Kernel Belief Propagation
Kernel Belief Propagation
复制标题
核置信传播
DOI：
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发表时间：
2011
期刊：
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通讯作者：
Carlos Guestrin
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文献类型：
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作者：
Le Song;A. Gretton;Danny Bickson;Yucheng Low;Carlos Guestrin
我们提出了对成对马尔可夫随机场的信念传播，内核信仰传播（KBP）的非参数概括。消息在复制的内核希尔伯特空间（RKHS）中表示为函数，消息更新是RKHS中简单的线性操作。 KBP没有任何经典BP算法中通常需要的假设：变量不必来自有限的域或高斯分布，它们的关系也不应采用任何特定的参数形式。相反，变量之间的关系是隐式表示的，并且是从训练数据中非参数学习的。 KBP的优点是，即使在未知的显式参数模型或不存在BP更新的明确参数模型的情况下，它也可以在定义内核的任何域（R D，字符串，组）中使用。 KBP中消息更新的计算成本在培训数据大小中是多项式。我们还通过使用少量基础函数表示消息来提出一个恒定的时间近似消息更新过程。在实验中，我们将KBP应用于图像降解，静止图像的深度预测以及蛋白质构型预测：KBP比竞争的经典和非参数方法快（在某些情况下通过数量级）快，同时提供了更准确的结果。
We propose a nonparametric generalization of belief propagation, Kernel Belief Propagation (KBP), for pairwise Markov random fields. Messages are represented as functions in a reproducing kernel Hilbert space (RKHS), and message updates are simple linear operations in the RKHS. KBP makes none of the assumptions commonly required in classical BP algorithms: the variables need not arise from a finite domain or a Gaussian distribution, nor must their relations take any particular parametric form. Rather, the relations between variables are represented implicitly, and are learned nonparametrically from training data. KBP has the advantage that it may be used on any domain where kernels are defined (R d , strings, groups), even where explicit parametric models are not known, or closed form expressions for the BP updates do not exist. The computational cost of message updates in KBP is polynomial in the training data size. We also propose a constant time approximate message update procedure by representing messages using a small number of basis functions. In experiments, we apply KBP to image denoising, depth prediction from still images, and protein configuration prediction: KBP is faster than competing classical and nonparametric approaches (by orders of magnitude, in some cases), while providing significantly more accurate results.