基于MAP译码的条件随机场Bethe学习
Bethe Learning of Conditional Random Fields via MAP Decoding
摘要：
许多机器学习任务都可以用预测结构化输出的方式来表达。在诸如结构化支持向量机（SVM-Struct）和结构化感知器的框架中，通过迭代地应用有效的最大后验（MAP）解码来学习判别函数。然而，最大似然估计（MLE）的概率模型在这些相同的结构化空间需要计算分区函数，这通常是棘手的。本文提出了一种利用Bethe逼近极大似然估计学习离散指数族模型的方法。值得注意的是，这个问题也减少到迭代（MAP）解码。这种连接出现相结合的贝特近似与弗兰克-沃尔夫（FW）算法的凸对偶目标，它绕过了棘手的分区函数。其结果是一个新的单循环算法MLE-Struct，这是更有效的比以前的双循环近似最大似然估计方法。我们的算法优于现有的方法，在实验中涉及图像分割，匹配问题的视觉，和一个新的数据集的大学室友分配。
英文摘要：
Many machine learning tasks can be formulated in terms of predicting structured outputs. In frameworks such as the structured support vector machine (SVM-Struct) and the structured perceptron, discriminative functions are learned by iteratively applying efficient maximum a posteriori (MAP) decoding. However, maximum likelihood estimation (MLE) of probabilistic models over these same structured spaces requires computing partition functions, which is generally intractable. This paper presents a method for learning discrete exponential family models using the Bethe approximation to the MLE. Remarkably, this problem also reduces to iterative (MAP) decoding. This connection emerges by combining the Bethe approximation with a Frank-Wolfe (FW) algorithm on a convex dual objective which circumvents the intractable partition function. The result is a new single loop algorithm MLE-Struct, which is substantially more efficient than previous double-loop methods for approximate maximum likelihood estimation. Our algorithm outperforms existing methods in experiments involving image segmentation, matching problems from vision, and a new dataset of university roommate assignments.
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