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REVIEW 3 major objections 6 minor 52 references

How Certain are Uncertainty Estimates? Three Novel Earth Observation Datasets for Benchmarking Uncertainty Quantification in Machine Learning

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

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Pith's one-line read This paper introduces three Earth observation benchmark datasets — for regression, segmentation, and classification — that provide reference aleatoric uncertainty values, so machine-learning uncertainty estimates can be measured against a…

desk verdict A useful benchmark suite with one solid regression dataset and one over-claimed segmentation reference; deserves peer review but needs to fix the ground-truth issue. read the letter →

arxiv 2412.06451 v1 pith:MGEPC2UI submitted 2024-12-09 cs.LG cs.AIeess.IV

Yuanyuan Wang , Qian Song , Dawood Wasif , Muhammad Shahzad , Christoph Koller , Jonathan Bamber , Xiao Xiang Zhu This is my paper · ORCID
classification cs.LGcs.AIeess.IV
keywords uncertaintyquantificationearthobservationbenchmarkdatasetsaleatoricmachinelearningregressionimagesegmentationsceneclassification
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's claim is that the lack of ground-truth uncertainty labels has made it impossible to judge how reliable machine-learning uncertainty estimates are in Earth observation, and that this gap can be closed by building benchmarks where the uncertainty of the reference is known by construction. Three datasets are introduced, one per common problem type: biomass regression with controlled input noise, building segmentation rendered from 3D models with simulated image and viewpoint noise, and local climate zone classification carrying ten expert votes per patch. Each dataset comes with a reference aleatoric uncertainty — the variance of the biomass prediction, the Shannon entropy of the segmentation softmax distribution, and the distributional label — so that any UQ method can be scored against it. If the construction holds, these would be the first EO-specific datasets designed to benchmark uncertainty estimates rather than only provide labels.

What carries the argument

The machinery that carries the argument is Monte Carlo propagation of controlled input noise through a trusted reference model. In the regression dataset, the reference model is the allometric equation $B = 0.0673(\rho D^2 H)^{0.976}$ from [36], with noise-free $D$ and $H$ drawn from Gamma distributions fitted to field data; noisy input points are simulated in bulk per noise level and the variance of the output around the true biomass is smoothed into a parametric reference curve. In the segmentation dataset, the reference model is a U-Net trained on noise-free renderings whose epistemic uncertainty is assumed negligible; for each noise configuration, 50 noisy images are passed through the network, each logit is modeled as a Gaussian $z_j \sim \mathcal{N}(\mu_j, \sigma_j^2)$, Monte Carlo samples of the logits are pushed through softmax, and the Shannon entropy of the resulting probability distribution is averaged over pixels and classes to give a single reference aleatoric entropy value per patch. In the classification dataset, the reference uncertainty is the distributional label $\mathbf{y}_{\text{distr}} = \mathbf{Y}/M$ formed from $M$ expert votes, and training with a KL-divergence loss against this distribution is the demonstrated use.

What would settle it

Train an ensemble of, say, ten U-Nets with different initializations on the same clean segmentation renderings and feed the same 50 noisy samples through each; if the reference aleatoric entropies differ materially across ensemble members, the single-network assumption fails and the reference conflates epistemic with aleatoric uncertainty.

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Extended reading notes

Core claim

The central claim is that reference aleatoric uncertainty can be constructed for three common Earth observation problem types by controlling the noise source. For regression, a published allometric equation for tropical-tree biomass is declared the ground-truth physical model, Gaussian noise with a known signal-to-noise ratio is added to tree height and diameter, and the variance of the equation output around the true biomass is taken as the reference uncertainty. For segmentation, noise-free baseline images are rendered from high-quality 3D building models, then Gaussian noise, Poisson noise, and camera-viewpoint variation are simulated; a baseline U-Net trained on the clean data is fed the noisy renderings, each logit is modeled as a Gaussian estimated from the 50 noisy samples, and the Shannon entropy of the resulting softmax distribution is the reference aleatoric entropy. For classification, ten remote-sensing-expert votes per image patch are turned into a distributional label that captures irreducible human label uncertainty. The authors demonstrate the benchmarks by comparing two regression UQ methods and two segmentation UQ methods against the references, and by showing that training an LCZ classifier on distributional labels roughly halves its expected calibration error.

Load-bearing premise

The load-bearing premise is that the reference model is accurate enough to isolate aleatoric uncertainty: the allometric equation is treated as the true physical relationship in regression, and a single well-trained U-Net is assumed to have negligible epistemic uncertainty in segmentation.

Editorial extensions

If this is right

  • Any UQ method can now be ranked by R² and RMSE against a per-patch reference uncertainty, instead of only by internal consistency or calibration.
  • The benchmarks show that aleatoric and epistemic uncertainties are not cleanly separable in practice: enlarging the regression training set from ×1 to ×16 improves the aleatoric-uncertainty score, implying residual epistemic contamination.
  • SegmentationUQ's 6 million patches enable isolating how different noise types with the same IoU affect measured uncertainty, not just prediction quality.
  • Using distributional labels from expert votes roughly halves expected calibration error on the LCZ classification task, indicating that human label uncertainty is a learnable signal rather than pure noise.

Reading between the lines

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

  • Outside the paper's scope, the segmentation reference could be stress-tested by using an ensemble of clean-trained U-Nets; the spread of reference entropies across ensemble members would directly bound how much epistemic uncertainty leaks into the 'aleatoric' benchmark.
  • The same Monte-Carlo-through-a-forward-model recipe transfers to other EO tasks with a known physical model, such as radiative-transfer-based retrievals, where the hard part is identifying a trustworthy reference model rather than generating noise.
  • The classification dataset's multiple votes could be used to benchmark label-noise-robust training methods beyond the demonstrated KL-divergence objective, giving a common testbed for a question the paper only touches 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 three Earth observation (EO) benchmark datasets for uncertainty quantification (UQ): RegressionUQ, a simulated single-tree biomass regression dataset in which the ground-truth label and reference aleatoric uncertainty are derived from the Chave allometric equation; SegmentationUQ, a rendered building segmentation dataset with simulated Gaussian, Poisson, and viewpoint noise, where a reference aleatoric entropy is computed by propagating noisy images through a trained U-Net; and ClassificationUQ, an extension of So2Sat LCZ42 with ten expert votes per image patch, converted into distributional labels. The authors describe data generation, reference uncertainty calculation, and demonstration experiments: two UQ methods on RegressionUQ, two UQ methods on SegmentationUQ, and a distributional-label training approach on ClassificationUQ. The central claim is that these are the first EO-specific benchmarks providing reference aleatoric uncertainty.

Significance. If the reference uncertainties are valid, the three datasets fill a genuine gap: existing EO benchmarks provide labels but no ground-truth uncertainty, making it impossible to score UQ methods objectively. The regression reference is anchored in an explicit physical equation and propagated via Monte Carlo simulation, which is a reproducible, parameter-free approach; the classification reference is anchored in external human votes, giving an independent measure of label ambiguity. The segmentation reference is the weakest link because it substitutes a learned surrogate for a physical ground-truth model. The paper also ships datasets and code, which supports community adoption. However, the validity of the segmentation benchmark is load-bearing for the paper's headline claim, and the current evidence for it is an unexamined belief rather than a verified property.

major comments (3)
  1. [III-B3 and V] The SegmentationUQ reference aleatoric entropy rests entirely on a single trained U-Net used as a ground-truth model. In Section III-B3 the authors write 'We believe the epistemic uncertainty of such model is minimized', and in Section V they concede that 'an inaccurate model causes the conflation of aleatoric and epistemic uncertainties, which was observed in both the experiments'. This is a direct admission that the reference may not isolate aleatoric uncertainty. Because the rendering pipeline knows the true noise models and the true LoD2 masks, a physically grounded reference is in principle available; the paper should either construct such a reference or validate that the U-Net-based reference is stable under changes in network architecture, random seed, and training set size. Without this, a UQ method benchmarked on SegmentationUQ is being scored on how well it reproduces the specific U-Net's noise sensitivity, not on how well it captures irreducible data uncertainty.
  2. [II-B3] The definition of the RegressionUQ reference is ambiguous. The text says that because a neural network is trained on pooled noisy data, 'a realistic reference aleatoric uncertainty from a neural network shall also be calculated from the pooled distribution', but the implementation uses '800 neighboring points' per input and a smoothing curve. It is unclear whether the reference is the local conditional variance Var(f(ρ,D,H) | D0,H0) for a clean input, or the variance of the mixture of outputs over the noisy training distribution, or something else. The estimand matters because each test sample receives a single reference value that is compared against the model's prediction. Please state the exact quantity being estimated, how the neighboring points are selected, and how the smoothing curve is fitted, and provide a Monte Carlo error estimate for the reference.
  3. [IV-C and Abstract] The abstract presents ClassificationUQ as one of three benchmarks for UQ, but the demonstration in Section IV-C is a training-time comparison of distributional-label learning against one-hot learning (accuracy, cross-entropy, ECE); no UQ method is benchmarked against a reference uncertainty. While the vote counts do permit users to compute a reference label distribution, the paper does not provide a precomputed reference uncertainty (e.g., entropy per patch) nor an example of benchmarking a model's predictive uncertainty against it. To substantiate the 'benchmark' claim for the classification dataset, either provide such a reference and a benchmarking demonstration, or explicitly scope ClassificationUQ as a label-uncertainty resource rather than a UQ benchmark.
minor comments (6)
  1. [II-B2] Figure 2, cited in the RegressionUQ section, is labeled as 'the training/test split in the SegmentationUQ dataset', but it plots tree diameter and height samples from the regression dataset; the caption or the figure label should be corrected.
  2. [II-B3] The sentence '20, 0002 noisy input points were simulated' appears to be a typo; it should read '20,000 noisy input points'.
  3. [I-A] Section I-A contains several typos: 'segmntation', 'ans test', and 'infared' (the last in Section I-B2).
  4. [II-A] In Section II-A, 'biomass datasets generated from allometric equations are still scars' should be 'scarce'.
  5. [III-B3] In Table V, step 4, the number N of Monte Carlo samples drawn from the Gaussian logit distribution is never specified; please state the value and justify its sufficiency for low-variance entropy estimates.
  6. [IV-B] Section IV-B says 'The dataset were created'; this should be 'The dataset was created'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the benchmark references are anchored in external physical equations, rendering models, and human votes, and the segmentation-model caveat is disclosed as a limitation rather than a self-referential derivation.

full rationale

The paper's three datasets generate reference uncertainties from external anchors rather than from the methods being benchmarked. RegressionUQ propagates simulated input noise through the Chave allometric equation, an independent physical model, to obtain reference variance. ClassificationUQ uses ten expert votes per patch, an empirical human source, to form distributional labels. SegmentationUQ renders images from 3D LoD2 building models and then computes reference aleatoric entropy by feeding noisy renders through a trained U-Net; the authors explicitly rely on the belief that the model's epistemic uncertainty is minimized. This is a modeling assumption with a validity caveat, not a circularity: the reference is not defined in terms of the benchmarked methods' outputs, and no equation or fitted parameter is reused as its own target. The paper itself flags the limitation in Section V: 'An inaccurate model causes the conflation of aleatoric and epistemic uncertainties, which was observed in both the experiments for the regression and segmentation datasets.' That statement weakens the strength of the segmentation benchmark, but it is an acknowledged epistemic risk, not a logical reduction of the claimed derivation to its inputs. Self-citations, including the use of [22] for the classification demonstration, are used as external peer-reviewed support or prior experimental details, not to close a derivation loop. No circular step satisfying the required quote-and-reduction standard is present.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The regression dataset rests on fitted Gamma distributions and a fixed wood density, plus an unspecified smoothing fit; the segmentation reference rests on the authors' U-Net as ground truth and Gaussian logit assumptions; the classification reference rests on expert votes collected in prior So2Sat work. No new physical entities are introduced.

free parameters (3)
  • Gamma distribution parameters for tree height and diameter in RegressionUQ = Diameter: shape 0.68, location 5.00, scale 30.18 cm; Height: shape 1.92, location 1.18, scale 7.75 m
    Fitted to the Chave et al. allometry dataset to make simulated tree populations resemble real forests; they shape the entire synthetic regression dataset (Table I).
  • Wood density constant = 0.65
    Fixed at a typical value from the Chave dataset rather than sampled, simplifying the simulated biomass model (Section II-B1).
  • Reference uncertainty smoothing curve = unspecified parametric form
    The MC-estimated reference variance is smoothed by fitting a parametric curve between uncertainty and inputs; the functional form and fitting procedure are not stated (Section II-B3).
assumptions (6)
  • domain assumption The allometric equation B = 0.0673 (rho D^2 H)^0.976 from Chave et al. is treated as the true physical model for biomass.
    Section II-B1: used to generate labels and reference uncertainty; if the equation is wrong, the reference is wrong.
  • domain assumption Measurement noise in tree diameter and height is Gaussian with standard deviation linearly proportional to the true value (sigma = alpha * value).
    Section II-B1: defines the aleatoric uncertainty structure being benchmarked; real EO measurement noise may differ.
  • ad hoc to paper The trained U-Net on clean data has negligible epistemic uncertainty, so its logits can serve as a ground-truth model for reference aleatoric entropy.
    Section III-B3: 'We believe the epistemic uncertainty of such model is minimized'; this is asserted, not measured; the paper later admits inaccuracies cause conflation.
  • domain assumption Logits for each pixel can be modeled as Gaussian with mean and variance estimated from 50 noisy samples, and the entropy of the resulting softmax distribution is the reference uncertainty.
    Section III-B3 and Table V: the 50-sample estimate and Gaussian logit assumption are approximations whose fidelity is not quantified.
  • domain assumption The 10 expert votes per image in the LCZ evaluation set capture irreducible human labeling uncertainty.
    Section IV-B: the votes are treated as a reference distributional label; inter-expert disagreement is assumed to represent aleatoric label uncertainty.
  • ad hoc to paper The checkerboard split is a valid way to test interpolation/extrapolation behavior for the regression benchmark.
    Section II-B2: the grid choice of 5x5 is heuristic ('shall neither be too small...'); the paper gives no analysis of how this split influences measured uncertainty performance.

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Pith. "Pith review of How Certain are Uncertainty Estimates? Three Novel Earth Observation Datasets for Benchmarking Uncertainty Quantification in Machine Learning." pith.science (2026). https://pith.science/paper/MGEPC2UI

@misc{pith2026241206451,
  author       = {Pith},
  title        = {Pith review of: How Certain are Uncertainty Estimates? Three Novel Earth Observation Datasets for Benchmarking Uncertainty Quantification in Machine Learning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MGEPC2UI}},
  note         = {Machine review of arXiv:2412.06451}
}
read the original abstract

Uncertainty quantification (UQ) is essential for assessing the reliability of Earth observation (EO) products. However, the extensive use of machine learning models in EO introduces an additional layer of complexity, as those models themselves are inherently uncertain. While various UQ methods do exist for machine learning models, their performance on EO datasets remains largely unevaluated. A key challenge in the community is the absence of the ground truth for uncertainty, i.e. how certain the uncertainty estimates are, apart from the labels for the image/signal. This article fills this gap by introducing three benchmark datasets specifically designed for UQ in EO machine learning models. These datasets address three common problem types in EO: regression, image segmentation, and scene classification. They enable a transparent comparison of different UQ methods for EO machine learning models. We describe the creation and characteristics of each dataset, including data sources, preprocessing steps, and label generation, with a particular focus on calculating the reference uncertainty. We also showcase baseline performance of several machine learning models on each dataset, highlighting the utility of these benchmarks for model development and comparison. Overall, this article offers a valuable resource for researchers and practitioners working in artificial intelligence for EO, promoting a more accurate and reliable quality measure of the outputs of machine learning models. The dataset and code are accessible via https://gitlab.lrz.de/ai4eo/WG_Uncertainty.

Figures

Figures reproduced from arXiv: 2412.06451 by the authors.

Figure 1
Figure 1. Error sources of predictive uncertainty in EO with a [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. shows this training/test split in the SegmentationUQ dataset, where dark green is the training set, and light green is the test sets. The number of grids was set to 5 by 5. It shall neither be too small, which would make the training ans test too distinct, nor too large, which would render the distributions of training and test sets very similar [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. The calculation of the reference variance of the biomass [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Histograms of correlation coefficients between esti [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: A collection of sample variations of the dataset under three different noise types i.e. 3D viewpoint variation (3D [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: Exemplary reliability diagrams as shown in [22]. [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]

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Pith tools

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