165 citations · 244 across the 23 of their papers we have counts for
24 papers
The Origins of Representation Manifolds in Large Language Models
Alexander Modell, Patrick Rubin-Delanchy, Nick Whiteley
There is a large ongoing scientific effort in mechanistic interpretability to map embeddings and internal representations of AI systems into human-understandable concepts. A key el…
How high is `high'? Rethinking the roles of dimensionality in topological data analysis and manifold learning
Hannah Sansford, Nick Whiteley, Patrick Rubin-Delanchy
We present a generalised Hanson-Wright inequality and use it to establish new statistical insights into the geometry of data point-clouds. In the setting of a general random functi…
Valid Conformal Prediction for Dynamic GNNs
Ed Davis, Ian Gallagher, Daniel John Lawson +1
Dynamic graphs provide a flexible data abstraction for modelling many sorts of real-world systems, such as transport, trade, and social networks. Graph neural networks (GNNs) are p…
A Simple and Powerful Framework for Stable Dynamic Network Embedding
Ed Davis, Ian Gallagher, Daniel John Lawson +1
In this paper, we address the problem of dynamic network embedding, that is, representing the nodes of a dynamic network as evolving vectors within a low-dimensional space. While t…
Intensity Profile Projection: A Framework for Continuous-Time Representation Learning for Dynamic Networks
Alexander Modell, Ian Gallagher, Emma Ceccherini +2
We present a new representation learning framework, Intensity Profile Projection, for continuous-time dynamic network data. Given triples , each representing a time-stampe…
Hierarchical clustering with dot products recovers hidden tree structure
Annie Gray, Alexander Modell, Patrick Rubin-Delanchy +1
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 o…
Implications of sparsity and high triangle density for graph representation learning
Hannah Sansford, Alexander Modell, Nick Whiteley +1
Recent work has shown that sparse graphs containing many triangles cannot be reproduced using a finite-dimensional representation of the nodes, in which link probabilities are inne…
Statistical exploration of the Manifold Hypothesis
Nick Whiteley, Annie Gray, Patrick Rubin-Delanchy
The Manifold Hypothesis is a widely accepted tenet of Machine Learning which asserts that nominally high-dimensional data are in fact concentrated near a low-dimensional manifold,…
Spectral embedding and the latent geometry of multipartite networks
Alexander Modell, Ian Gallagher, Joshua Cape +1
Spectral embedding finds vector representations of the nodes of a network, based on the eigenvectors of a properly constructed matrix, and has found applications throughout science…
Spectral embedding for dynamic networks with stability guarantees
Ian Gallagher, Andrew Jones, Patrick Rubin-Delanchy
We consider the problem of embedding a dynamic network, to obtain time-evolving vector representations of each node, which can then be used to describe changes in behaviour of indi…
Matrix factorisation and the interpretation of geodesic distance
Nick Whiteley, Annie Gray, Patrick Rubin-Delanchy
Given a graph or similarity matrix, we consider the problem of recovering a notion of true distance between the nodes, and so their true positions. We show that this can be accompl…
Spectral clustering under degree heterogeneity: a case for the random walk Laplacian
Alexander Modell, Patrick Rubin-Delanchy
This paper shows that graph spectral embedding using the random walk Laplacian produces vector representations which are completely corrected for node degree. Under a generalised r…
Spectral clustering on spherical coordinates under the degree-corrected stochastic blockmodel
Francesco Sanna Passino, Nicholas A. Heard, Patrick Rubin-Delanchy
Spectral clustering is a popular method for community detection in network graphs: starting from a matrix representation of the graph, the nodes are clustered on a low dimensional…
The multilayer random dot product graph
Andrew Jones, Patrick Rubin-Delanchy
We present a comprehensive extension of the latent position network model known as the random dot product graph to accommodate multiple graphs -- both undirected and directed -- wh…
Manifold structure in graph embeddings
Patrick Rubin-Delanchy
Statistical analysis of a graph often starts with embedding, the process of representing its nodes as points in space. How to choose the embedding dimension is a nuanced decision i…
Persistent Homology of Graph Embeddings
Vinesh Solanki, Patrick Rubin-Delanchy, Ian Gallagher
Popular network models such as the mixed membership and standard stochastic block model are known to exhibit distinct geometric structure when embedded into using…
Spectral embedding of weighted graphs
Ian Gallagher, Andrew Jones, Anna Bertiger +2
When analyzing weighted networks using spectral embedding, a judicious transformation of the edge weights may produce better results. To formalize this idea, we consider the asympt…
A statistical interpretation of spectral embedding: the generalised random dot product graph
Patrick Rubin-Delanchy, Joshua Cape, Minh Tang +1
Spectral embedding is a procedure which can be used to obtain vector representations of the nodes of a graph. This paper proposes a generalisation of the latent position network mo…
Choosing Between Methods of Combining p-values
Nicholas Heard, Patrick Rubin-Delanchy
Combining p-values from independent statistical tests is a popular approach to meta-analysis, particularly when the data underlying the tests are either no longer available or are…
Consistency of adjacency spectral embedding for the mixed membership stochastic blockmodel
Patrick Rubin-Delanchy, Carey E. Priebe, Minh Tang
The mixed membership stochastic blockmodel is a statistical model for a graph, which extends the stochastic blockmodel by allowing every node to randomly choose a different communi…
Meta-analysis of mid-p-values: some new results based on the convex order
Patrick Rubin-Delanchy, Nicholas A. Heard, Daniel John Lawson
The mid-p-value is a proposed improvement on the ordinary p-value for the case where the test statistic is partially or completely discrete. In this case, the ordinary p-value is c…
Posterior predictive p-values and the convex order
Patrick Rubin-Delanchy, Daniel John Lawson
Posterior predictive p-values are a common approach to Bayesian model-checking. This article analyses their frequency behaviour, that is, their distribution when the parameters and…
A test for dependence between two point processes on the real line
Patrick Rubin-Delanchy, Nicholas A. Heard
Many scientific questions rely on determining whether two sequences of event times are associated. This article introduces a likelihood ratio test which can be parameterised in sev…
An algorithm to compute the power of Monte Carlo tests with guaranteed precision
Axel Gandy, Patrick Rubin-Delanchy
This article presents an algorithm that generates a conservative confidence interval of a specified length and coverage probability for the power of a Monte Carlo test (such as a b…