Alexander Jenkins

Alexander Jenkins, Imad Jaimoukha, Ljubisa Stankovic et al.

Forming the right combination of students in a group promises to enable a powerful and effective environment for learning and collaboration. However, defining a group of students is a complex task which has to satisfy multiple constraints. This work introduces an unsupervised algorithm for fair and skill-diverse student group formation. This is achieved by taking account of student course marks and sensitive attributes provided by the education office. The skill sets of students are determined using unsupervised dimensionality reduction of course mark data via the Laplacian eigenmap. The problem is formulated as a constrained graph partitioning problem, whereby the diversity of skill sets in each group are maximised, group sizes are upper and lower bounded according to available resources, and `balance' of a sensitive attribute is lower bounded to enforce fairness in group formation. This optimisation problem is solved using integer programming and its effectiveness is demonstrated on a dataset of student course marks from Imperial College London.

Alexander Jenkins, Zehua Chen, Fu Siong Ng et al.

Pulsative signals such as the electrocardiogram (ECG) are extensively collected as part of routine clinical care. However, noisy and poor-quality recordings are a major issue for signals collected using mobile health systems, decreasing the signal quality, leading to missing values, and affecting automated downstream tasks. Recent studies have explored the imputation of missing values in ECG with probabilistic time-series models. Nevertheless, in comparison with the deterministic models, their performance is still limited, as the variations across subjects and heart-beat relationships are not explicitly considered in the training objective. In this work, to improve the imputation and forecasting accuracy for ECG with probabilistic models, we present a template-guided denoising diffusion probabilistic model (DDPM), PulseDiff, which is conditioned on an informative prior for a range of health conditions. Specifically, 1) we first extract a subject-level pulsative template from the observed values to use as an informative prior of the missing values, which personalises the prior; 2) we then add beat-level stochastic shift terms to augment the prior, which considers variations in the position and amplitude of the prior at each beat; 3) we finally design a confidence score to consider the health condition of the subject, which ensures our prior is provided safely. Experiments with the PTBXL dataset reveal that PulseDiff improves the performance of two strong DDPM baseline models, CSDI and SSSD$^{S4}$, verifying that our method guides the generation of DDPMs while managing the uncertainty. When combined with SSSD$^{S4}$, PulseDiff outperforms the leading deterministic model for short-interval missing data and is comparable for long-interval data loss.

Andrea Cini, Alexander Jenkins, Danilo Mandic et al.

We address the problem of uncertainty quantification in time series forecasting by exploiting observations at correlated sequences. Relational deep learning methods leveraging graph representations are among the most effective tools for obtaining point estimates from spatiotemporal data and correlated time series. However, the problem of exploiting relational structures to estimate the uncertainty of such predictions has been largely overlooked in the same context. To this end, we propose a novel distribution-free approach based on the conformal prediction framework and quantile regression. Despite the recent applications of conformal prediction to sequential data, existing methods operate independently on each target time series and do not account for relationships among them when constructing the prediction interval. We fill this void by introducing a novel conformal prediction method based on graph deep learning operators. Our approach, named Conformal Relational Prediction (CoRel), does not require the relational structure (graph) to be known a priori and can be applied on top of any pre-trained predictor. Additionally, CoRel includes an adaptive component to handle non-exchangeable data and changes in the input time series. Our approach provides accurate coverage and achieves state-of-the-art uncertainty quantification in relevant benchmarks.

Alexander Jenkins, Andrea Cini, Joseph Barker et al.

Catheter ablation of Atrial Fibrillation (AF) consists of a one-size-fits-all treatment with limited success in persistent AF. This may be due to our inability to map the dynamics of AF with the limited resolution and coverage provided by sequential contact mapping catheters, preventing effective patient phenotyping for personalised, targeted ablation. Here we introduce FibMap, a graph recurrent neural network model that reconstructs global AF dynamics from sparse measurements. Trained and validated on 51 non-contact whole atria recordings, FibMap reconstructs whole atria dynamics from 10% surface coverage, achieving a 210% lower mean absolute error and an order of magnitude higher performance in tracking phase singularities compared to baseline methods. Clinical utility of FibMap is demonstrated on real-world contact mapping recordings, achieving reconstruction fidelity comparable to non-contact mapping. FibMap's state-spaces and patient-specific parameters offer insights for electrophenotyping AF. Integrating FibMap into clinical practice could enable personalised AF care and improve outcomes.

Alexander Jenkins, Thiernithi Variddhisai, Ahmed El-Medany et al.

Graph Signal Processing (GSP) provides a powerful framework for analysing complex, interconnected systems by modelling data as signals on graphs. While recent advances have enabled graph topology learning from observed signals, existing methods often struggle with time-varying systems and real-time applications. To address this gap, we introduce AdaCGP, a sparsity-aware adaptive algorithm for dynamic graph topology estimation from multivariate time series. AdaCGP estimates the Graph Shift Operator (GSO) through recursive update formulae designed to address sparsity, shift-invariance, and bias. Through comprehensive simulations, we demonstrate that AdaCGP consistently outperforms multiple baselines across diverse graph topologies, achieving improvements exceeding 83% in GSO estimation compared to state-of-the-art methods while maintaining favourable computational scaling properties. Our variable splitting approach enables reliable identification of causal connections with near-zero false alarm rates and minimal missed edges. Applied to cardiac fibrillation recordings, AdaCGP tracks dynamic changes in propagation patterns more effectively than established methods like Granger causality, capturing temporal variations in graph topology that static approaches miss. The algorithm successfully identifies stability characteristics in conduction patterns that may maintain arrhythmias, demonstrating potential for clinical applications in diagnosis and treatment of complex biomedical systems.