图模型中推理的复杂性
Complexity of Inference in Graphical Models
摘要：
众所周知，图模型中的推理在最坏的情况下是困难的，但是对于具有有界树宽的模型是容易处理的。我们问树宽是否是唯一的结构标准的基础图形，使易处理的推理。换句话说，是否存在一类树宽无界的结构，在这种结构中，推理是容易处理的？根据Robertson等人（1994）的组合假设，我们证明了低树宽确实是唯一可以确保易处理性的结构限制。因此，即使对于“最佳情况”图结构，也不存在在树宽上具有复杂性多项式的推理算法。
英文摘要：
It is well-known that inference in graphical models is hard in the worst case, but tractable for models with bounded treewidth. We ask whether treewidth is the only structural criterion of the underlying graph that enables tractable inference. In other words, is there some class of structures with unbounded treewidth in which inference is tractable? Subject to a combinatorial hypothesis due to Robertson et al. (1994), we show that low treewidth is indeed the only structural restriction that can ensure tractability. Thus, even for the "best case" graph structure, there is no inference algorithm with complexity polynomial in the treewidth.
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