利用LP松弛约束组合搜索的MAP精确推理
Exact MAP-Inference by Confining Combinatorial Search with LP Relaxation
摘要：
我们考虑图模型的MAP推理问题，这是一个定义在实数上的具有自然求和运算的值约束满足问题。我们提出了一个家庭的松弛（不同于著名的Sherali-Adams层次结构），自然定义其最佳的下界。这个家庭总是包含一个紧松弛，我们给出了一个算法能够找到它，因此，解决了初始的非放松NP-难问题。我们考虑的松弛分解成两个不重叠的部分原来的问题：一个简单的LP紧的一部分，一个困难的。对于后一部分，必须使用组合求解器。正如我们在实验中所展示的，在许多应用中，第二个困难部分只占整个问题的一小部分。这个属性允许显着减少组合求解器的计算时间，从而解决以前无法解决的问题。
英文摘要：
We consider the MAP-inference problem for graphical models, which is a valued constraint satisfaction problem defined on real numbers with a natural summation operation. We propose a family of relaxations (different from the famous Sherali-Adams hierarchy), which naturally define lower bounds for its optimum. This family always contains a tight relaxation and we give an algorithm able to find it and therefore, solve the initial non-relaxed NP-hard problem. The relaxations we consider decompose the original problem into two non-overlapping parts: an easy LP-tight part and a difficult one. For the latter part a combinatorial solver must be used. As we show in our experiments, in a number of applications the second, difficult part constitutes only a small fraction of the whole problem. This property allows to significantly reduce the computational time of the combinatorial solver and therefore solve problems which were out of reach before.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
