Lifted Relational Probabilistic Inference via Implicit Learning

• URL: http://arxiv.org/abs/2602.14890v1
• Date: Mon, 16 Feb 2026 16:24:13 GMT
• Title: Lifted Relational Probabilistic Inference via Implicit Learning
• Authors: Luise Ge, Brendan Juba, Kris Nilsson, Alison Shao,
• Abstract summary: We study the problem of answering queries in a first-order probabilistic logic through a joint effort of learning and reasoning.<n>Traditional lifted inference assumes access to a complete model and exploits symmetry to evaluate queries.<n>We reconcile these two challenges through implicit learning to reason and first-order probabilistic inference techniques.
• Score: 9.419317852220315
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Reconciling the tension between inductive learning and deductive reasoning in first-order relational domains is a longstanding challenge in AI. We study the problem of answering queries in a first-order relational probabilistic logic through a joint effort of learning and reasoning, without ever constructing an explicit model. Traditional lifted inference assumes access to a complete model and exploits symmetry to evaluate probabilistic queries; however, learning such models from partial, noisy observations is intractable in general. We reconcile these two challenges through implicit learning to reason and first-order relational probabilistic inference techniques. More specifically, we merge incomplete first-order axioms with independently sampled, partially observed examples into a bounded-degree fragment of the sum-of-squares (SOS) hierarchy in polynomial time. Our algorithm performs two lifts simultaneously: (i) grounding-lift, where renaming-equivalent ground moments share one variable, collapsing the domain of individuals; and (ii) world-lift, where all pseudo-models (partial world assignments) are enforced in parallel, producing a global bound that holds across all worlds consistent with the learned constraints. These innovations yield the first polynomial-time framework that implicitly learns a first-order probabilistic logic and performs lifted inference over both individuals and worlds.

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