二进制和多类MRF的基于半定规划的高效推理
Efficient semidefinite-programming-based inference for binary and multi-class MRFs
摘要：
成对马尔可夫随机场（MRF）中的概率推理，即计算分区函数或计算变量的MAP估计，是概率图模型中的一个基本问题。半定规划松弛一直是分析概率推理性质的理论上强有力的工具，但由于求解所得SDP的典型求解器的高计算成本而不实用。在本文中，我们提出了一种有效的方法来计算分区函数或MAP估计在成对MRF，而不是利用最近提出的基于坐标下降的快速半定解算器。我们还将半定松弛从典型的二进制MRF到完整的多类设置，并开发了一个紧凑的半定松弛，可以再次有效地解决使用求解器。我们表明，该方法大大优于（无论是在解决方案的质量和速度方面）现有的最先进的近似推理，从以前的工作中得出的基准问题。我们还表明，我们的方法可以扩展到大型MRF域，如计算机视觉中使用的全连接成对CRF模型。
英文摘要：
Probabilistic inference in pairwise Markov Random Fields (MRFs), i.e. computing the partition function or computing a MAP estimate of the variables, is a foundational problem in probabilistic graphical models. Semidefinite programming relaxations have long been a theoretically powerful tool for analyzing properties of probabilistic inference, but have not been practical owing to the high computational cost of typical solvers for solving the resulting SDPs. In this paper, we propose an efficient method for computing the partition function or MAP estimate in a pairwise MRF by instead exploiting a recently proposed coordinate-descent-based fast semidefinite solver. We also extend semidefinite relaxations from the typical binary MRF to the full multi-class setting, and develop a compact semidefinite relaxation that can again be solved efficiently using the solver. We show that the method substantially outperforms (both in terms of solution quality and speed) the existing state of the art in approximate inference, on benchmark problems drawn from previous work. We also show that our approach can scale to large MRF domains such as fully-connected pairwise CRF models used in computer vision.
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