Wednesday, Aug 6: 8:30 AM - 10:20 AM
0233
Invited Paper Session
Music City Center
Room: CC-Davidson Ballroom B
Applied
No
Main Sponsor
Royal Statistical Society
Co Sponsors
Section on Statistical Learning and Data Science
Section on Statistics in Defense and National Security
Presentations
We describe a model for a network time series whose evolution is governed by an underlying stochastic process, known as the latent position process, in which network evolution can be represented in Euclidean space by a curve, called the Euclidean mirror. We define the notion of a first-order changepoint for a time series of networks, and construct a family of latent position process networks with underlying first-order changepoints. We prove that a spectral estimate of the associated Euclidean mirror localizes these changepoints, even when the graph distribution evolves continuously, but at a rate that changes. Simulated and real data examples on organoid networks show that this localization captures empirically significant shifts in network evolution.
Keywords
dynamic network
changepoint
spectral
organoid
A graphon is a limiting object used to describe the behaviour of large networks through a function that captures the probability of edge formation between nodes. Although the merits of graphons to describe large and unlabelled networks are clear, they traditionally are used for describing only binary edge information, which limits their utility for more complex relational data. Decorated graphons were introduced to extend the graphon framework by incorporating richer relationships, such as edge weights and types. This specificity in modelling connections provides more granular insight into network dynamics. We develop estimation methods for decorated graphons, extending existing techniques from traditional graphon estimation to accommodate these richer interactions. We derive the rate of convergence for our method and show that it is consistent with traditional non-parametric theory when the decoration space is finite. Simulations confirm that these theoretical rates are achieved in practice. Our method, tested on synthetic and empirical data, effectively captures additional edge information, resulting in improved network models. This advancement extends the scope of graphon estimation to encompass more complex networks, such as multiplex networks and attributed graphs, thereby increasing our understanding of their underlying structures.
Keywords
network
multiplex network
weighted network
From a graph-based perspective, anomaly detection techniques currently deployed in enterprise cyber-security typically act on individual nodes or edges, for example, tracking connectivity patterns of a network host over time or detecting unusual volumes or periodicity in data transfers between two network nodes. Techniques which leverage the full network graph are less common; global network models have typically proved too simplistic in their assumptions, such as the well-studied but arguably overused stochastic block model. A new anomaly detection framework is proposed, which seeks to fully quantify uncertainty in node positions for latent position network graph models. Such a framework admits the possibility for nodes to be identified as outlying through, for example, unusual entropy levels in their perceived graph position rather than simply relying on detecting spatial outliers.
Keywords
graph embedding
Speaker
Nick Heard, Imperial College of Science & Technology
The talk considers the DIverse MultiPLEx Generalized Random Dot Product Graph (DIMPLE-GRDPG) network model
where all layers of the network have the same collection of nodes and follow the Generalized Random Dot Product Graph (GRDPG) model. In addition, all layers can be partitioned into groups such that the layers in the same group are embedded in the same ambient subspace but otherwise all matrices of connection probabilities can be different. While this is already a very difficult model, in addition we assume that layers of the network are very sparse. We shall use tensor-based approaches to recovery of the groups of layers in such network and subsequent estimation of the ambient subspaces.
Keywords
Random network
Clustering
Tensor
We present a new algorithmic framework, Intensity Profile Projection, for learning continuous-time representations of the nodes of a dynamic network, characterised by a node set and a collection of instantaneous interaction events which occur in continuous time. Our framework consists of three stages: estimating the intensity functions underlying the interactions between pairs of nodes, e.g. via kernel smoothing; learning a projection which minimises a notion of intensity reconstruction error; and inductively constructing evolving node representations via the learned projection. We show that our representations preserve the underlying structure of the network, and are temporally coherent, meaning that node representations can be meaningfully compared at different points in time. We develop estimation theory which elucidates the role of smoothing as a bias-variance trade-off, and shows how we can reduce smoothing as the signal-to-noise ratio increases on account of the algorithm `borrowing strength' across the network.
Keywords
network
clustering
polarization
Embedding