arXiv:2504.20784cs.AIcs.DS2025-04IJCAI被引 3

提出ε-ACP算法,让关系模型在不完全相同的情况下也能高效推理。

Approximate Lifted Model Construction

  • 引入ε-ACP,允许潜在函数有微小偏差仍能识别相似对象
  • 理论证明近似误差严格可控,实际中误差接近零
  • 适合处理真实数据中因噪声导致的非精确相似性问题

概率关系模型如参数化因子图可通过利用对象不可区分性实现高效(提升式)推理。在提升推理中,使用不可区分对象的代表进行计算。为获得关系(即提升)表示,当前最先进的方法是高级颜色传递(ACP)算法。然而,ACP算法要求潜在函数基于势能分解时必须完全匹配,才能识别并利用不可区分性。因此,在实际应用中,即使对象不可区分,从数据中学习到的势能也难免存在偏差,使得ACP不适用。为缓解此问题,我们提出ε-高级颜色传递(ε-ACP)算法,允许势能根据超参数ε存在一定偏差。ε-ACP能高效发现并利用非精确的不可区分性。我们证明了ε-ACP引入的近似误差严格有界,实验表明实际近似误差接近零。

原文摘要 · Abstract (English)

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.

概率推理提升推理关系模型近似算法

Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。