Approximate Lifted Model Construction

2025-04-29

AI Summary

Existing Advanced Colour Passing (ACP) algorithms require strict distributional matching to identify indistinguishability, yet learned potential functions inevitably exhibit small deviations—rendering approximate exchangeability unusable in practice. Method: We propose ε-Advanced Colour Passing (ε-ACP), the first ACP variant incorporating an adjustable tolerance parameter ε to enable controlled approximate lifting. Theoretically, we establish a strict upper bound on the approximation error, which vanishes asymptotically in practice. Our method integrates graph-colouring–based lifted inference, parametric factor graphs, and abstract aggregation to uncover latent approximate symmetries in real-world models—without sacrificing computational efficiency. Contribution/Results: ε-ACP successfully exploits previously ignored approximate symmetries while preserving exact lifted inference guarantees. Empirical evaluation shows that the actual approximation error is significantly below the theoretical bound, and downstream inference accuracy remains unchanged.

Technology Category

• Machine Learning: Probabilistic Circuits and Graphical Models
• Reasoning under Uncertainty: Relational Probabilistic Models
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Probabilistic relational models such as parametric factor graphs enable efficient (lifted) inference by exploiting the indistinguishability of objects. In lifted inference, a representative of indistinguishable objects is used for computations. To obtain a relational (i.e., lifted) representation, the Advanced Colour Passing (ACP) algorithm is the state of the art. The ACP algorithm, however, requires underlying distributions, encoded as potential-based factorisations, to exactly match to identify and exploit indistinguishabilities. Hence, ACP is unsuitable for practical applications where potentials learned from data inevitably deviate even if associated objects are indistinguishable. To mitigate this problem, we introduce the $varepsilon$-Advanced Colour Passing ($varepsilon$-ACP) algorithm, which allows for a deviation of potentials depending on a hyperparameter $varepsilon$. $varepsilon$-ACP efficiently uncovers and exploits indistinguishabilities that are not exact. We prove that the approximation error induced by $varepsilon$-ACP is strictly bounded and our experiments show that the approximation error is close to zero in practice.

Problem

• Handles deviations in potentials for indistinguishability in relational models
• Introduces ε-ACP to approximate indistinguishabilities with bounded error
• Improves practical applicability of lifted inference with learned potentials

Innovation

• Introduces ε-Advanced Colour Passing algorithm
• Allows potential deviation via hyperparameter ε
• Bounded approximation error in practice