance of the induced joint under projection and use the extensions to provide a minimal structural extension of two factor graphs to the smalles common measurable space as well as to a common graphical structure by a deterministic algorithm. In addition, we discuss structural and measure-theoretic properties and identify promising criteria for comparison methodologies.
