Lifted Relational Probabilistic Inference via Implicit Learning

TL;DR

This paper introduces a novel polynomial-time framework that combines implicit learning with lifted inference techniques to efficiently perform probabilistic reasoning in first-order relational domains without explicit model construction.

Contribution

It presents the first polynomial-time method merging implicit learning with lifted inference for first-order probabilistic logic, handling both individuals and worlds simultaneously.

Findings

Merges incomplete axioms with sampled data into SOS hierarchy.

Performs grounding-lift and world-lift simultaneously.

Achieves polynomial-time inference in relational probabilistic logic.

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.