Approximate Lifted Model Construction
This addresses a practical limitation for researchers and practitioners in probabilistic AI, enabling lifted inference in real-world applications with learned data, though it is incremental as it modifies an existing algorithm.
The paper tackles the problem that the state-of-the-art Advanced Colour Passing (ACP) algorithm for lifted inference in probabilistic relational models fails when potentials learned from data deviate, even for indistinguishable objects. It introduces the ε-ACP algorithm, which allows for potential deviations with a hyperparameter ε, proving a strict bound on approximation error and showing in experiments that the error is close to zero in practice.
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.