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REVIEW 3 major objections 6 minor 40 references

Fundus Image-based Visual Acuity Assessment with PAC-Guarantees

T0 review · 3 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Fundus-image AI can give visual-acuity estimates a PAC coverage guarantee.

desk verdict A clean, modest first application of PAC prediction intervals to VA screening, but the missing patient-level split detail leaves the central empirical claim under-specified. read the letter →

arxiv 2412.06624 v1 pith:PLTF6W6O submitted 2024-12-09 eess.IV cs.AIcs.CV

Sooyong Jang , Kuk Jin Jang , Hyonyoung Choi , Yong-Seop Han , Seongjin Lee , Jin-hyun Kim , Insup Lee This is my paper · ORCID
classification eess.IVcs.AIcs.CV
keywords VisualAcuityPredictionFundusImagesIntervalsPACGuaranteesUncertaintyQuantificationClopper-PearsonGaussianRegression
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

The paper sets out to give visual acuity (VA) predictions from fundus images a formal reliability certificate: instead of a single point estimate, the model outputs an interval that contains the true VA with probability at least $1-\epsilon$, with high confidence $1-\delta$. The proposed method trains a regressor whose output is a Gaussian distribution (mean and standard deviation), then calibrates one width multiplier $c$ on a validation set so that the interval $[f_\mu(x) - c f_\sigma(x), f_\mu(x) + c f_\sigma(x)]$ satisfies the PAC guarantee of Eq. (1). On a 54,781-image fundus dataset with VA labels 0–10, the method empirically meets the coverage bound for $\epsilon=0.2$, $0.3$, $0.4$ across four architectures, with the narrowest average width 3.04 at $\epsilon=0.3$ (EfficientNetV2-S). The practical payoff is that screening tools could hand clinicians intervals with a stated long-run coverage rate, something prior VA prediction models did not offer.

What carries the argument

The load-bearing object is the Gaussian-parameterized regressor: $f(x) = (f_\mu(x), f_\sigma(x))$, trained with negative log-likelihood loss. The standard deviation output $f_\sigma(x)$ sets the per-example interval half-width, so the interval is $C_c(x) = f_\mu(x) \pm c f_\sigma(x)$. The calibration constant $c$ is chosen by solving $\min c$ subject to the condition that the Clopper-Pearson lower confidence bound for the coverage of $C_c$ on the validation set is at least $1-\epsilon$ at significance $\delta$; this one step is what confers the PAC guarantee.

What would settle it

Draw a fresh iid validation and test split from the same source and repeat the calibration 1,000 times; if the empirical coverage is below $1-\epsilon$ in a fraction of repetitions much larger than $\delta$, the Clopper-Pearson calibration is not delivering the stated guarantee. Alternatively, take the exact pipeline and evaluate on fundus images from a different device or with Gaussian blur kernel size 9 as in the paper; the coverage falling below the bound in that setting would falsify any claim that the guarantee survives distribution shift.

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Extended reading notes

Core claim

The paper's central claim is that a regression model for visual acuity, trained to output both a mean and a standard deviation, can be converted into a PAC prediction interval $C_c(x) = [f_\mu(x) - c f_\sigma(x), f_\mu(x) + c f_\sigma(x)]$ by choosing the scalar $c$ through a Clopper-Pearson binomial confidence bound on a validation set (at significance $\delta$). The authors report that on the fundus dataset, the empirical coverage stays above the target bound $1-\epsilon$ for all tested architectures and values of $\epsilon$, with EfficientNetV2-S achieving average width 3.04 at a 70% coverage target. They further report performance comparable to or better than two earlier VA prediction studies that provide no guarantees, and they show that interval width adapts to the model's estimated per-example uncertainty.

Load-bearing premise

The guarantee is only as good as the assumption that the validation set used to pick the width multiplier and the test images are exchangeable draws from the same distribution; if deployment data is shifted (different camera, different population, degraded images), coverage can fall below the bound, as the paper's own blur experiment with kernel sizes 7 and 9 shows.

Editorial extensions

If this is right

  • With a PAC guarantee in place, a clinician can state that the true VA lies inside the reported interval with a known minimum long-run probability, rather than relying on an unguaranteed point estimate.
  • Interval widths are example-dependent: images the model is unsure about receive wider intervals, which is a step toward flagging low-quality or atypical images.
  • The method reaches comparable or better point-estimate performance than prior VA prediction models while adding the coverage guarantee.
  • Because the guarantee is conditional on exchangeability, deployment requires monitoring for dataset shift; the paper's blur experiment shows coverage can drop below the bound when that condition is violated.
  • The same PAC calibration procedure is proposed by the authors for downstream classification tasks such as diabetic retinopathy and glaucoma detection.

Reading between the lines

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

  • The calibration step is agnostic to the base architecture, so the same pipeline could be dropped onto stronger backbones (e.g., EfficientNetV2-L or retinal foundation models) that the paper names as future work, potentially shrinking widths while preserving the guarantee.
  • Because the interval width scales linearly with the predicted standard deviation, the method implicitly treats 'hard' images (blurry, or from underrepresented acuity classes) as higher-uncertainty; a direct test would be to check whether the coverage gap between the guaranteed bound and empirical coverage widens for the minority classes.
  • The paper's robustness result under mild blur (kernel size up to 5) suggests that the method may tolerate mild distribution shift, but the sharp failure at kernel sizes 7–9 indicates a natural safety threshold that deployment systems could detect and act on.
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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 / 6 minor

Summary. The paper proposes a method for constructing prediction intervals for visual acuity (VA) estimates from fundus images, using a regressor that outputs both a mean and a standard deviation, and then calibrating a width multiplier c on a validation set via a Clopper-Pearson-based PAC bound. The central claim, expressed in Eq. (1), is that the interval C_c(x) = [f_mu(x) - c f_sigma(x), f_mu(x) + c f_sigma(x)] satisfies a PAC coverage guarantee: with probability at least 1-delta over the validation set, the true coverage on future data from the same distribution is at least 1-epsilon. Experiments on a 54,781-image fundus dataset with four base models and five random splits report that the coverage bound is satisfied; for epsilon=0.3 and delta=0.001%, EfficientNetV2-S achieves 71.49% coverage with an average width of 3.04. The paper also compares point- and interval-level performance with Bayesian neural networks, vanilla conformal prediction, and two prior VA prediction studies.

Significance. If the central claim is accepted, the paper would provide a clinically relevant application of PAC-style uncertainty quantification to visual acuity prediction, a task where prior work offers only point predictions without guarantees. The positive aspects are that the method uses a finite-sample exact calibration tool (Clopper-Pearson), the experiments are repeated over multiple splits, the code is made available, and the authors are transparent about the degradation of coverage under severe distribution shift in Appendix B.2. The methodological novelty is limited because the PAC calibration machinery is imported from Park et al. (2019), and the paper's contribution is mainly in the application and in the empirical demonstration on a real medical dataset. However, a load-bearing detail is missing: the paper does not state whether the data split is at the image level or the patient level, and this determines whether the i.i.d. assumption in Eq. (1) holds. The significance of the empirical result therefore cannot be fully assessed as written.

major comments (3)
  1. [Section 4.1, Eq. (1)] The paper states that the dataset is 'randomly divided' into 6:2:2 training/validation/test splits but never specifies the sampling unit. Fundus image datasets of this size routinely contain multiple images per patient and per eye. If the split is image-level, images from the same patient can appear in all three sets, and the calibration indicators W_i = 1{y_i in C_c(x_i)} are not independent Bernoulli draws as required by the Clopper-Pearson bound used in Section 3.3. Positively correlated indicators make the binomial-based lower confidence bound anti-conservative, so the reported coverage rates, e.g., 71.49% for epsilon=0.3 in Table 2, could reflect patient leakage rather than a genuine PAC guarantee. The paper must report the number of unique patients, the number of images per patient, and results with a patient-disjoint split, or justify explicitly why image-level independence is an appropriate model for this dataset.
  2. [Section 3.3] The optimization problem defining c* is not coherent as written. The text reads 'c* = arg min_c c subject to c >= 1 - epsilon, where [c, c] is the Clopper-Pearson interval for W = {1(y_i in C_c(x_i)) | (x_i, y_i) in Z} with significance level delta.' This mixes the width multiplier c with a coverage threshold: the constraint 'c >= 1 - epsilon' does not make sense dimensionally, and the notation '[c, c]' for the Clopper-Pearson interval is undefined. The intended condition is presumably that the lower Clopper-Pearson confidence bound for the coverage of C_c on the validation set is at least 1-epsilon. The authors should restate the optimization correctly, specify the search procedure for c (e.g., grid range and step), and report the validation-set size used in the calibration. As written, Section 3.3 is not reproducible.
  3. [Section 4.5, Abstract] The abstract and conclusion claim that the proposed method is 'comparable to or better than' the two prior works (Kim et al., 2022; Paul et al., 2023). The comparison in Section 4.5 is based on different datasets, different label schemes, different evaluation metrics (macro-accuracy on a balanced test set vs. coverage on the full imbalanced test set), and the authors themselves note that 'a fair comparison is challenging.' These limitations mean the headline claim is not supported by the reported numbers. The claim should be softened to 'comparable in reported point-prediction metrics on separate datasets' or the comparisons should be made under matched conditions, such as applying the prior methods to the same data.
minor comments (6)
  1. [Section 3.3] The notation '[c, c]' should be replaced with explicit lower and upper confidence bounds, e.g., [L(c), U(c)], to avoid confusion with the width multiplier c.
  2. [Section 4.1] Please report the number of unique patients and the per-patient image count; this information is essential for assessing the validity of the i.i.d. assumption and for the reproducibility of the dataset split.
  3. [Figure 4] The red dotted line indicating the coverage bound is only drawn in the left-column plots; the right-column width plots should either include a note that no bound applies or use a different labeling to avoid implying a width bound.
  4. [Section 4.3.2] The sentence 'However, for practical usage with this 70% coverage, we require a slightly narrower width, around 2, which aligns with the variability in VA measurement by humans' is a value judgment that mixes clinical heuristics with the reported results; it could be better phrased as a clinical requirement that should be validated with domain experts.
  5. [Footnote 1] The code repository URL in the footnote contains a space ('va pred pac') and is not a clickable link in the provided text; please provide the correct and complete URL.
  6. [Section 4.5.1, Table 4] The explanation of why MA-ACC can be lower than the guaranteed coverage appears as a footnote; this caveat is important and should be moved into the main text so that readers do not misinterpret the comparison.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation found: the PAC interval is calibrated on a validation split and tested on an independent test split, with the self-cited PAC theorem serving as an external result rather than an input redefined as the target.

full rationale

The derivation chain is linear and empirically falsifiable. Section 3.2 trains a Gaussian-output regressor on the training split; Section 3.3 selects a single scalar c on the validation split using the Clopper-Pearson lower bound; Section 4.3.2 then evaluates the fixed interval C_c(x)=[f_mu(x)-c f_sigma(x), f_mu(x)+c f_sigma(x)] on a separate test split. The reported coverage, e.g. 71.49% for epsilon=0.3, is an outcome on data not used to choose c: it could have fallen below the 70% bound, and indeed Appendix B.2 shows coverage drops below the bound when Gaussian blur with kernel size 7 or 9 violates the distributional assumption. The PAC guarantee itself is imported from Park et al. (2019, 2022a), whose authorship overlaps with co-author Insup Lee; this is self-citation, but it is not circular. The cited theorem is stated with assumptions (iid draws from D) that do not include the target VA-coverage result, and the present paper does not redefine its target in terms of its own fitted values. The fitted multiplier c is calibration, not a prediction masquerading as a result. The main caveat, which is a validity/correctness concern rather than a circularity, is that Section 4.1 says the 54,781 images are 'randomly divided' without stating whether the split is by patient. If multiple images per patient appear in both calibration and test sets, the binomial/Clopper-Pearson calibration can be anti-conservative and the empirical coverage claim would not establish the PAC guarantee for the true sampling process. That concern does not make the derivation circular, so no circular step is reported.

Assumptions & free parameters 2 free parameters · 3 assumptions · 0 invented entities

The method is a pipeline of standard components: a Gaussian-output regressor, an NLL loss, and a Clopper-Pearson-calibrated width multiplier. Its load-bearing assumptions are exchangeable calibration data and validity of the cited PAC theorem. The only data-fitted constant is c. There are no invented entities.

free parameters (2)
  • interval-width multiplier c = not reported as a number; inferred from widths and f_sigma
    Selected on the validation set via Clopper-Pearson (Section 3.3). This is the main calibration parameter and determines interval width while preserving coverage.
  • network training hyperparameters (learning rate, batch size, epochs, image preprocessing) = not reported
    Hand-chosen details affecting point accuracy and interval width; the paper does not list them, so exact replication is not possible.
assumptions (3)
  • domain assumption Calibration (validation) and future test data are drawn identically and independently from the same distribution D.
    Eq. (1) defines the guarantee with Dn = D x ... x D, and Section 3.1 says the bound holds 'as long as the test data follows the same distribution D as the training and calibration data.' Section 4.6 names dataset shift as a central practical threat.
  • domain assumption The PAC interval construction of Park et al. (2019) is valid; the paper uses it without re-deriving it.
    Section 3.3 states the optimization problem and asserts the guarantee citing Park et al. (2019, 2022a). The theorem is not proved in this paper and is from the same research group (Insup Lee is a coauthor of both works).
  • domain assumption The Gaussian output f_sigma provides a useful per-example estimate of predictive uncertainty.
    Section 3.2 uses sigma to define example-dependent interval widths; Section 4.6's Figure 5 gives supporting evidence for EfficientNetV2-S on one seed, but this calibration between error and sigma is not formally guaranteed.

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Cite this review

Pith. "Pith review of Fundus Image-based Visual Acuity Assessment with PAC-Guarantees." pith.science (2026). https://pith.science/paper/PLTF6W6O

@misc{pith2026241206624,
  author       = {Pith},
  title        = {Pith review of: Fundus Image-based Visual Acuity Assessment with PAC-Guarantees},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PLTF6W6O}},
  note         = {Machine review of arXiv:2412.06624}
}
read the original abstract

Timely detection and treatment are essential for maintaining eye health. Visual acuity (VA), which measures the clarity of vision at a distance, is a crucial metric for managing eye health. Machine learning (ML) techniques have been introduced to assist in VA measurement, potentially alleviating clinicians' workloads. However, the inherent uncertainties in ML models make relying solely on them for VA prediction less than ideal. The VA prediction task involves multiple sources of uncertainty, requiring more robust approaches. A promising method is to build prediction sets or intervals rather than point estimates, offering coverage guarantees through techniques like conformal prediction and Probably Approximately Correct (PAC) prediction sets. Despite the potential, to date, these approaches have not been applied to the VA prediction task.To address this, we propose a method for deriving prediction intervals for estimating visual acuity from fundus images with a PAC guarantee. Our experimental results demonstrate that the PAC guarantees are upheld, with performance comparable to or better than that of two prior works that do not provide such guarantees.

Figures

Figures reproduced from arXiv: 2412.06624 by the authors.

Figure 1
Figure 1. Uncertainties in VA prediction: Although VA prediction is based on fundus im￾ages, the ground truth acuity measure￾ments were not obtained from these im￾ages. The VA test (e.g., using a Snellen chart) measures visual acuity, and the VA regressor estimates value measured by a human. Additionally, the human measure￾ment process itself introduces uncertainty. 1984) or to employ Conformal Prediction (Vovk et al., 2005),… view at source ↗
Figure 2
Figure 2. Overall process: First, we train a Gaussian Distribution output model with the training data. Next, we find c for the coverage bound with the validation data. Lastly, we compute the prediction intervals using the test data. 2.1. VA prediction from fundus images The Visual acuity (VA) prediction task is to estimate VA from fundus images. VA can be represented in various ways, such as a decimal number (e.g., 0.5, 1.0)… view at source ↗
Figure 3
Figure 3. MAE of models over 5 repetitions 4.2. Models We employ four different base models: Simple￾CNN, ResNet18, ResNet50 (He et al., 2016), and EfficientNetV2-S (Tan and Le, 2021). All models have the final fully connected layer with two out￾put nodes for the two Gaussian distribution param￾eters. The Simple-CNN model that we implemented comprises two convolutional layers followed by three fully connected layers. All layer… view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: PAC Guarantee Analysis Results (significance level δ = 0.001 %). The left column displays the coverage, while the right column shows the average width. In the left column figures, the red dotted line represents the coverage bound. For all ϵ and base models, our result …
Figure 5
Figure 5. Figure 5: MAE and standard deviations: Absolute errors are binned by equal mass, and aver￾age error and standard deviations are com￾puted for each bin, plotted with a 95 % confidence interval. strates better accuracy and produces narrower pre￾diction intervals compared to less c…

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.