基于图模型迭代松弛推理的最大持久性
Maximum Persistency via Iterative Relaxed Inference with Graphical Models
摘要：
本文研究了无向离散图模型的MAP-推理的NP-困难问题。我们提出了一个多项式时间和实际有效的算法，找到其最优解的一部分。具体来说，我们的算法将所考虑的图模型的一些标签标记为（i）最优的，这意味着它们属于推理问题的所有最优解;（ii）非最优的，如果它们可证明不属于任何解。随着访问一个精确的求解器的线性规划松弛的MAP推理问题，我们的算法标记的最大可能（在指定的意义上）的标签数。我们还提出了一个版本的算法，它可以访问一个次优的双求解器，仍然可以确保（非）标记标签的最优性，虽然标记标签的总数可能会减少。我们提出了一个有效的实现，它运行的时间相当于一个次优双求解器的单次运行。我们的方法具有良好的可扩展性，并在机器学习和计算机视觉的计算基准上显示了最先进的结果。
英文摘要：
We consider the NP-hard problem of MAP-inference for undirected discrete graphical models. We propose a polynomial time and practically efficient algorithm for finding a part of its optimal solution. Specifically, our algorithm marks some labels of the considered graphical model either as (i) optimal, meaning that they belong to all optimal solutions of the inference problem; (ii) non-optimal if they provably do not belong to any solution. With access to an exact solver of a linear programming relaxation to the MAP-inference problem, our algorithm marks the maximal possible (in a specified sense) number of labels. We also present a version of the algorithm, which has access to a suboptimal dual solver only and still can ensure the (non-)optimality for the marked labels, although the overall number of the marked labels may decrease. We propose an efficient implementation, which runs in time comparable to a single run of a suboptimal dual solver. Our method is well-scalable and shows state-of-the-art results on computational benchmarks from machine learning and computer vision.
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