# Learning the Markov order of paths in a network

@article{Petrovic2020LearningTM, title={Learning the Markov order of paths in a network}, author={Luka V. Petrovi'c and Ingo Scholtes}, journal={ArXiv}, year={2020}, volume={abs/2007.02861} }

We study 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 modelling techniques that explicitly account for the graph constraint. Adopting a multi-order modelling framework for paths, we develop a Bayesian learning technique that (i) more reliably detects the…

## 2 Citations

### HOTVis: Higher-Order Time-Aware Visualisation of Dynamic Graphs

- Computer ScienceGraph Drawing
- 2020

A novel dynamic graph visualisation algorithm that utilises higher-order graphical models of causal paths in time series data to compute time-aware static graph visualisations that combine the simplicity and interpretability of static graphs with a time- aware layout algorithm that highlights patterns in the causal topology that result from the temporal dynamics of edges.

### Wikipedia Reader Navigation: When Synthetic Data Is Enough

- Computer ScienceWSDM
- 2022

This study systematically quantify the differences between real navigation sequences and synthetic sequences generated from the clickstream data, in 6 analyses across 8 Wikipedia language versions, and finds that the differences are statistically significant, but with small effect sizes.

## References

SHOWING 1-10 OF 49 REFERENCES

### Representing higher-order dependencies in networks

- Computer ScienceScience Advances
- 2016

The higher-order network (HON) representation is proposed, including accuracy, scalability, and direct compatibility with the existing suite of network analysis methods, and it is illustrated how HON can be applied to a broad variety of tasks, such as random walking, clustering, and ranking.

### Inferring Markov chains: Bayesian estimation, model comparison, entropy rate, and out-of-class modeling.

- Computer Science, MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2007

This work shows how to infer kth order Markov chains, for arbitrary k, from finite data by applying Bayesian methods to both parameter estimation and model-order selection and establishes a direct relationship between Bayesian evidence and the partition function.

### Detecting Memory and Structure in Human Navigation Patterns Using Markov Chain Models of Varying Order

- Computer SciencePloS one
- 2014

This work thoroughly presents a diverse array of advanced inference methods for determining the appropriate Markov chain order and reveals that the complexity of higher order models grows faster than their utility, and thus confirms that the memoryless model represents a quite practical model for human navigation on a page level.

### Testing the Order of Markov Dependence in DNA Sequences

- Mathematics
- 2011

DNA or protein sequences are usually modeled as probabilistic phenomena. The simplest model is created on the assumption that the nucleotides at the various sites are independently distributed.…

### HONEM: Network Embedding Using Higher-Order Patterns in Sequential Data

- Computer ScienceArXiv
- 2019

It is demonstrated that the higher-order network embedding (HONEM) method is able to extract higher- order dependencies from HON to construct theHigher-order neighborhood matrix of the network, while existing methods are not able to capture these higher-orders.

### Markov chain order estimation with parametric significance tests of conditional mutual information

- MathematicsSimul. Model. Pract. Theory
- 2016

### Bayesian inference on biopolymer models

- BiologyBioinform.
- 1999

This paper presents a tutorial style description of a Bayesian inference procedure for segmentation of a sequence based on the heterogeneity in its composition, and shows how this goal can be achieved for most bioinformatics methods that use dynamic programming.

### Higher-order aggregate networks in the analysis of temporal networks: path structures and centralities

- Computer ScienceArXiv
- 2015

A novel framework for the study of path-based centralities in higher-order aggregate networks, a recently proposed generalization of the commonly used static representation of time-stamped data is introduced.

### HONEM: Learning Embedding for Higher Order Networks

- Computer ScienceBig Data
- 2020

HONEM is a higher order network embedding method that captures the non-Markovian higher order dependencies in a network and outperforms other state-of-the-art methods in node classification, network reconstruction, link prediction, and visualization for networks that contain non- MarkovianHigher order dependencies.

### ST ] 2 J un 2 01 1 Markov Chain Order Estimation and χ 2 − divergence measure

- Mathematics
- 2011

We use the χ2 − divergence as a measure of diversity between probability densities and review the basic properties of the estimator D2(.‖.). In the sequence we define a few objects which capture…