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Alexander Modell

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4 papers

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NeurIPS Conference 2025 Conference Paper

Multiresolution Analysis and Statistical Thresholding on Dynamic Networks

Raphael Romero
Tijl De Bie
Nick Heard
Alexander Modell

Detecting structural change in dynamic network data has wide-ranging applications. Existing approaches typically divide the data into time bins, extract network features within each bin, and then compare these features over time. This introduces an inherent tradeoff between temporal resolution and the statistical stability of the extracted features. Despite this tradeoff, reminiscent of time–frequency tradeoffs in signal processing, most methods rely on a \emph{fixed temporal resolution}. Choosing an appropriate resolution parameter is typically difficult, and can be especially problematic in domains like cybersecurity, where anomalous behavior may emerge at multiple time scales. We address this challenge by proposing ANIE ($\textbf{A}$daptive $\textbf{N}$etwork $\textbf{I}$ntensity $\textbf{E}$stimation), a multi-resolution framework designed to automatically identify the time scales at which network structure evolves, enabling the joint detection of both rapid and gradual changes. Modeling interactions as Poisson processes, our method proceeds in two steps: (1) estimating a low-dimensional subspace of node behavior, and (2) deriving a set of novel *empirical affinity coefficients* that measure change in interaction intensity between latent factors and support statistical testing for structural change across time scales. We provide theoretical guarantees for subspace estimation and the asymptotic behavior of the affinity coefficients, enabling model-based change detection. Experiments on synthetic networks show that ANIE adapts to the appropriate time resolution, and is able to capture sharp structural changes while remaining robust to noise. Furthermore, applications to real-world data showcase the practical benefits of ANIE’s multiresolution approach to detecting structural change over fixed resolution methods. An open-source implementation of the method is available at [https: //github. com/aida-ugent/anie].

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NeurIPS Conference 2024 Conference Paper

Entrywise error bounds for low-rank approximations of kernel matrices

Alexander Modell

In this paper, we derive entrywise error bounds for low-rank approximations of kernel matrices obtained using the truncated eigen-decomposition (or singular value decomposition). While this approximation is well-known to be optimal with respect to the spectral and Frobenius norm error, little is known about the statistical behaviour of individual entries. Our error bounds fill this gap. A key technical innovation is a delocalisation result for the eigenvectors of the kernel matrix corresponding to small eigenvalues, which takes inspiration from the field of Random Matrix Theory. Finally, we validate our theory with an empirical study of a collection of synthetic and real-world datasets.

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NeurIPS Conference 2023 Conference Paper

Hierarchical clustering with dot products recovers hidden tree structure

Annie Gray
Alexander Modell
Patrick Rubin-Delanchy
Nick Whiteley

In this paper we offer a new perspective on the well established agglomerative clustering algorithm, focusing on recovery of hierarchical structure. We recommend a simple variant of the standard algorithm, in which clusters are merged by maximum average dot product and not, for example, by minimum distance or within-cluster variance. We demonstrate that the tree output by this algorithm provides a bona fide estimate of generative hierarchical structure in data, under a generic probabilistic graphical model. The key technical innovations are to understand how hierarchical information in this model translates into tree geometry which can be recovered from data, and to characterise the benefits of simultaneously growing sample size and data dimension. We demonstrate superior tree recovery performance with real data over existing approaches such as UPGMA, Ward's method, and HDBSCAN.

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NeurIPS Conference 2023 Conference Paper

Intensity Profile Projection: A Framework for Continuous-Time Representation Learning for Dynamic Networks

Alexander Modell
Ian Gallagher
Emma Ceccherini
Nick Whiteley
Patrick Rubin-Delanchy

We present a new representation learning framework, Intensity Profile Projection, for continuous-time dynamic network data. Given triples $(i, j, t)$, each representing a time-stamped ($t$) interaction between two entities ($i, j$), our procedure returns a continuous-time trajectory for each node, representing its behaviour over time. The framework consists of three stages: estimating pairwise intensity functions, e. g. via kernel smoothing; learning a projection which minimises a notion of intensity reconstruction error; and constructing evolving node representations via the learned projection. The trajectories satisfy two properties, known as structural and temporal coherence, which we see as fundamental for reliable inference. Moreoever, we develop estimation theory providing tight control on the error of any estimated trajectory, indicating that the representations could even be used in quite noise-sensitive follow-on analyses. The theory also elucidates the role of smoothing as a bias-variance trade-off, and shows how we can reduce the level of smoothing as the signal-to-noise ratio increases on account of the algorithm `borrowing strength' across the network.

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