We propose a novel sequence prediction method for sequential data capturing node traversals in graphs. Our method builds on a statistical modelling framework that combines multiple higher-order network models into a single multi-order model. We develop a technique to fit such multi-order models in empirical sequential data and to select the optimal maximum order. Our framework facilitates both next-element and full sequence prediction given a sequence-prefix of any length. We evaluate our model based on six empirical data sets containing sequences from website navigation as well as public transport systems. The results show that our method out-performs state-of-the-art algorithms for next-element prediction. We further demonstrate the accuracy of our method during out-of-sample sequence prediction and validate that our method can scale to data sets with millions of sequences.

中文翻译：

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使用具有多个高阶的网络模型预测图中遍历节点的序列

我们提出了一种新的序列预测方法，用于在图中捕获节点遍历的顺序数据。我们的方法建立在一个统计建模框架之上，该框架将多个高阶网络模型组合成一个单一的多阶模型。我们开发了一种技术来在经验序列数据中拟合这种多阶模型并选择最佳的最大阶数。我们的框架在给定任何长度的序列前缀的情况下促进下一个元素和完整序列预测。我们根据六个经验数据集评估我们的模型，这些数据集包含来自网站导航和公共交通系统的序列。结果表明，我们的方法优于最先进的下一个元素预测算法。