Lifted probabilistic inference exploits symmetries in a probabilistic model to allow for tractable probabilistic inference with respect to domain sizes of logical variables. We found that the current state-of-the-art algorithm to construct a lifted representation in form of a parametric factor graph misses symmetries between factors that are exchangeable but scaled differently, thereby leading to a less compact representation. In this paper, we propose a generalisation of the advanced colour passing (ACP) algorithm, which is the state of the art to construct a parametric factor graph. Our proposed algorithm allows for potentials of factors to be scaled arbitrarily and efficiently detects more symmetries than the original ACP algorithm. By detecting strictly more symmetries than ACP, our algorithm significantly reduces online query times for probabilistic inference when the resulting model is applied, which we also confirm in our experiments.

翻译：提升概率推理利用概率模型中的对称性，使得在逻辑变量域大小方面进行可处理的概率推理成为可能。我们发现，当前最先进的构建参数化因子图形式提升表示的算法，会遗漏可交换但缩放比例不同的因子之间的对称性，从而导致表示不够紧凑。本文提出了一种先进色彩传递（ACP）算法的泛化版本，该算法是构建参数化因子图的最先进方法。我们提出的算法允许因子势能任意缩放，并能比原始ACP算法更高效地检测更多对称性。通过检测比ACP严格更多的对称性，我们的算法在应用所得模型时显著减少了概率推理的在线查询时间，这一点也在我们的实验中得到了证实。