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We summarise our recent research on statistical relational formalisms that allow for incorporating relative frequencies within a possible-worlds semantics (known as Type III probability logic). In a setting of lifted Bayesian networks, we evaluate conditional probability logic as a recent proposal using discrete relative frequency cut-offs and introduce our own formalism, functional lifted Bayesian networks, for integrating continuous relative frequency boundaries. Our main result is a strong asymptotic convergence theorem, which yields uniform convergence in parametric families. This is particularly important in what we consider the most important application of such asymptotic results, estimating the parameters of a statistical relational model from randomly sampled subsets. Version of record: Journal of Artificial Intelligence Research 80, 1407–1436 (2024). https://doi.org/10.1613/JAIR.1.15679

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Probabilities of the Third Type: Statistical Relational Learning and Reasoning with Relative Frequencies

  • 会议论文

  • 发表日期：

    2026年

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  • Felix Weitkämper

摘要

We summarise our recent research on statistical relational formalisms that allow for incorporating relative frequencies within a possible-worlds semantics (known as Type III probability logic). In a setting of lifted Bayesian networks, we evaluate conditional probability logic as a recent proposal using discrete relative frequency cut-offs and introduce our own formalism, functional lifted Bayesian networks, for integrating continuous relative frequency boundaries. Our main result is a strong asymptotic convergence theorem, which yields uniform convergence in parametric families. This is particularly important in what we consider the most important application of such asymptotic results, estimating the parameters of a statistical relational model from randomly sampled subsets. Version of record: Journal of Artificial Intelligence Research 80, 1407–1436 (2024). https://doi.org/10.1613/JAIR.1.15679