Nest is a

Mathematical research collaboration

between Imperial College, Oxford, Bath, LSE, York and Edinburgh on “Network Stochastic Processes and Time Series”, funded by a multimillion pound EPSRC programme grant and several industry and government partners.

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Nest is a

Mathematical research collaboration

Hero banner image

between Imperial College, Oxford, Bath, LSE, York and Edinburgh on “Network Stochastic Processes and Time Series”, funded by a multimillion pound EPSRC programme grant and several industry and government partners.

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What we do

This 6-year programme (2022-2028) will bring probabilists, statisticians and data scientists together to study large dynamic networks with applications in medicine, transport, cybersecurity, environmental protection, finance, biology and economics.

Events

Upcoming Events

Date icon14-16 June 2024

2024 Workshop on Statistical Network Analysis and Beyond (SNAB 2024)

The 2024 Workshop on Statistical Network Analysis and Beyond (SNAB2024) is scheduled to take place on June 14-16, 2023 at the Courtyard by Marriott Nassau Downtown/Junkanoo Beach. Over the span of three days, this workshop aims to unite researchers in the field of network science and related disciplines, providing an avenue for the exchange of innovative ideas and recent findings. The workshop will encompass a wide range of topics, ranging from statistical network modeling to more extensive fields such as tensor modeling, deep learning, and text analysis.

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Past Events

Date icon2023-10-03

1st NeST Away day and Annual Meeting 2023

We are pleased to announce the successful conclusion of NeST’s first Away Day and Annual Meeting, which took place on 3rd-4th October in York. The two-day event featured a rich program of individual and snapshot presentations delivered by leading mid

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Date icon2023-05-24

1st NeST International Steering and Oversight Committee (ISOC)

Our first ISOC meeting took place on Wednesday, 24 May. It was a productive and engaging session, marked by valuable insights and thoughtful discussions. During the meeting, we had the privilege of having esteemed individuals from diverse backgrounds

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Date icon2023-04-21

Kick-Off Workshop

The first joint event took place online on the 21st of April 2023. There were 70 registered attendees (PhD candidates, Research Assistants, established researchers) from the following institutions: LSE, The Alan Turing Institute, Max Planck Institute

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Our Research

Our programme of research is dedicated to creating realistic models and developing associated statistical inference tools for dynamic network data, supported by rigorous mathematical theory.

We also aim to provide the community with curated network datasets and freely available software for practitioners and scientists wishing to analyse network data.

News

Recent Publications

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Update to GNAR to version 1.1.3

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New Methods for Network Count Time Series Cover Image

New Methods for Network Count Time Series

The original generalized network autoregressive models are poor for modelling count data as they are based on the additive and constant noise assumptions, which is usually inappropriate for count data. We introduce two new models (GNARI and NGNAR) for count network time series by adapting and extending existing count-valued time series models. We present results on the statistical and asymptotic properties of our new models and their estimates obtained by conditional least squares and maximum likelihood. We conduct two simulation studies that verify successful parameter estimation for both models and conduct a further study that shows, for negative network parameters, that our NGNAR model outperforms existing models and our other GNARI model in terms of predictive performance. We model a network time series constructed from COVID-positive counts for counties in New York State during 2020--22 and show that our new models perform considerably better than existing methods for this problem.

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New tools for network time series Cover Image

New tools for network time series

Network time series are becoming increasingly important across many areas in science and medicine and are often characterised by a known or inferred underlying network structure, which can be exploited to make sense of dynamic phenomena that are often high-dimensional. For example, the Generalised Network Autoregressive (GNAR) models exploit such structure parsimoniously. We use the GNAR framework to introduce two association measures: the network and partial network autocorrelation functions, and introduce Corbit (correlation-orbit) plots for visualisation. As with regular autocorrelation plots, Corbit plots permit interpretation of underlying correlation structures and, crucially, aid model selection more rapidly than using other tools such as AIC or BIC. We additionally interpret GNAR processes as generalised graphical models, which constrain the processes' autoregressive structure and exhibit interesting theoretical connections to graphical models via utilization of higher-order interactions. We demonstrate how incorporation of prior information is related to performing variable selection and shrinkage in the GNAR context. We illustrate the usefulness of the GNAR formulation, network autocorrelations and Corbit plots by modelling a COVID-19 network time series of the number of admissions to mechanical ventilation beds at 140 NHS Trusts in England & Wales. We introduce the Wagner plot that can analyse correlations over different time periods or with respect to external covariates. In addition, we introduce plots that quantify the relevance and influence of individual nodes. Our modelling provides insight on the underlying dynamics of the COVID-19 series, highlights two groups of geographically co-located `influential' NHS Trusts and demonstrates superior prediction abilities when compared to existing techniques.

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Autoregressive Networks Cover Image

Autoregressive Networks

We propose a first-order autoregressive (i.e. AR(1)) model for dynamic network processes in which edges change over time while nodes remain unchanged. The model depicts the dynamic changes explicitly. It also facilitates simple and efficient statistical inference methods including a permutation test for diagnostic checking for the fitted network models. The proposed model can be applied to the network processes with various underlying structures but with independent edges. As an illustration, an AR(1) stochastic block model has been investigated in depth, which characterizes the latent communities by the transition probabilities over time. This leads to a new and more effective spectral clustering algorithm for identifying the latent communities. We have derived a finite sample condition under which the perfect recovery of the community structure can be achieved by the newly defined spectral clustering algorithm. Furthermore the inference for a change point is incorporated into the AR(1) stochastic block model to cater for possible structure changes. We have derived the explicit error rates for the maximum likelihood estimator of the change-point. Application with three real data sets illustrates both relevance and usefulness of the proposed AR(1) models and the associate inference methods.

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A two – way heterogeneity model for dynamic networks Cover Image

A two – way heterogeneity model for dynamic networks

Analysis of networks that evolve dynamically requires the joint modelling of individual snapshots and time dynamics. This paper proposes a new flexible two-way heterogeneity model towards this goal. The new model equips each node of the network with two heterogeneity parameters, one to characterize the propensity to form ties with other nodes statically and the other to differentiate the tendency to retain existing ties over time. With n observed networks each having p nodes, we develop a new asymptotic theory for the maximum likelihood estimation of 2p parameters when np→∞. We overcome the global non-convexity of the negative log-likelihood function by the virtue of its local convexity, and propose a novel method of moment estimator as the initial value for a simple algorithm that leads to the consistent local maximum likelihood estimator (MLE). To establish the upper bounds for the estimation error of the MLE, we derive a new uniform deviation bound, which is of independent interest. The theory of the model and its usefulness are further supported by extensive simulation and a data analysis examining social interactions of ants.

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The GNAR – edge model: A network autoregressive model fornetworks with time – varying edge weights Cover Image

The GNAR – edge model: A network autoregressive model fornetworks with time – varying edge weights

In economic and financial applications, there is often the need for analysing multivariate time series, comprising of time series for a range of quantities. In some applications such complex systems can be associated with some underlying network describing pairwise relationships among the quantities. Accounting for the underlying network structure for the analysis of this type of multivariate time series is required for assessing estimation error and can be particularly informative for forecasting. Our work is motivated by a dataset consisting of time series of industry-to-industry transactions. In this example, pairwise relationships between Standard Industrial Classification (SIC) codes can be represented using a network, with SIC codes as nodes, while the observed time series for each pair of SIC codes can be regarded as time-varying weights on the edges. Inspired by Knight et al. (2019), we introduce the GNAR-edge model which allows modelling of multiple time series utilising the network structure, assuming that each edge weight depends not only on its past values, but also on past values of its neighbouring edges, for a range of neighbourhood stages. The method is validated through simulations. Results from the implementation of the GNAR-edge model on the real industry-to-industry data show good fitting and predictive performance of the model. The predictive performance is improved when sparsifying the network using a lead-lag analysis and thresholding edges according to a lead-lag score.

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Career

Employment

Chapman Fellow in Mathematics

Applications are invited for Chapman Fellowships in the Department of Mathematics, commencing September 2024. There are several positions available, which will each be fixed term for 2 years. These posts provide an excellent opportunity for those seeking to pursue an academic career in Mathematics.

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Research Officer in Statistics

Applications are invited for a Research Officer in Statistics in the Department of Statistics at the London School of Economics. Commencing in September 2024, this is a fixed term appointment for 3 years. Closing date: 12 January 2024 (23.59 UK time); Interviews: 24 January 2024.

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Postdoctoral Research Associate in Statistics

Applications are invited for a Postdoctoral Research Associate in Statistics in the Department of Statistics at the University of Oxford. Commencing in September 2024, this is a fixed term appointment for 3 years. Closing date: 12 January 2024 (12.00 noon, UK time); Interviews: 24 January 2024.

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Research Associate in Statistics

We invite applications for a Postdoctoral Research Associate to work on the EPSRC-funded programme grant ‘Network Stochastic Processes and Time Series (NeST)’ . NeST brings together the Universities of Bath, Edinburgh, Imperial College London, the London School of Economics and Political Science, Oxford and York, with industrial and government partners. This configuration has advantages for postdoctoral researchers as you will not only have access to your project leaders and team, but ultimately to all project members across the six institutions and the flow of ideas and problems across NeST. Stochastic network data are of rapidly increasing ubiquity in many fields such as medicine, transportation, cybersecurity, the environment, finance, biology and economics, and NeST aims to achieve a step change in the modelling and prediction of evolving, inter-connected stochastic network processes. As part of the NeST team, you will contribute to realising a substantial coordinated push to create, develop and apply innovative new models, computational techniques and underpinning theory, in response to real applied problems spurred by dynamic networks in many contexts. The research at the University of York will be led by Prof. Marina Knight and focus on the modelling and prediction of dynamically collected data at the nodes and edges of e.g. biological networks. The statistical challenge in such contexts is to more accurately reflect data characteristics in network time series models, where the data may be high-dimensional and for example exhibit nonstationarity, long-range dependence, and/or be driven by external factors. The position is full-time and will be held for 36 months, starting as soon as possible and ideally before 2 September 2024. Closing date: 13 March 2024; Interviews: 25 March 2024

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