Network Stochastic Processes and Time Series

Project: Research council

Project Details


Dynamic networks occur in many fields of science, technology and medicine, as well as everyday life. Understanding their behaviour has important applications. For example, whether it is to uncover serious crime on the dark web, intrusions in a computer network, or hijacks at global internet scales, better network anomaly detection tools are desperately needed in cyber-security. Characterising the network structure of multiple EEG time series recorded at different locations in the brain is critical for understanding neurological disorders and therapeutics development. Modelling dynamic networks is of great interest in transport applications, such as for preventing accidents on highways and predicting the influence of bad weather on train networks. Systematically identifying, attributing, and preventing misinformation online requires realistic models of information flow in social networks.

Whilst simple random networks theory is well-established in maths and computer science, the recent explosion of dynamic network data has exposed a large gap in our ability to process real-life networks. Classical network models have led to a body of beautiful mathematical theory, but do not always capture the rich structure and temporal dynamics seen in real data, nor are they geared to answer practitioners' typical questions, e.g. relating to forecasting, anomaly detection or data ethics issues. Our NeST programme will develop robust, principled, yet computationally feasible ways of modelling dynamically changing networks and the statistical processes on them.

Some aspects of these problems, such as quantifying the influence of policy interventions on the spread of misinformation or disease, require advances in probability theory. Dynamic network data are also notoriously difficult to analyse. At a computational level, the datasets are often very large and/or only available "on the stream". At a statistical level, they often come with important collection biases and missing data. Often, even understanding the data and how they may relate to the analysis goal can be challenging. Therefore, to tackle these research questions in a systematic way we need to bring probabilists, statisticians and application domain experts together.

NeST's six-year programme will see probabilists and statisticians with theoretical, computational, machine learning and data science expertise, collaborate across six world-class institutes to conduct leading and impactful research. In different overlapping groups, we will tackle questions such as: How do we model data to capture the complex features and dynamics we observe in practice? How should we conduct exploratory data analysis or, to quote a famous statistician, "Looking at the data to see what it seems to say" (Tukey, 1977)? How can we forecast network data, or detect anomalies, changes, trends? To ground techniques in practice, our research will be informed and driven by challenges in many key scientific disciplines through frequent interaction with industrial & government partners in energy, cyber-security, the environment, finance, logistics, statistics, telecoms, transport, and biology. A valuable output of work will be high-quality, curated, dynamic network datasets from a broad range of application domains, which we will make publicly available in a repository for benchmarking, testing & reproducibility (responsible innovation), partly as a vehicle to foster new collaborations. We also have a strategy to disseminate knowledge through a diverse range of scientific publication routes, high-quality free software (e.g. R packages, Python notebooks accompanying data releases), conferences, patents and outreach activities. NeST will also carefully nurture and develop the next generation of highly-trained and research-active people in our area, which will contribute strongly to satisfying the high demand for such people in industry, government and academia.
Effective start/end date3/11/222/11/28

Collaborative partners

  • University of Bath
  • Imperial College London (lead)
  • London School of Economics
  • University of Bristol
  • University of Oxford
  • University of York


  • Engineering and Physical Sciences Research Council

RCUK Research Areas

  • Mathematical sciences
  • Non-linear Systems Mathematics
  • Statistics and Applied Probability


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