因子图中交换因子的有效检测
Efficient Detection of Commutative Factors in Factor Graphs
AI总结：
本文提出 DECOR 算法，通过有效识别限制条件大幅减少检查因子交换性所需的迭代次数，解决了因子图中交换因子检测的计算效率问题。
摘要：
提升概率推理利用概率图模型中的对称性，从而允许相对于域大小的可处理概率推理。为了利用例如因子图中的对称性，识别交换因子至关重要，即由于参数可交换而其内部具有对称性的因子。当前用于检查因子是否相对于其参数子集具有交换性的最先进方法，需遍历因子参数的所有可能子集，即在最坏情况下，对于具有 $n$ 个参数的因子需要 $O(2^n)$ 次迭代。在本文中，我们高效地解决了在因子图中检测交换因子的问题。具体而言，我们引入了交换因子检测（DECOR）算法，该算法使我们能够在实践中大幅减少检查因子是否可交换的计算量。我们证明了 DECOR 能够有效识别限制条件以大幅减少所需迭代次数，并在实证评估中验证了 DECOR 的效率。
英文摘要：
Lifted probabilistic inference exploits symmetries in probabilistic graphical models to allow for tractable probabilistic inference with respect to domain sizes. To exploit symmetries in, e.g., factor graphs, it is crucial to identify commutative factors, i.e., factors having symmetries within themselves due to their arguments being exchangeable. The current state of the art to check whether a factor is commutative with respect to a subset of its arguments iterates over all possible subsets of the factor's arguments, i.e., $O(2^n)$ iterations for a factor with $n$ arguments in the worst case. In this paper, we efficiently solve the problem of detecting commutative factors in a factor graph. In particular, we introduce the detection of commutative factors (DECOR) algorithm, which allows us to drastically reduce the computational effort for checking whether a factor is commutative in practice. We prove that DECOR efficiently identifies restrictions to drastically reduce the number of required iterations and validate the efficiency of DECOR in our empirical evaluation.
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