Philip J. Aston

Temesgen Mehari, Ashish Sundar, Alen Bosnjakovic et al.

Feature importance methods promise to provide a ranking of features according to importance for a given classification task. A wide range of methods exist but their rankings often disagree and they are inherently difficult to evaluate due to a lack of ground truth beyond synthetic datasets. In this work, we put feature importance methods to the test on real-world data in the domain of cardiology, where we try to distinguish three specific pathologies from healthy subjects based on ECG features comparing to features used in cardiologists' decision rules as ground truth. Some methods generally performed well and others performed poorly, while some methods did well on some but not all of the problems considered.

Philip J. Aston, Oliver Junge

We consider a generalisation of Ulam's method for approximating invariant densities of one-dimensional chaotic maps. Rather than use piecewise constant polynomials to approximate the density, we use polynomials of degree n which are defined by the requirement that they preserve the measure on n+1 neighbouring subintervals. Over the whole interval, this results in a discontinuous piecewise polynomial approximation to the density. We prove error results where this approach is used to approximate smooth densities. We also consider the computation of the Lyapunov exponent using the polynomial density and show that the order of convergence is one order better than for the density itself. Together with using cubic polynomials in the density approximation, this yields a very efficient method for computing highly accurate estimates of the Lyapunov exponent. We illustrate the theoretical findings with some examples.

Mohammad Moulaeifard, Ciaran Bench, Philip J. Aston et al.

Uncertainty quantification (UQ) is critical for safety-critical domains like healthcare, yet it is rarely evaluated under realistic out-of-distribution (OOD) conditions. Here, we assessed predictive performance and uncertainty reliability for deep learning-based blood pressure (BP) estimation from photoplethysmography (PPG) signals under both in-distribution (ID) and OOD settings. Using an XResNet1D-50 trained on PulseDB and tested on four external datasets, we compared deep ensembles (DE) and Monte Carlo dropout (MCD) with Gaussian negative log-likelihood (GNLL) and mean squared error (MSE) losses, optionally followed by post-hoc recalibration via conformal prediction (CP), temperature scaling (TS), and isotonic regression (IR). The key findings of our study are as follows: (1) DE provides stronger predictive robustness under domain shift than MCD, an advantage that becomes clear primarily under external shift. (2) Recalibrated GNLL-based methods yield the best uncertainty calibration (e.g., GNLL+DE+CP for systolic blood pressure (SBP), GNLL+DE+TS for diastolic blood pressure (DBP)), while MSE-based uncertainty requires recalibration to become practically useful. (3) Across settings, CP and TS offer the most consistent gains, with IR remaining competitive in several cases. Overall, our results identify DE-based methods as most robust for predictive performance under domain shift, GNLL as strongest for native UQ, and recalibration as essential for making MSE-based uncertainty practical. These findings highlight the need to jointly assess predictive accuracy and calibration on external data for trustworthy cuffless BP estimation

Ciaran Bench, Oskar Pfeffer, Vivek Desai et al.

In principle, deep learning models trained on medical time-series, including wearable photoplethysmography (PPG) sensor data, can provide a means to continuously monitor physiological parameters outside of clinical settings. However, there is considerable risk of poor performance when deployed in practical measurement scenarios leading to negative patient outcomes. Reliable uncertainties accompanying predictions can provide guidance to clinicians in their interpretation of the trustworthiness of model outputs. It is therefore of interest to compare the effectiveness of different approaches. Here we implement an unprecedented set of eight uncertainty quantification (UQ) techniques to models trained on two clinically relevant prediction tasks: Atrial Fibrillation (AF) detection (classification), and two variants of blood pressure regression. We formulate a comprehensive evaluation procedure to enable a rigorous comparison of these approaches. We observe a complex picture of uncertainty reliability across the different techniques, where the most optimal for a given task depends on the chosen expression of uncertainty, evaluation metric, and scale of reliability assessed. We find that assessing local calibration and adaptivity provides practically relevant insights about model behaviour that otherwise cannot be acquired using more commonly implemented global reliability metrics. We emphasise that criteria for evaluating UQ techniques should cater to the model's practical use case, where the use of a small number of measurements per patient places a premium on achieving small-scale reliability for the chosen expression of uncertainty, while preserving as much predictive performance as possible.

Mohammad Moulaeifard, Philip J. Aston, Peter H. Charlton et al.

Photoplethysmography (PPG) is one of the most widely captured biosignals for clinical prediction tasks, yet PPG-based algorithms are typically trained on small-scale datasets of uncertain quality, which hinders meaningful algorithm comparisons. We present a comprehensive benchmark for PPG-based clinical prediction using the \dbname~dataset, establishing baselines across the full spectrum of clinically relevant applications: multi-class heart rhythm classification, and regression of physiological parameters including respiratory rate (RR), heart rate (HR), and blood pressure (BP). Most notably, we provide the first comprehensive assessment of PPG for general arrhythmia detection beyond atrial fibrillation (AF) and atrial flutter (AFLT), with performance stratified by BP, HR, and demographic subgroups. Using established deep learning architectures, we achieved strong performance for AF detection (AUROC = 0.96) and accurate physiological parameter estimation (RR MAE: 2.97 bpm; HR MAE: 1.13 bpm; SBP/DBP MAE: 16.13/8.70 mmHg). Cross-dataset validation demonstrates excellent generalizability for AF detection (AUROC = 0.97), while clinical subgroup analysis reveals marked performance differences across subgroups by BP, HR, and demographic strata. These variations appear to reflect population-specific waveform differences rather than systematic bias in model behavior. This framework establishes the first integrated benchmark for multi-task PPG-based clinical prediction, demonstrating that PPG signals can effectively support multiple simultaneous monitoring tasks and providing essential baselines for future algorithm development.

Mohammad Moulaeifard, Loic Coquelin, Mantas Rinkevičius et al.

Photoplethysmography (PPG) is a widely used non-invasive physiological sensing technique, suitable for various clinical applications. Such clinical applications are increasingly supported by machine learning methods, raising the question of the most appropriate input representation and model choice. Comprehensive comparisons, in particular across different input representations, are scarce. We address this gap in the research landscape by a comprehensive benchmarking study covering three kinds of input representations, interpretable features, image representations and raw waveforms, across prototypical regression and classification use cases: blood pressure and atrial fibrillation prediction. In both cases, the best results are achieved by deep neural networks operating on raw time series as input representations. Within this model class, best results are achieved by modern convolutional neural networks (CNNs). but depending on the task setup, shallow CNNs are often also very competitive. We envision that these results will be insightful for researchers to guide their choice on machine learning tasks for PPG data, even beyond the use cases presented in this work.