Abstract:Graph Signal Processing (GSP) provides a powerful framework for analysing complex, interconnected systems by modelling data as signals on graphs. Recent advances in GSP have enabled the learning of graph structures from observed signals, but these methods often struggle with time-varying systems and real-time applications. Adaptive filtering techniques, while effective for online learning, have seen limited application in graph topology estimation from a GSP perspective. To this end, we introduce AdaCGP, an online algorithm for adaptive estimation of the Graph Shift Operator (GSO) from multivariate time series. The GSO is estimated from an adaptive time-vertex autoregressive model through recursive update formulae designed to address sparsity, shift-invariance and bias. Through simulations, we show that AdaCGP performs consistently well across various graph topologies, and achieves improvements in excess of 82% for GSO estimation compared to baseline adaptive vector autoregressive models. In addition, our online variable splitting approach for enforcing sparsity enables near-perfect precision in identifying causal connections while maintaining low false positive rates upon optimisation of the forecast error. Finally, AdaCGP's ability to track changes in graph structure is demonstrated on recordings of ventricular fibrillation dynamics in response to an anti-arrhythmic drug. AdaCGP is shown to be able to identify the stability of critical conduction patterns that may be maintaining the arrhythmia in an intuitive way, together with its potential to support diagnosis and treatment strategies.
Abstract:Pulsative signals such as the electrocardiogram (ECG) are extensively collected as part of routine clinical care. However, noisy and poor-quality recordings, leading to missing values, are a major issue for signals collected using mobile health systems, decreasing the signal quality and affecting the automated downstream tasks. Recent studies have explored imputation of missing values for 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 ECG imputation and forecasting accuracy with probabilistic models, we present an template-guided denoising diffusion probabilistic model, PulseDiff, which is conditioned an informative prior for a range of health conditions. Specifically, 1) we first extract a subject-level pulsative template from the observation as an informative prior of missing values, which captures the personal characteristics; 2) we then add beat-level stochastic shift terms on the template for prior augmentation, which considers the beat-level variance of positioning and amplitude; 3) we finally design a confidence score to consider the health condition of subject, which ensures our prior is provided in a safe way. Experiments with the PTBXL dataset reveal PulseDiff improves the performance of two strong DDPMs baseline models, CSDI and SSSD$^{S4}$, verifying our method guides the generation of DDPMs while managing the uncertainty. When combining with SSSD$^{S4}$, our PulseDiff method outperforms the leading deterministic model for short-interval missing data and is comparable for long-interval data loss.
Abstract: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.