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PAA: The Probabilistic Allen Algebra: A Generative and Complete Probabilistic Extension of Allen's Interval Relations

The paper introduces the Probabilistic Allen Algebra (PAA), a generative and complete extension of Allen’s interval algebra that assigns relation probabilities based on Gaussian distributions over interval boundaries rather than fixed scores. In PAA, time points, interval midpoints, and durations are modeled with Gaussian and truncated‑Gaussian distributions, allowing all thirteen base relations to be expressed as boundary‑ordering predicates within a single probability space. The framework incorporates tolerance bands for contact relations, preserves Allen’s taxonomy through hierarchical unions of relations, and is validated via Monte‑Carlo simulations, with the implementation released as an open, tested Python package.

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arXiv AI
Sep 18

PAA: The Probabilistic Allen Algebra: A Generative and Complete Probabilistic Extension of Allen's Interval Relations

The paper introduces the Probabilistic Allen Algebra (PAA), a generative and complete extension of Allen's interval algebra that assigns relation probabilities based on Gaussian distributions over interval boundaries. PAA models time points and intervals with Gaussian and truncated‑Gaussian parameters, enabling graded temporal expressions and a tolerance band for contact relations. The algebra preserves Allen's taxonomy, supports scale invariance, and is validated through Monte‑Carlo simulations, with the implementation released as an open Python package.

By Julian Eggert (Honda Research Institute Europe, Offenbach, Germany)
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arXiv Machine Learning
Sep 11

The observational partial order of causal structures with latent variables

The paper studies observational dominance among causal structures with latent variables, defining one structure as dominating another if it can realize all distributions that the other can over the same visible variables. It provides a full characterization of this dominance partial order for three visible variables and a partial one for four, and shows that many equivalence classes are distinguished by nontrivial inequality constraints similar to Bell or instrumental inequalities. The authors also demonstrate that constraint‑based causal discovery algorithms relying only on conditional independence are much less powerful than those incorporating nested Markov and inequality constraints.

By Marina Maciel Ansanelli, Elie Wolfe, Robert W. Spekkens
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