arXiv subjects

Nando Hegemann

Publications and source records attributed to Nando Hegemann.

7 recordsLinked to original sources

arXiv2026

Estimating systematic errors in Bayesian inversion using transport maps

In indirect measurements, the sought parameters have to be determined by solving an inverse problem, typically in a Bayesian framework. Often, the accurate numerical simulation of the measuring process is computationally demanding, making it necessary to rely on approximate models. These surrogates, however, introduce an additional model error and thus may distort the resulting parameter distribution. Moreover, even with the additional speed granted by the surrogate, posterior determination through conventional means such as Markov chain Monte Carlo might be cost intensive, specifically for complicated posterior shapes. In this paper, we propose a unified framework that combines Bayesian inference, model error correction and a transport-based sampling scheme to address these issues. To train the transport scheme, we investigate two different losses: one equivalent to the Kullback-Leibler divergence associated to the transport problem and one based on an upper bound of this loss, generally known as the evidence lower bound. We demonstrate that training the transport based on the latter changes the optimisation landscape drastically, potentially introducing an undesired bias in approximating the target posterior. We compare the computational cost of our approach with established methods and underline the theoretical results with numerical examples.

stat.ME↗

arXiv2026

Apnea Burden-Guided Framework: Enhancing Out-of-Distribution Generalization in PPG-Based Sleep Apnea Characterization

Sleep apnea is a common sleep-related breathing disorder associated with substantial cardiovascular and metabolic risk. Although overnight polysomnography remains the reference standard for diagnosis, its complexity and cost limit its suitability for long-term preventive monitoring at home. In wearable systems, arterial blood oxygen saturation (SpO2) is commonly used as the main predictor, whereas additional morphological features of the photoplethysmographic (PPG) pulse wave are usually underexplored. This study proposes a novel apnea burden prediction-based framework for sleep apnea severity assessment and investigates the influence of PPG features on model performance and out-of-distribution (OOD) generalization. The proposed framework first predicts apnea burden as a continuous measure, which is subsequently converted into the clinically relevant apnea-hypopnea index for subject-level classification into four severity groups in both in-distribution (ID) and OOD data. Three artificial neural network architectures were evaluated, and the performance metrics were averaged over five independent runs with different fixed random seeds. During OOD testing, the combination of PPG features and SpO2 led to increases of approximately 15.72% in macro-sensitivity, 9.22% in macro-accuracy, 16.01% in macro-F1-score, 11.08% in Cohen's kappa, and 13.22% in Matthews correlation coefficient, compared with using SpO2 alone. The low-complexity convolutional-recurrent models achieved the highest overall performance. The results indicated that the proposed apnea burden-guided framework, combined with PPG features and SpO2, improves sleep apnea characterization while showing encouraging OOD performance on an independent external dataset. Moreover, simpler hybrid architectures demonstrated strong potential for robust home-based preventive monitoring.

eess.SP↗

arXiv2026

Benchmark Problems and Benchmark Datasets for the evaluation of Machine and Deep Learning methods on Photoplethysmography signals: the D4 report from the QUMPHY project

This report is part of the Qumphy project (22HLT01 Qumphy) that is funded by the European Union and is dedicated to the development of measures to quantify the uncertainties associated with Machine Learning algorithms applied to medical problems, in particular the analysis and processing of Photoplethysmography (PPG) signals. In this report, a list of six medical problems that are related to PPG signals and serve as Benchmark Problems is given. Suitable Benchmark datasets and their usage are described also.

cs.LG↗

arXiv2026

Machine-learning for photoplethysmography analysis: Benchmarking feature, image, and signal-based approaches

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.

cs.LG↗

arXiv2025

Sample-based almost-sure quasi-optimal approximation in reproducing kernel Hilbert spaces

This paper addresses the problem of approximating an unknown function from point evaluations. When obtaining these point evaluations is costly, minimising the required sample size becomes crucial, and it is unreasonable to reserve a sufficiently large test sample for estimating the approximation accuracy. Therefore, an approximation with a certified quasi-optimality factor is required. This article shows that such an approximation can be obtained when the sought function lies in a reproducing kernel Hilbert space (RKHS) and is to be approximated in a finite-dimensional linear subspace $\mathcal{V}_d$. However, selecting the sample points to minimise the quasi-optimality factor requires optimising over an infinite set of points and computing exact inner products in RKHS, which is often infeasible in practice. Extending results from optimal sampling for $L^2$ approximation, the present paper proves that random points, drawn independently from the Christoffel sampling distribution associated with $\mathcal{V}_d$, can yield a controllable quasi-optimality factor with high probability. Inspired by this result, a novel sampling scheme, coined subspace-informed volume sampling, is introduced and evaluated in numerical experiments, where it outperforms classical i.i.d. Christoffel sampling and continuous volume sampling. To reduce the size of such a random sample, an additional greedy subsampling scheme with provable suboptimality bounds is introduced. Our presentation is of independent interest to the inverse problems community, as it offers a simpler interpretation of the parametrised background data weak (PBDW) method.

math.NA↗

arXiv2025

A systematic evaluation of uncertainty quantification techniques in deep learning: a case study in photoplethysmography signal analysis

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.

cs.LG↗

arXiv2024

On the convergence of adaptive Galerkin FEM for parametric PDEs with lognormal coefficients

Numerically solving high-dimensional random parametric PDEs poses a challenging computational problem. It is well-known that numerical methods can greatly benefit from adaptive refinement algorithms, in particular when functional approximations in polynomials are computed as in stochastic Galerkin finite element methods. This work investigates a residual based adaptive algorithm, akin to classical adaptive FEM, used to approximate the solution of the stationary diffusion equation with lognormal coefficients, i.e. with a non-affine parameter dependence of the data. It is known that the refinement procedure is reliable but the theoretical convergence of the scheme for this class of unbounded coefficients remains a challenging open question. This paper advances the theoretical state-of-the-art by providing a quasi-error reduction result for the adaptive solution of the lognormal stationary diffusion problem. The presented analysis generalizes previous results in that guaranteed convergence for uniformly bounded coefficients follows directly as a corollary. Moreover, it highlights the fundamental challenges with unbounded coefficients that cannot be overcome with common techniques. A computational benchmark example illustrates the main theoretical statement.

math.NA↗