让不同变量集的概率模型可比较，只需补全缺失变量。
Inducing Comparability of Factorised Probability Distributions
- 用条件均匀分布补全差异变量，保持原分布语义不变
- 补全后联合分布仅差常数因子，投影结果完全一致
- 适合需要精确比较概率图模型的研究者
为在非相同变量集上定义的两个概率图模型提供合理比较基础，需将其提升至共同可测空间。为此，我们提出一种通用扩展方案：对未匹配组件使用条件均匀（Laplace）扩展，使所得联合分布仅与原分布相差乘性常数，并在投影下完全一致。该方法保留了概率语义，同时支持定义良好的分布差异度量。我们证明了诱导联合分布的投影不变性，并通过确定性算法实现两个因子图向最小共同可测空间及共同图结构的最小结构性扩展。此外，讨论了其结构与测度论性质，并识别出有前景的比较方法准则。
原文摘要 · Abstract (English)
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.
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