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REVIEW 4 major objections 5 minor 74 references

Scalable Modeling of Spatiotemporal Data using the Variational Autoencoder: an Application in Glaucoma

T0 review · 4 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A variational autoencoder trained on thousands of visual fields predicts future glaucoma damage more accurately than classical spatiotemporal models, especially when only a few baseline visits are available.

desk verdict Useful VAE-based visual-field forecasting with a real held-out evaluation; the unvalidated linear latent trajectory is the main thing to fix before endorsing the clinical claim. read the letter →

arxiv 1908.09195 v1 pith:FT2X5FKT submitted 2019-08-24 stat.AP stat.ML

Samuel I. Berchuck , Felipe A. Medeiros , Sayan Mukherjee This is my paper · ORCID
classification stat.APstat.ML MSC 62P10
keywords variationalautoencoderspatiotemporalmodelingglaucomaprogressionvisualfieldsdeepgenerativemodelscalablespatialstatisticsprediction
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 tries to show that a variational autoencoder (VAE) can serve as a scalable method for modeling large collections of spatiotemporal data, and that it predicts future visual fields in glaucoma more accurately than a classical spatiotemporal model or pointwise regression. The proposed two-stage procedure first trains a VAE on all visual fields as independent images to learn an eight-dimensional latent representation of the visual field, then fits a separate linear regression in time to each latent dimension and decodes the predicted latent point back into a visual-field image. The claim matters because glaucoma care often requires forecasting how a patient's vision will worsen from only a few early examinations. The paper reports that the VAE's advantage grows when fewer baseline visits are used and predictions reach further into the future, and is most pronounced in glaucoma patients.

What carries the argument

The central object is a two-stage variational autoencoder. Stage one uses a convolutional encoder that maps each padded 12-by-12 visual field to an eight-dimensional latent vector, with maximum mean discrepancy as the regularization loss and a decoder that returns a de-noised reconstruction; it treats every visual field in the training cohort as an independent image. Stage two models each latent dimension separately as a linear function of visit number, extrapolates to a future visit, and feeds the predicted latent vector through the decoder to produce a predicted visual field. The mechanism that carries the argument is the generative decoder: because the latent space is trained on the full cohort, the decoder turns a modest extrapolation in latent coordinates into a smoothed spatial image that borrows the spatial structure learned from thousands of fields.

What would settle it

If a reader re-runs the case study and splits test patients according to whether their latent-coordinate trajectories curve (e.g., sudden worsening after stable years), the central claim would fail if mean absolute prediction error is substantially higher for those patients than for linear progressors. A sharper version: replace the independent linear regressions with a latent autoregressive model trained on sequences; if the sequence model beats the two-stage VAE on the same test set, the independence assumption is the bottleneck.

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Extended reading notes

Core claim

The central claim is that the two-stage VAE provides more accurate predictions of future visual fields than a patient-level spatiotemporal autoregressive model and pointwise linear regression, particularly when only three to five baseline visits are available. In a cohort of 3,832 eyes with 29,161 visual fields, the VAE was trained jointly on all fields, projected each field into eight latent dimensions, and extrapolated each dimension with an independent linear regression; decoding the extrapolated latent point produced a de-noised predicted field. Across simulation settings generated from three different data-generating processes, the VAE with sufficiently large training data had consistently lower mean absolute prediction error than the spatiotemporal and pointwise baselines, even when the data were generated by the spatiotemporal model itself. In the clinical case study, the VAE predicted five future visits from the third, fifth, or eighth visit with lower MAE than both comparators, and the gap widened for glaucoma-only patients.

Load-bearing premise

The load-bearing premise is that treating every visual field as an independent training image, then extrapolating each of the eight latent coordinates with a straight line in time, yields future latent positions whose decoded images match how glaucoma actually progresses.

Editorial extensions

If this is right

  • With at least one thousand training samples, the VAE predicts three future visits accurately even when the data were generated by a spatiotemporal process, a pointwise process, or the VAE itself; the classical spatiotemporal model predicts well only in its own generative setting.
  • Using three baseline visits, the VAE's prediction advantage over both comparators grows for longer forecasting horizons, so early clinical decisions could be supported by generative forecasts from minimal follow-up.
  • The decoded predictions are deliberately de-noised: the VAE strips spatial variability from the raw field before forecasting, so predicted images represent the underlying progression pattern rather than visit-specific noise.
  • The latent space separates healthy, suspect, and glaucoma eyes, and movement through the space corresponds to worsening in particular visual-field regions, which makes the prediction mechanism interpretable rather than a black box.

Reading between the lines

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

  • A direct test of the linear-trajectory assumption: split patients by whether their observed latent paths are approximately linear, and compare VAE prediction error in the two groups; if nonlinear progressors are systematically worse, a latent autoregressive or recurrent stage would be needed.
  • The two-stage template should transfer to other longitudinal imaging biomarkers (e.g., retinal layer thickness maps or brain MRI morphometry), but the required training cohort size and latent dimension would need recalibration.
  • Because the VAE is trained on the full cohort, its extrapolation assumes that future disease patterns resemble patterns already present in training; cohorts with rare fast-progressing phenotypes may require targeted augmentation or patient-specific fine-tuning.
  • If temporal dependence in the latent space matters beyond linear trends, a single-stage temporal VAE trained on sequences could improve both clustering of disease trajectories and forecast accuracy; the paper's current design cannot detect that failure.
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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

4 major / 5 minor

Summary. The paper proposes a two-stage variational autoencoder (VAE) pipeline for spatiotemporal image data with a large number of subjects. Stage one trains a VAE on all images as independent samples, using an MMD regularizer, a deterministic encoder, and a decoder with constant variance, yielding an 8-dimensional latent representation of 12x12 visual fields. Stage two fits independent linear regressions over time for each latent dimension separately, extrapolates each patient's latent trajectory, and decodes the predicted latent vector to obtain a predicted visual field. The authors compare this approach with a classical spatiotemporal model (Rushworth et al., 2014) and pointwise regression in a simulation study and on 29,161 visual fields from 3,832 eyes, reporting lower mean absolute error (MAE) for the VAE, especially when few baseline visits are used to predict several future visits and in patients with glaucoma.

Significance. If the predictive gains hold up, the paper offers a computationally scalable and clinically relevant alternative for monitoring glaucoma progression, and the two-stage recipe is simple enough to be ported to other large imaging cohorts. The manuscript's strengths are the patient-level train/validation/test split, the large real dataset, the availability of R code, and the explicit focus on forecasting rather than reconstruction. The held-out case study is the most credible piece of evidence. However, the simulation component is weakened by a circular data-generating design, and the second-stage temporal model is asserted rather than validated; these gaps need to be closed before the central claim can be accepted.

major comments (4)
  1. [Section 4, Simulation Study] The simulation's VAE data generating process uses the encoder and decoder trained on the Section 5 visual field data, and the VAE variants are then trained on data simulated from that same process. This makes the VAE's good simulation performance partly self-fulfilling and does not provide evidence about robustness to misspecification. The authors should either replace this DGP with one that is independent of the evaluated model, or explicitly add misspecified DGPs (e.g., nonlinear latent trajectories, cross-dimension coupling) and report whether the VAE advantage persists.
  2. [Section 3.5, A Two-Stage Approach] The claim that independent linear regressions per latent dimension 'proves sufficient' is not supported by any diagnostics. Because the final prediction is the decoded image at an extrapolated latent point, biased latent extrapolations would directly produce biased image predictions; with T=3 baseline visits each latent regression has one residual degree of freedom, and 5-step-ahead forecasts amplify slope error by the horizon. The authors should provide residual diagnostics for the latent regressions, check cross-dimension residual correlations, compare against an AR or multivariate alternative, and report latent-space prediction error on held-out patients. Without this, the few-visit advantage could be an artifact of the smoothing decoder rather than evidence of faithful latent dynamics.
  3. [Section 5, VAE in Glaucoma: A Clinical Impact] The latent dimension is a key user-specified parameter, yet it is fixed at eight based on the authors' own prior work (Berchuck et al., 2019a) without sensitivity analysis. The paper should report whether the MAE comparisons and qualitative conclusions are stable across a range of latent dimensions (e.g., 4, 8, 16), or at least justify why a dimension optimized for a related estimation task transfers to the forecasting task studied here.
  4. [Section 5, Prediction results (Figure 6)] The case study's central claim is based on visual inspection of MAE boxplots; no formal comparison is provided, such as paired differences with confidence intervals or multiplicity-adjusted tests across horizons. Given the correlated, repeated-measures structure of the data, the authors should quantify the differences and their uncertainty, and report the number of patients contributing to each cell in Figure 6.
minor comments (5)
  1. [Section 3.4, Equation (3.6)] The Gaussian kernel is written as k(x,x') = exp{|x-x'|/(2 tau^2)}; this should be exp(-||x-x'||^2/(2 tau^2)), with the squared norm and the negative sign.
  2. [Sections 3.2-3.3] The notation for the approximate posterior is inconsistent: Equation (3.5) uses q_phi(z|x_i), while the surrounding text sometimes writes q_phi(x|z); please unify the notation.
  3. [Section 2, Assumptions for Modeling Visual Fields] There is a duplicated phrase 'In in this study' that should be corrected.
  4. [Figure 3] The axis labels are inconsistent between the caption ('Residual Standard Error') and the panels ('Residual Standard Deviation'), and the dense point overlays make the boxplots difficult to read; please align terminology and consider separate panels or clearer legends.
  5. [General] The paper uses many abbreviations (ST, PW, VAE, TD, MD, PSD, HFA-II) without a single point of definition; a glossary or a table of abbreviations would improve readability.

Circularity Check

2 steps flagged · score 4.0 of 10

Main real-data comparison is non-circular, but the VAE simulation arm is self-referential and a key architecture hyperparameter is imported from the authors' own prior work.

  1. self definitional [Section 4, Simulation Study (VAE data-generating process; Figure 3)]
    "Finally, we simulated data from the VAE. To obtain realistic datasets, we defined the encoder and decoder using trained parameters from the data analysis of visual fields from Section 5. Then, to generate datasets we simulated latent features and used the decoder to generate the simulated longitudinal visual field objects."

    The VAE simulation arm defines its target data using the very VAE decoder that the prediction method later learns and evaluates. Test objects are decoded from the Section 5 VAE's latent generative process, and the VAE variants are trained on additional samples from the same generative family. The strong VAE performance in the 'VAE' row of Figure 3 therefore largely measures self-reconstruction of the model's own generative process, not independent predictive skill. This does not invalidate the held-out real-data comparison, but it makes the simulation-based claim that the VAE has 'robust prediction properties irrespective to the data generating mechanism' partly circular.

  2. self citation load bearing [Section 5, VAE in Glaucoma (neural network architecture paragraph)]
    "The dimension of the latent space must be user specified and was chosen to be eight based on Berchuck et al. (2019a), which showed that it is optimal for visual field data."

    The key architecture choice, an 8-dimensional latent space, is justified solely by a citation to the authors' own prior work, which at the time was an unreviewed preprint rather than an independently verified, machine-checked, or externally reproduced result. All prediction comparisons in Figure 6 are computed under this imported hyperparameter, so a component of the method's configuration is taken on the authors' own authority. This is load-bearing self-citation, although the central test-set prediction comparison does not reduce by construction to the cited work.

full rationale

The paper's central claim is an empirical comparison on held-out test patients: VAE predictions of future visual fields are scored with MAE against observed fields, with patient-level train/test splitting, so that comparison itself is not circular. However, the simulation section contains a self-referential arm: data are generated from the Section 5 VAE's decoder, after which the VAE is trained and evaluated on data from the same generative family, so its good performance in that arm is partly built in. In addition, the latent dimension is imported from a self-cited preprint, reducing independent support for the architecture choice. The second-stage assumption that independent linear regressions in latent space suffice is asserted without diagnostics, but that is a model-misspecification concern rather than circularity. Overall the central real-data result stands on its own, but the supporting simulation and hyperparameter justification are partially circular, giving a score of 4.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central claim rests on a standard VAE foundation, plus several domain assumptions: independence of images during training (explicitly acknowledged), linearity of latent trajectories (asserted without evidence), representativeness of one classical ST model, and a self-referential simulation DGP. Free parameters include the latent dimension (from self-cited prior work) and unreported MMD bandwidth and decoder variance.

free parameters (3)
  • Latent dimension l = 8
    Set from self-cited prior work (Berchuck et al. 2019a) and not re-validated here; the prediction results depend on this dimension (Section 5).
  • MMD Gaussian kernel bandwidth tau^2 = Not reported
    Section 3.4 calls tau^2 a fixed tuning parameter but does not state its value; the regularization loss depends on it.
  • Decoder variance sigma^2 = Not reported
    Section 3.4 fixes p_theta(x|z) to N(mu_theta(z), sigma^2 I) but does not report sigma^2; it scales the reconstruction loss.
assumptions (5)
  • standard math Standard variational autoencoder machinery: ELBO, reparameterization trick, and MMD as a distribution matching objective are valid for learning the latent space.
    Sections 3.2-3.4 rely on these established results from Kingma and Welling (2013), Rezende et al. (2014), and Zhao et al. (2017a).
  • domain assumption Treating all images as independent during VAE training is acceptable for downstream longitudinal prediction.
    The authors state in Section 3.2 that independence across images 'is necessary in the VAE' and acknowledge in the Discussion that this is a limitation.
  • ad hoc to paper Latent trajectories can be modeled with independent linear regressions per latent dimension.
    Section 3.5 asserts 'we have found that independent linear regressions across each latent dimension proves sufficient' without reporting a comparison to alternative longitudinal models.
  • domain assumption The Rushworth et al. (2014) multivariate AR model with Leroux CAR prior is representative of classical ST methods for the purpose of comparison.
    The simulation and case study use only this ST model as the classical counterpart; other scalable or joint ST models are not benchmarked.
  • ad hoc to paper Simulated VAE datasets generated from the Section 5 trained VAE are representative of real glaucoma progression for method validation.
    Section 4 says 'we defined the encoder and decoder using trained parameters from the data analysis of visual fields from Section 5'; this self-referential setup limits the independence of the simulation evidence.

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Cite this review

Pith. "Pith review of Scalable Modeling of Spatiotemporal Data using the Variational Autoencoder: an Application in Glaucoma." pith.science (2026). https://pith.science/paper/FT2X5FKT

@misc{pith2026190809195,
  author       = {Pith},
  title        = {Pith review of: Scalable Modeling of Spatiotemporal Data using the Variational Autoencoder: an Application in Glaucoma},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FT2X5FKT}},
  note         = {Machine review of arXiv:1908.09195}
}
read the original abstract

As big spatial data becomes increasingly prevalent, classical spatiotemporal (ST) methods often do not scale well. While methods have been developed to account for high-dimensional spatial objects, the setting where there are exceedingly large samples of spatial observations has had less attention. The variational autoencoder (VAE), an unsupervised generative model based on deep learning and approximate Bayesian inference, fills this void using a latent variable specification that is inferred jointly across the large number of samples. In this manuscript, we compare the performance of the VAE with a more classical ST method when analyzing longitudinal visual fields from a large cohort of patients in a prospective glaucoma study. Through simulation and a case study, we demonstrate that the VAE is a scalable method for analyzing ST data, when the goal is to obtain accurate predictions. R code to implement the VAE can be found on GitHub: https://github.com/berchuck/vaeST.

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.