Inducing Comparability of Factorised Probability Distributions

Abstract: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.

Artificial Intelligence (cs.AI)

arXiv:2607.20502 [cs.AI]

(or arXiv:2607.20502v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2607.20502 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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