Publication
Towards Explainability of Approximate Lifted Model Construction: A Geometric Perspective
Jan Speller; Malte Luttermann; Marcel Gehrke; Tanya Braun
In: Sylvia Melzer; Hagen Peukert; Stefan Thiemann; Magnus Bender; Özgür L. Özçep; Nele Russwinkel; Kai Sauerwald; Diedrich Wolter (Hrsg.). Proceedings of the Joint Workshop on Humanities-Centred Artificial Intelligence and Formal & Cognitive Reasoning co-located with 48th German Conference on Artificial Intelligence. Joint Workshop on Humanities-Centred Artificial Intelligence and Formal & Cognitive Reasoning (CHAI and FCR-2025), located at 48th German Conference on Artificial Intelligence (KI-2025), September 16-19, Potsdam, Germany, Pages 41-56, Vol. 4058, CEUR, 10/2025.
Abstract
Advanced colour passing (ACP) is the state-of-the-art algorithm for lifting a propositional probabilistic model to
a first-order level by combining exchangeable factors, enabling the use of lifted inference algorithms to allow for
tractable probabilistic inference with respect to domain sizes. More recently, an approximate version of ACP,
called e-ACP, ensures the practical applicability of ACP by accounting for inaccurate estimates of underlying
distributions. e-ACP permits underlying distributions, encoded as potential-based factorisations, to slightly
deviate depending on a hyperparameter e while maintaining a bounded approximation error. To navigate through
different levels of compression versus accuracy, a hierarchical version of e-ACP has emerged that builds a
hierarchy of e values. In a drive towards interpretability of results, this paper looks at geometric properties of
e-equivalence, a central notion employed by e-ACP and its hierarchical version to quantify the maximum allowed
deviation between potentials. Specifically, we present a unified view on the results for e-ACP and its hierarchical
version and provide a geometric interpretation of e-equivalence in L^p, thereby making results more interpretable.