Domain-Size Aware Markov Logic Networks
Domain-Size Aware Markov Logic Networks
复制标题
域大小感知马尔可夫逻辑网络
DOI：
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发表时间：
2019
期刊：
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通讯作者：
Parag Singla
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文献类型：
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作者：
Happy Mittal;Ayush Bhardwaj;Vibhav Gogate;Parag Singla
AI中的几个领域需要表示关系结构以及模型不确定性。马尔可夫逻辑是一种强大的形式主义，它通过在有限的一阶逻辑中给公式附加权重来实现这一点。虽然马尔可夫逻辑网络（MLN）已被用于各种各样的应用，一个重大的挑战仍然存在
当训练域大小与测试期间看到的不同时，权重不能很好地泛化。特别是，它已被观察到，边际概率趋于极端的域大小增加的限制。作为我们工作的第一个贡献，我们进一步描述了分布特征并表明
边际概率趋向于一个与权重无关的常数，并不总是像以前观察到的那样极端。作为我们的第二个贡献，我们提出了一个原则性的解决方案，这个问题通过定义域大小感知马尔可夫逻辑网络（DA-MLNs），可以被看作是重新参数化的MLNs考虑域大小后。对于一些简单但有代表性的MLN公式，我们正式证明了DA-MLN定义的概率是良好的行为。在实践方面，DA-MLN允许我们将在小规模训练数据上学习的权重推广到更大的领域。三个不同的基准MLN的实验表明，我们的方法相比，现有的方法在显着的性能增益。
Several domains in AI need to represent the relational structure as well as model uncertainty. Markov Logic is a powerful formalism which achieves this by attaching weights to formulas in finite first-order logic. Though Markov Logic Networks (MLNs) have been used for a wide variety of applications, a significant challenge remains
that weights do not generalize well when training domain sizes are different from those seen during testing. In particular, it has been observed that marginal probabilities tend to extremes in the limit of increasing domain sizes. As the first contribution of our work, we further characterize the distribution and show that
marginal probabilities tend to a constant independent of weights and not always to extremes as was previously observed. As our second contribution, we present a principled solution to this problem by defining Domain-size Aware Markov Logic Networks (DA-MLNs) which can be seen as re-parameterizing the MLNs after taking domain size into consideration. For some simple but representative MLN formulas, we formally prove that probabilities defined by DA-MLNs are well behaved. On a practical side, DA-MLNs allow us to generalize the weights learned over small-sized training data to much larger domains. Experiments on three different benchmark MLNs show that our approach results in significant performance gains compared to existing methods.