Transformation of Markov Random Fields for marginal distribution estimation
Transformation of Markov Random Fields for marginal distribution estimation
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DOI：
10.1109/cvpr.2015.7298680
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发表时间：
2015-06
期刊：
影响因子：
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通讯作者：
Masaki Saito;Takayuki Okatani
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文献类型：
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作者：
Masaki Saito;Takayuki Okatani
本文提出了一种通用的方法转换MRF的边缘推理问题。它的主要应用是缩小MRF以加快计算速度。与MAP推理不同，对于边缘推理问题，只有经典的算法，如BP等，需要大量的计算成本。虽然缩小MRF应直接降低计算成本，但没有系统的方法来做到这一点，因为不清楚如何获得缩小MRF的MRF能量，以及如何将其边际分布的估计值转换为原始MRF的估计值。所提出的方法解决了这些问题的一种新的概率公式的MRF变换。其核心思想是将MRF的联合分布与变换后的MRF的联合分布进行表示，其中变换后的MRF的变量被视为潜变量。我们还表明，所提出的方法可以适用于连续MRF的变量空间的离散化，并可以与马尔可夫链蒙特卡罗方法。实验结果证明了该方法的有效性。
This paper presents a generic method for transforming MRFs for the marginal inference problem. Its major application is to downsize MRFs to speed up the computation. Unlike the MAP inference, there are only classical algorithms for the marginal inference problem such as BP etc. that require large computational cost. Although downsizing MRFs should directly reduce the computational cost, there is no systematic way of doing this, since it is unclear how to obtain the MRF energy for the downsized MRFs and also how to translate the estimates of their marginal distributions to those of the original MRFs. The proposed method resolves these issues by a novel probabilistic formulation of MRF transformation. The key idea is to represent the joint distribution of an MRF with that of the transformed one, in which the variables of the latter are treated as latent variables. We also show that the proposed method can be applied to discretization of variable space of continuous MRFs and can be used with Markov chain Monte Carlo methods. The experimental results demonstrate the effectiveness of the proposed method.