Learning the Markov Order of Paths in Graphs

Abstract

We address the problem of learning the Markov order in categorical sequences that represent paths in a network, i.e., sequences of variable lengths where transitions between states are constrained to a known graph. Such data pose challenges for standard Markov order detection methods and demand modeling techniques that explicitly account for the graph constraint. Adopting a multi-order modeling framework for paths, we develop a Bayesian learning technique that (i) detects the correct Markov order more reliably than a competing method based on the likelihood ratio test, (ii) requires considerably less data than methods using AIC or BIC, and (iii) is robust against partial knowledge of the underlying constraints. We further show that a recently published method that uses a likelihood ratio test exhibits a tendency to overfit the true Markov order of paths, which is not the case for our Bayesian technique. Our method is important for data scientists analyzing patterns in categorical sequence data that are subject to (partially) known constraints, e.g. click stream data or other behavioral data on the Web, information propagation in social networks, mobility trajectories, or pathway data in bioinformatics. Addressing the key challenge of model selection, our work is also relevant for the growing body of research that emphasizes the need for higher-order models in network analysis.