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Uncertainty quantification with approximate variational learning for wearable photoplethysmography prediction tasks

T0 review · 3 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read For PPG heart predictions, sampling stochasticity controls which uncertainty you get and how well it is calibrated.

desk verdict Useful, honest empirical study of MCD/IVON hyperparameters for PPG uncertainty, but the headline 'composition' claim rests on a disentanglement method the authors themselves have not validated. read the letter →

arxiv 2505.11412 v1 pith:UZES6TRO submitted 2025-05-16 cs.LG eess.SP

Ciaran Bench , Vivek Desai , Mohammad Moulaeifard , Nils Strodthoff , Philip Aston , Andrew Thompson This is my paper · ORCID
classification cs.LGeess.SP
keywords uncertaintyquantificationMonteCarloDropoutImprovedVariationalOnlineNewtonphotoplethysmographyatrialfibrillationbloodpressureestimationmodelcalibrationaleatoricandepistemic
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tests two scalable uncertainty-quantification techniques—Monte Carlo Dropout and Improved Variational Online Newton—on deep networks that classify atrial fibrillation and regress blood pressure from raw wearable photoplethysmography (PPG) time series. It finds that the hyperparameter controlling how randomly the model parameters are sampled at evaluation (dropout rate for MCD, Hessian initialisation for IVON) has a large effect on both predictive accuracy and the quality and composition of the predicted uncertainties. In particular, more stochastic sampling raises the fraction of uncertainty attributed to the model (epistemic) rather than the data (aleatoric), and on the whole population of test examples it improves calibration of class probabilities. The paper also shows that per-class calibration can differ sharply from global calibration, so an evaluation protocol that checks local and adaptive calibration is needed before these uncertainties are used in clinical decisions.

What carries the argument

The central mechanism is the stochasticity of model parameter sampling at evaluation time. For Monte Carlo Dropout this is set by the dropout rate $p$; for Improved Variational Online Newton it is set by the Hessian initialisation $h_0$, which controls the width of the approximate Gaussian posterior. This single dial determines how much of the total predictive variance is labelled epistemic (model uncertainty) as opposed to aleatoric (inherent data noise), and it correlates with how well the final class probabilities are calibrated. The supporting machinery is the standard heteroscedastic likelihood modelling from Kendall and Gal (Gaussian negative log-likelihood for regression; Monte-Carlo-averaged softmax for classification), the law-of-total-variance decomposition for regression and the entropy-concavity decomposition $H_{\text{ale}}\le H_{\text{total}}$ for classification, and a multi-metric evaluation protocol (ECE, UCE, ENCE, CCE, bivariate error-vs-uncertainty histograms, per-class curves) that exposes where calibration fails locally.

What would settle it

Retrain the blood-pressure regression models on a VitalDB split in which no patient appears in more than one set, and recompute the ENCE and CCE orderings across dropout rates (1%, 5%, 40%). If the ordering of calibration quality with dropout rate changes or the local calibration differences vanish, the paper's regression conclusions describe per-patient adaptation rather than generalisable model behaviour.

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Extended reading notes

Core claim

The central claim is that the reliability of uncertainty estimates from MCD and IVON on PPG prediction tasks is governed largely by the stochasticity of the parameter sampling, controlled by the dropout rate and by the Hessian initialisation respectively. Larger dropout rates (and smaller $h_0$ for IVON) increase the proportion of total uncertainty labelled epistemic and produce better-calibrated class probabilities as measured by the expected calibration error (ECE) over the whole test population, while the best predictive accuracy occurs at intermediate settings. The same stochasticity also shifts the balance between aleatoric and epistemic components, and the two components, when disentangled with standard formulas, turn out to be highly correlated, so the decomposition must be interpreted cautiously. Because per-class calibration curves diverge from global ones, the paper argues that evaluating uncertainty quality requires both individual and adaptive calibration metrics, not just aggregate scores.

Load-bearing premise

The blood-pressure regression results use the same 1,293 ICU patients in training, validation, and test sets, so the claims about "previously unseen test data" assume that this patient-overlapping split behaves like a true generalization test.

Editorial extensions

If this is right

  • Uncertainty estimates from MCD and IVON on PPG tasks are not trustworthy as-is: the dropout rate and $h_0$ must be tuned on the chosen calibration metric, because the optimal setting for accuracy, for ECE, and for UCE are not the same.
  • The proportion of predicted uncertainty attributed to epistemic versus aleatoric sources is largely an artefact of the sampling-stochasticity hyperparameter, not a stable property of the data or model.
  • Whole-test-set calibration can hide severe per-class miscalibration; for AF screening, low-uncertainty predictions are predominantly non-AF, so a highly confident decision rule would produce many false negatives.
  • For BP regression, the two disentangled uncertainty components are highly correlated, so users should not interpret the separated numbers as independent sources of doubt.
  • Greater stochasticity in model sampling produced better whole-population calibration of class probabilities for both techniques, suggesting a common principle: more posterior exploration helps probability calibration on this task.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the sampling-stochasticity/ECE relationship holds on other physiological time-series tasks, hyperparameter scans for UQ should report both ECE and an entropy-based calibration metric such as UCE, because the two can rank configurations oppositely (in the AF results, dropout 40% had the best ECE but a worse UCE than dropout 10%).
  • The high correlation between aleatoric and epistemic estimates hints that a single total-uncertainty score may be a more honest summary than the separated components for clinical use, until disentanglement methods are validated on physiological data.
  • An external, patient-disjoint evaluation of the BP models would test whether the dropout-rate effects on regression calibration persist under true generalization; this follows naturally from the paper's current split, which shares all 1,293 patients across sets.
  • A similar tuning of sampling stochasticity could be tried with other approximate Bayesian schemes, such as deep ensembles with different initialisations, to see whether calibration quality likewise improves with wider posterior sampling.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper evaluates two approximate variational uncertainty quantification techniques, Monte Carlo Dropout (MCD) and Improved Variational Online Newton (IVON), for deep learning models that detect atrial fibrillation from raw PPG time series and predict blood pressure from VitalDB PPG signals. The authors train AF classifiers with several MCD dropout rates and IVON Hessian initializations, and BP regression models with several MCD dropout rates, then assess predictive performance and calibration using ECE, UCE, ENCE, coverage calibration error, and per-class calibration curves. The central claims are that hyperparameter choices substantially affect both predictive performance and the quality and composition of predicted uncertainties, that the degree of sampling stochasticity determines the estimated aleatoric/epistemic split, and that per-class calibration differs meaningfully from population-level calibration. The manuscript also proposes a new entropy-based decomposition of classification uncertainty and cautions that standard disentanglement methods may not separate aleatoric from epistemic uncertainty.

Significance. If the central findings hold, the paper provides a practically useful, large-scale comparison of MCD and IVON on two clinically relevant PPG tasks and makes a strong case that calibration should be evaluated per class and with multiple metrics. The authors are explicit about several limitations, including the known entanglement of the regression disentanglement and the uncertainty about their own classification decomposition, which is a genuine strength. The novelty is incremental rather than foundational, but the empirical observations about hyperparameter sensitivity and adaptive calibration are valuable for practitioners building uncertainty-aware wearable-health models. The main contributions that would survive scrutiny are the evaluation protocol and the specific empirical comparisons; the compositional and generalization claims need additional support before they can be accepted.

major comments (3)
  1. [§3.4.3, Table 5, §7.1, §7.3] The compositional component of the headline claim, that sampling stochasticity determines the proportion of total uncertainty that is aleatoric, rests on the disentanglement procedures in Eqs. (3)-(4) and Algorithm 3, but these procedures are never validated against ground-truth aleatoric and epistemic components. The manuscript itself reports high Pearson correlations between the estimated components (0.72-0.81 in Table 5), states in §7.3 that "without verifying our method for disentangling uncertainties, we cannot be certain that the observed increases in our predicted epistemic uncertainty is truly epistemic uncertainty," and concludes in §7.1 that the estimates are "likely not completely disentangled." Because the classification decomposition in Algorithm 3 is a new construct and its interpretation as pure aleatoric uncertainty is not established, the composition results should be presented as properties of the decomposition formulas rather than as properties of the models unless a synthetic or otherwise ground-truth benchmark is provided.
  2. [§4.2, Table 2] The VitalDB blood pressure evaluation uses the same 1,293 patients in the training, validation, and test splits, as stated in §4.2 and Table 2. The BP regression performance and calibration numbers in Tables 3-4 and Fig. 2 therefore do not measure generalization to previously unseen patients; the text in §4.2 acknowledges this overlap, but Section 1's general framing about "poor generalisation to previously unseen test data" and the clinical motivation imply a generalization claim. Because within-patient correlation can inflate apparent performance and calibration, the authors should either add a patient-disjoint evaluation or explicitly reframe the BP results as describing a patient-specific calibration scenario.
  3. [Tables 3-9] All reported comparisons are single training/evaluation runs without repeated seeds, confidence intervals, or other variance estimates. Several differences that support the paper's central message are small in magnitude, such as the AF MCD AUC of 0.84 vs. 0.85 and F1 of 0.70 vs. 0.72 in Table 6, and the IVON total ECE of 0.073 vs. 0.074 in Table 9. Without repeated runs or interval estimates, the claim that hyperparameters have a "considerable effect" on predictive performance and calibration is not quantitatively supported for these close comparisons. At minimum, the key configurations should be repeated over multiple seeds and reported as means with standard deviations or confidence intervals.
minor comments (4)
  1. [Throughout] There are numerous typographical errors, including "sigificant" in §1.1, "a a single" in §1, "uncertainies" in §3.2.1, and "incompatable" in §6; a careful proofreading pass is needed.
  2. [§3.2.2, Algorithm 3] The entropy operator H is used in Algorithm 3 and Eqs. (5)-(6) but is not defined until after the algorithm; it would be clearer to define it immediately before the algorithm.
  3. [Figure 2] Several axis labels in Figure 2 are truncated or missing symbols, such as "DBP: vs. Error" and "Predicted " with no variance symbol shown; these should be corrected for readability.
  4. [§6.1] The decision not to train IVON on the BP regression task is explained, but the phrase "given our interest in comparing calibration quality... for similar model architectures" is a bit confusing because no IVON regression comparison is presented; consider clarifying that the comparison applies only to classification.

Circularity Check

2 steps flagged · score 6.0 of 10

The paper's headline composition-of-uncertainty claims reduce to its own entropy and variance decompositions; the calibration and performance findings remain empirical and non-circular.

  1. self definitional [Section 3.2.2, Algorithm 3 and Eqs. (5)-(6); Results Section 7.3]
    "Hale = 1/K Σ H(¯pk) ... Htotal = H( 1/K Σ ¯pk). We note that Hale ≤ Htotal due to the concavity of the entropy function. ... The use of a higher dropout rate increases the proportion of the total uncertainty that is epistemic."

    Under the paper's definitions, the quantity called epistemic uncertainty is Htotal - Hale, which is exactly the Jensen gap H(E[p]) - E[H(p)]. Increasing the dropout rate makes the per-pass probability vectors more variable, and Jensen's inequality mechanically increases this gap. Thus the abstract's statement that 'the stochasticity of the model parameter sampling determines the proportion of the total uncertainty that is aleatoric' is a mathematical consequence of the chosen decomposition, not an independently validated empirical property of the model's uncertainty sources.

  2. self definitional [Section 3.2.1, Eqs. (3)-(4); Results Section 7.1 and Table 5]
    "the law of total variance can be applied to disentangle the uncertainties, where the epistemic uncertainty can be evaluated by computing the variance of the predicted means ... These results suggest that our own estimates are likely not completely disentangled."

    In Eqs. (3)-(4), epistemic uncertainty is defined as the variance of predicted means across dropout passes and aleatoric uncertainty as the mean of the predicted variances; total variance is their sum. The dropout rate directly controls the magnitude of between-pass variation, so the finding that larger dropout rates make a larger share of total variance 'epistemic' is a restatement of the variance decomposition rather than a validated measurement of two independent sources. The paper's Section 7.1 explicitly warns that the disentangled estimates are 'likely not completely disentangled.' Hence the regression composition claim, like the classification one, is a definitional property of the formulas and the dropout mechanism, not an independent empirical result.

full rationale

The paper's strongest non-circular contributions are its empirical evaluations: predictive performance metrics, error-based calibration metrics (ECE, UCE, ENCE, CCE), per-class calibration curves, and the conclusion that greater sampling stochasticity improves ECE in the studied classification models. These are assessed against held-out labels and do not fit constants to the target conclusions, so they are not circular. The circularity arises specifically in the prominently featured composition-of-uncertainty claims. The classification disentanglement in Algorithm 3 / Eqs. (5)-(6) defines aleatoric and epistemic components via an entropy decomposition, making the observed dependence on dropout rate an algebraic outcome of Jensen's inequality. The regression disentanglement in Eqs. (3)-(4) is the standard law-of-total-variance decomposition, and the observed dependence on dropout rate is likewise built into the formulas. In both cases the paper itself flags the missing validation: Section 7.1 says the estimates are 'likely not completely disentangled,' and Section 7.3 says 'without verifying our method for disentangling uncertainties, we cannot be certain that the observed increases in our predicted epistemic uncertainty is truly epistemic uncertainty.' These admissions are weighed in the verdict and confirm that the composition claims are not independently established. Self-citations, including the use of the authors' own benchmark paper [62] for dataset splits, are not load-bearing in a circular sense: the splits are external data-processing choices, and the main hyperparameter sensitivity and calibration comparisons would stand or fall on their own experimental evidence. Overall, the abstract and conclusion give substantial weight to a composition claim that reduces by construction to the chosen decompositions, warranting a partial-circularity score of 6 rather than a clean bill.

Assumptions & free parameters 5 free parameters · 5 assumptions · 1 invented entities

Most free parameters are standard training hyperparameters; the load-bearing swept parameters are the MCD dropout rate and IVON Hessian initialisation, which the paper explicitly links to uncertainty composition. The main unvalidated construct is the classification entropy decomposition, which the authors flag as uncertain. No physical entities are introduced.

free parameters (5)
  • MCD dropout rate (AF classification) = 5%, 10%, 40%
    Swept hyperparameter that controls stochasticity at training and evaluation; central to the paper's main finding on uncertainty composition and calibration.
  • MCD dropout rate (BP regression) = 1%, 5%, 40%
    Swept across three values; changes predictive MAE and the epistemic share of total variance.
  • IVON Hessian initialisation h0 = 0.001, 0.01, 0.5
    Swept for AF classification; controls posterior concentration and thus the stochasticity of parameter sampling.
  • Monte Carlo evaluation sizes K, T, J = K=100 (classification), K=50 (regression), T=100, J=100 at test and 60 at training for IVON
    Chosen for computational feasibility; the uncertainty estimates are Monte Carlo averages and depend on these choices.
  • Optimisation hyperparameters = Learning rates 1e-3 (MCD SGD), 2e-2 (IVON), 5e-5 (BP Adam); weight decay 1e-10 or 1e-8; batch size 64 or 128; momentum…
    Set by hand and not the focus of the sweep, but they co-determine predictive performance and calibration in all reported models.
assumptions (5)
  • domain assumption PPG time series contain learnable information for AF detection and blood pressure estimation
    Used throughout Sections 5 and 6 as the basis for the prediction tasks; supported by cited medical literature but not re-derived in this paper.
  • domain assumption The likelihood models are adequate: categorical distribution for AF logits and heteroscedastic Gaussian for SBP and DBP
    The training losses in Algorithms 2 and 4 and in Section 6.1 assume these distributions; the paper does not test other likelihood choices.
  • domain assumption Dropout and IVON sampling provide useful approximations to Bayesian posterior predictive distributions
    MCD relies on Gal and Ghahramani's approximation and IVON relies on Shen et al.; the paper adopts both as given.
  • domain assumption The test labels, clinical AF labels and ICU blood pressure measurements, are accurate enough to serve as calibration ground truth
    Calibration metrics in Section 3.4 compare predicted uncertainties against these labels without modeling label noise.
  • ad hoc to paper The entropy-based decomposition H_ale = mean H(p_k) and H_total = H(mean p_k) separates aleatoric from epistemic uncertainty
    Presented as a novel method in Section 3.2.2 and Algorithm 3; the authors later acknowledge that disentanglement may not be reliable (Section 8), so this is an unvalidated paper-specific construct.
invented entities (1)
  • Classification aleatoric and epistemic entropy decomposition (H_ale, H_total)
    purpose: To express and disentangle uncertainties in AF classification outputs without a regression variance head.
    Claimed novel in Section 3.2.2 but not validated against any external oracle; the paper itself cautions that disentangled uncertainties may be correlated and should be interpreted with care (Sections 7.1 and 8).

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Cite this review

Pith. "Pith review of Uncertainty quantification with approximate variational learning for wearable photoplethysmography prediction tasks." pith.science (2026). https://pith.science/paper/UZES6TRO

@misc{pith2026250511412,
  author       = {Pith},
  title        = {Pith review of: Uncertainty quantification with approximate variational learning for wearable photoplethysmography prediction tasks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UZES6TRO}},
  note         = {Machine review of arXiv:2505.11412}
}
read the original abstract

Photoplethysmography (PPG) signals encode information about relative changes in blood volume that can be used to assess various aspects of cardiac health non-invasively, e.g.\ to detect atrial fibrillation (AF) or predict blood pressure (BP). Deep networks are well-equipped to handle the large quantities of data acquired from wearable measurement devices. However, they lack interpretability and are prone to overfitting, leaving considerable risk for poor performance on unseen data and misdiagnosis. Here, we describe the use of two scalable uncertainty quantification techniques: Monte Carlo Dropout and the recently proposed Improved Variational Online Newton. These techniques are used to assess the trustworthiness of models trained to perform AF classification and BP regression from raw PPG time series. We find that the choice of hyperparameters has a considerable effect on the predictive performance of the models and on the quality and composition of predicted uncertainties. E.g. the stochasticity of the model parameter sampling determines the proportion of the total uncertainty that is aleatoric, and has varying effects on predictive performance and calibration quality dependent on the chosen uncertainty quantification technique and the chosen expression of uncertainty. We find significant discrepancy in the quality of uncertainties over the predicted classes, emphasising the need for a thorough evaluation protocol that assesses local and adaptive calibration. This work suggests that the choice of hyperparameters must be carefully tuned to balance predictive performance and calibration quality, and that the optimal parameterisation may vary depending on the chosen expression of uncertainty.

Figures

Figures reproduced from arXiv: 2505.11412 by the authors.

Figure 1
Figure 1. Distributions of ground truth blood pressure (BP) values in the a) training set, b) validation set, and c) test set. [PITH_FULL_IMAGE:figures/full_fig_p013_1.png] view at source ↗
Figure 2
Figure 2. Evaluation of uncertainty calibration for blood pressure (BP) regression models trained with Monte Carlo [PITH_FULL_IMAGE:figures/full_fig_p016_2.png] view at source ↗
Figure 3
Figure 3. Uncertainty disentanglement for blood pressure (BP) regression models trained with Monte Carlo Dropout [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Evaluation of uncertainty calibration for Atrial Fibrillation (AF) classification models trained with Monte [PITH_FULL_IMAGE:figures/full_fig_p019_4.png]
Figure 5
Figure 5. Figure 5: Evaluation of uncertainty calibration for Atrial Fibrillation (AF) classification models trained with IVON. [PITH_FULL_IMAGE:figures/full_fig_p020_5.png]

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.