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Learning Steady-States of Iterative Algorithms over Graphs(附PDF版全文下载)

发布时间:2018-07-15 23:38:57 文章来源:SCI论文网 我要评论

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Learning Steady-States of Iterative Algorithms over Graphs
Hanjun Dai ,Zornitsa Kozareva , Bo Dai , Alexander J. Smola ,Le Song 


        Many graph analytics problems can be solved via iterative algorithms where the solutions are often characterized by a set of steady-state conditions.Different algorithms respect to different set of fixed point constraints, so instead of using these traditional algorithms, can we learn an algorithm which can obtain the same steady-state solutions automatically from examples, in an effective and scalable way? How to represent the meta learner for such algorithm and how to carry out the learning? In this paper, we propose an embedding representation for iterative algorithms over graphs, and design a learning method which alternates between updating the embeddings and projecting them onto the steadystate constraints. We demonstrate the effectiveness of our framework using a few commonly used graph algorithms, and show that in some cases, the learned algorithm can handle graphs with more than 100,000,000 nodes in a single machine.


       许多图形分析问题可以通过迭代算法来求解,其中解决方案的特征往往是一组稳态条件。 Xed点约束,因此,我们可以学习一种算法,它可以从实例中自动获得相同的稳态解,而不是使用这些传统的算法。 可平息的方式?该算法如何代表元学习者,如何进行学习?本文给出了图和DES上迭代算法的嵌入表示。 IGN是一种学习方法,它在更新嵌入并将它们投影到稳态约束上。我们使用几种常用的图形算法演示了我们的框架的有效性,并展示了在某些情况下, 算法可以在一台机器上处理超过100,000,000个节点的图形。


       1. Introduction
       Graphs and networks arise in various real-world applications and machine learning problems, such as social network analysis (Hamilton et al., 2017b), molecule screening (Hachmann et al., 2011; Duvenaud et al., 2015; Lei et al., 2017) and knowledge base reasoning (Trivedi et al., 2017). Many graph analytics problems can be solved via iterative algorithms according to the graph structure, and the solutions of the algorithms are often characterized by a set of steady-state conditions. For instance, the PageRank (Page et al., 1999) score of a node in a graph can be computed iteratively by averaging the scores of its neighbors, until the node score and this neighbor averaging are approximately equal. Mean field inference for the posterior distribution of a variable in a graphical model can be updated iteratively by aggregating the messages from
its neighbors until the posterior is approximately equal to the results of the aggregation operator.

      1. 介绍

      在各种实际应用和机器学习问题中出现了图表和网络,例如社会网络分析(Hamilton等人,2017b),分子筛选(Hachmann等人,2011年;Duvena)。 ud等人,2015年;Ray等人,2017年)和知识库推理(Trivedi等人,2017年)。许多图分析问题都可以根据图的结构通过迭代算法来求解。 算法的解的特征往往是一组稳态条件.例如,图中节点的PageRank(Page等人,1999年)得分可以由Avera迭代计算。 把它的邻居的分数加起来,直到节点的分数和这个邻居的平均值大致相等为止。图模型中变量后验分布的平均场推断 e通过聚合来自它的邻居直到后部近似等于聚合算子的结果。




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