Fine Grained Weight Learning in Markov Logic Networks
Fine Grained Weight Learning in Markov Logic Networks
复制标题
马尔可夫逻辑网络中的细粒度权重学习
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Shubhankar Suman Singh
中科院分区：
文献类型：
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作者：
Happy Mittal;Shubhankar Suman Singh
马尔可夫逻辑网络（MLN）使用一组加权一阶公式表示底层域，并已成功应用于各种真实的世界问题。做出参数绑定假设，即，来自相同的一阶逻辑公式的基础公式具有相同的权重。这种假设在许多情况下可能是不准确的，并可能导致学习过程中的高偏差。在另一个极端，人们可以为每个基础学习不同的权重，从而产生具有高方差的模型。在本文中，我们提出了一种原则性的方法来利用这种权衡，通过对来自隐藏子类型的每个常数进行建模，并仅为那些具有相同子类型的公式接地的参数绑定参数。我们提出了两种不同的方法来自动发现子类型和学习模型的参数1）基于K均值聚类的方法B）使用基于EM的公式的联合学习方法。上述两个极端是我们公式的一个特例。基准MLN上的初步实验表明，我们的算法可以学习更好的参数相比，可用的替代品。
Markov logic networks (MLNs) represent the underlying domain using a set of weighted first-order formulas and have been successfully applied to a variety of real world problems. A parameter tying assumption is made, i.e., ground formulas coming from the same first-order logic formula have identical weights. This assumption may be inaccurate in many scenarios and can lead to high bias during learning. On the other extreme, one could learn a different weight for each grounding resulting in a model with high variance. In this paper, we present a principled approach to exploit this trade-off by modeling each constant coming from a hidden subtype, and tying the parameters only for those formula groundings which have the same subtype(s) for the respective arguments. We propose two different approaches for automatically discovering the subtypes and learning the parameters of the model 1) a K-means clustering based approach b) a joint learning approach using an EM based formulation. The two extremes described above fall out as a special case of our formulation. Preliminary experiments on a benchmark MLN show that our algorithm can learn significantly better parameters compared to available alternatives.