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REVIEW 4 major objections 4 minor 39 references

Uncertainty separation via ensemble quantile regression

T0 review · 4 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read An ensemble of quantile regression models, combined with iterative sampling in uncertain regions, separates aleatoric from epistemic uncertainty more reliably than Deep Ensembles or Monte Carlo dropout.

desk verdict A clever but unproven heuristic for separating aleatoric and epistemic uncertainty; the idea is worth a look, but the paper as written overclaims and the algorithm has concrete bugs. read the letter →

arxiv 2412.13738 v1 pith:FRPGSO3R submitted 2024-12-18 cs.LG cs.AIcs.CE

Navid Ansari , Hans-Peter Seidel , Vahid Babaei This is my paper · ORCID
classification cs.LGcs.AIcs.CE
keywords uncertaintyquantificationaleatoricepistemicquantileregressiondeepensemblesprogressivesamplingBayesianoptimizationactivelearning
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 claims that combining an ensemble of quantile regression models with iterative sampling in uncertain regions separately recovers aleatoric and epistemic uncertainty more reliably than Deep Ensembles or Monte Carlo dropout. This matters because in Bayesian optimization, active learning, and inverse design, treating irreducible noise as a knowledge gap wastes queries, while treating missing data as inherent noise corrupts the uncertainty map. The proposed algorithm adds data to regions flagged as uncertain, retrains, and compares the initial and final uncertainty maps with an XOR operation to label vanished regions as epistemic and persistent ones as aleatoric. On two synthetic benchmarks, a toy function with known noise and a multi-joint robotic arm with an excluded joint, the paper reports correct separation in one and four iterations respectively.

What carries the argument

The load-bearing object is the ensemble of quantile regression models (E-QR), trained with pinball loss to predict upper and lower quantiles per output; the spread between quantiles gives aleatoric uncertainty, and the disagreement across ensemble members gives epistemic uncertainty. The load-bearing procedure is Algorithm 1, which uses progressive sampling in binarized regions of high common uncertainty, followed by retraining and an XOR comparison of normalized total-uncertainty maps to classify regions as epistemic, those that vanish, or aleatoric, those that persist.

What would settle it

Take a synthetic function with two region types, one with fixed irreducible noise and one with data simply absent, and run Algorithm 1 with a known number of iterations and threshold. If the final XOR map labels any part of the known-noise region as epistemic, or the surviving total-uncertainty map labels any part of the known-missing region as aleatoric, the separation assumption is violated. The claim would also be weakened if increasing the number of iterations causes the aleatoric uncertainty estimate to shrink substantially, since the method presumes aleatoric uncertainty is invariant to added data.

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Extended reading notes

Core claim

The central claim is that the two failure modes of uncertainty separation, aleatoric uncertainty leaking into epistemic estimates and epistemic uncertainty leaking into aleatoric estimates, share a single root cause: insufficient local data in the affected regions. Because each ensemble member is trained on a subsample, sparse regions cause members to overfit noise, producing an aleatoric-to-epistemic leak, or to produce unreliable quantile fits, producing an epistemic-to-aleatoric leak. The paper's resolution is Algorithm 1: build a common uncertainty map across outputs by normalizing and multiplying per-output total uncertainties, binarize that map, acquire new data in those regions from the native forward process, retrain, and iterate. Once epistemic uncertainty has vanished with the added data, an XOR between the final total-uncertainty map and the initial one isolates the epistemic regions of the original dataset, while the surviving total uncertainty is declared aleatoric.

Load-bearing premise

The method assumes that after enough rounds of extra sampling in uncertain regions, the total uncertainty map contains only aleatoric uncertainty, because epistemic uncertainty disappears as data is added while aleatoric uncertainty does not; this premise is not validated on a real benchmark or with a formal argument.

Editorial extensions

If this is right

  • On the reported synthetic benchmarks, E-QR plus Algorithm 1 separates aleatoric from epistemic uncertainty more accurately than Deep Ensembles and MC dropout.
  • Progressive sampling resolves leakage in both directions: irresducible noise is no longer misreported as epistemic, and missing-data regions are no longer misreported as aleatoric.
  • E-QR trains quantiles in a single pinball-loss step, which the paper argues is computationally cheaper than Deep Ensembles' two-step NLL training.
  • The framework is scalable to large datasets, making it applicable to simulation-driven scientific and engineering tasks where uncertainty separation guides data acquisition.
  • In applications such as Bayesian optimization and active learning, the separated uncertainty maps let a decision-maker target epistemic regions while avoiding regions dominated by irreducible noise.

Reading between the lines

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

  • An implication the paper leaves implicit is that Algorithm 1's cost scales with the number of retraining rounds and the amount of newly simulated data, so its practical value depends on how cheap the native forward process is; for expensive simulators, the iterative acquisition budget would need to be counted alongside the uncertainty-separation gain.
  • A testable extension would be to run the same progressive-sampling scheme on a real dataset with a known noise floor and track the per-iteration change in the aleatoric map; if the aleatoric estimate shrinks systematically, the XOR procedure would be biased toward labeling persistent regions as aleatoric.
  • The paper argues, but does not isolate in an ablation, that pinball loss makes E-QR less sensitive to initialization and learning rate than NLL-based Deep Ensembles; a controlled comparison with identical architectures and seeds would make that claimed stability measurable.
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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 / 4 minor

Summary. The paper proposes an ensemble quantile regression (E-QR) approach for uncertainty estimation and separation, combined with an iterative progressive-sampling algorithm (Algorithm 1) that adds data in regions of high total uncertainty and then uses an XOR between initial and final uncertainty maps to separate aleatoric and epistemic uncertainty. The evaluation is conducted on two synthetic tasks, a toy function and a multi-joint robot arm, with qualitative visual inspection of uncertainty maps as the only form of validation, and the paper claims superiority over Deep Ensembles and Monte Carlo dropout.

Significance. If validated, the method would address a practically important problem: scalable uncertainty separation for large-scale data, and the use of quantile regression as the underlying uncertainty estimator is a plausible alternative to deep ensembles. However, the manuscript provides no quantitative comparisons against the claimed baselines, no error bars, no convergence guarantees for the core iterative procedure, and the algorithm as written contains a concrete implementation bug. The central claims of superiority and reliable separation are therefore not supported by the evidence presented in the manuscript.

major comments (4)
  1. [Section 4, Figures 3 and 4] The abstract claims that E-QR surpasses Deep Ensembles and Monte Carlo dropout, but the evaluation contains no quantitative comparison with DE or MC dropout; the only evidence is visual inspection of uncertainty maps. Because the central claim is superiority over these baselines, the absence of measurements such as calibration error, separation accuracy, AUROC, or any metric on a dataset with known ground-truth uncertainty decomposition is a load-bearing gap.
  2. [Section 3.2, Algorithm 1] The method's validity rests on the premise that after Q progressive-sampling iterations, the total uncertainty map contains only aleatoric uncertainty. This premise is asserted in the pseudocode comment ('After sufficient number of iterations the total uncertainty map only contains aleatoric uncertainty') but never validated by a convergence argument, a stopping criterion, or an empirical check on a benchmark with known uncertainty types. Section 3.1 itself describes how aleatoric uncertainty leaks into epistemic estimates when data is insufficient; adding data only in high-uncertainty regions could still leave the model's aleatoric fit unreliable in those regions, so the XOR could misclassify persisting leakage as epistemic.
  3. [Algorithm 1 pseudocode] The loop over outputs is not implemented as described in Section 3.2: the line 'U_j_total = UE + UA' is assigned inside the loop over j, overwriting the same variable each iteration, while 'U_total_total' is used on the right-hand side before being initialized and is never reset for each iteration i. As written, the algorithm does not compute the product of per-output uncertainty maps described in the text, and it is unclear whether the intended common-region accumulation is actually what was executed to produce Figures 3 and 4.
  4. [Section 4.2, 4.3, and Algorithm 1 inputs] The algorithm depends on a binarization threshold T and iteration count Q, but the text and experiments do not specify how these values are chosen; Sections 4.2 and 4.3 use one and four iterations respectively without justification, and no sensitivity analysis is provided. In addition, the experimental section omits the neural-network architecture, training hyperparameters, ensemble size, and quantile levels, which are free choices that materially affect the results and make the experiments difficult to reproduce or compare.
minor comments (4)
  1. [Introduction and Section 3.1] Typos: 'Guassian' should be 'Gaussian'; the sentence 'the fit of aleatoric uncertainty estimates can become arbitrarily' in Section 3.1 is incomplete, seemingly missing a word such as 'bad' or 'inaccurate'.
  2. [Algorithm 1 output lines] The final lines of Algorithm 1 are confusingly written: 'UA, DU_A, PU_A ← U_total_total' appears twice, once before and once after the XOR line, with the second assignment using the same variable names; this makes it hard to tell which quantities are the separated aleatoric and epistemic outputs.
  3. [Terminology] Algorithm 1 says 'Train the BNN surrogate' and the text uses 'BNN' in places, but the method is an ensemble of quantile regression models (E-QR), not a Bayesian neural network; inconsistent terminology may confuse readers.
  4. [Figures 3 and 4] The figure captions reference 'Step 1', 'Step 2', etc., but the number of steps and their correspondence to Algorithm 1 iterations are not defined; adding explicit iteration numbers or matching caption text to the algorithm would clarify the presentation.

Circularity Check

1 steps flagged · score 2.0 of 10

The epistemic/aleatoric split is operationalized as 'what disappears vs. what remains' under progressive sampling, and the evaluation confirms epistemicity with that same disappearance criterion, producing a mild self-definitional validation. The core method still has independent synthetic ground truth and no load-bearing self-citation chain.

  1. self definitional [Section 3.2, Algorithm 1, Figure 3/4 captions]
    "Iteratively repeating this process diminishes regions of epistemic uncertainty while areas of aleatoric uncertainty remain unchanged. By performing a logical XOR operation between the final uncertainty map and the initial one, we can isolate the initial epistemic uncertainty present in our initial dataset. ... After sufficient number of iterations the total uncertainty map only contains aleatoric uncertainty. ... After two iterations, only the regions with aleatoric uncertainty remain in the uncertainty map, confirming that the vanished uncertain areas were indeed epistemic."

    The algorithm defines its epistemic output by construction: the final total uncertainty map is assumed to contain only aleatoric uncertainty, and epistemic regions are then obtained by XOR with the initial total map. Thus 'epistemic' is, by construction, whatever disappears after progressive sampling. The evaluation then uses the same disappearance as confirmation: vanished areas 'were indeed epistemic' and uncertainty that 'vanishes when the uncertain regions are filled' is declared epistemic. This restates the construction rather than testing it against an independent criterion.

full rationale

The central derivation is not a fitted-input-called-prediction or a self-citation-forced result. Algorithm 1's progressive-sampling loop is a direct operationalization of the standard definition of epistemic uncertainty as reducible with additional data, and the synthetic experiments include externally known aleatoric regions (injected noise) and epistemic regions (omitted joint behavior), which can independently test the algorithm's behavior. However, the text's confirmation language is partly tautological: the algorithm labels uncertainty as epistemic because it vanishes after adding data, and then the experiments 'confirm' epistemicity because the uncertainty vanished. That is a self-definitional validation loop rather than independent evidence. The paper does not provide a quantitative convergence criterion for Q or a formal argument that the final uncertainty map contains only aleatoric uncertainty, but that gap is a correctness/robustness concern rather than a circularity. Self-citations to Ansari et al. (2022, 2023) and Wijaya et al. (2024) are background and motivation, not load-bearing for the main claim. Overall, the circularity is minor and localized to the evaluation phrasing, so the score is 2.

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

The method's central claim depends on several unstated assumptions and free parameters: the threshold T, iteration count Q, and the assumption that adding data removes epistemic but not aleatoric uncertainty. No new physical entities are introduced. The assumptions are not validated with quantitative experiments.

free parameters (3)
  • Threshold T for binarizing the uncertainty map
    Used in Algorithm 1 to create a mask for selecting regions to sample. The value is not specified, so it is likely chosen by hand or tuned to make the method work.
  • Number of progressive sampling iterations Q = 1 or 4 depending on the experiment
    The number of data-augmentation rounds is not derived or justified. The paper uses different values for the toy problem (1) and the robot arm (4), which suggests it was chosen to reach the desired separation result.
  • Quantile levels for pinball loss
    The specific quantiles used (e.g., 0.1 and 0.9) are not stated, but they affect the width of the quantile interval and hence the aleatoric uncertainty estimate.
assumptions (3)
  • domain assumption Epistemic uncertainty decreases with additional data, while aleatoric uncertainty remains unchanged.
    This is the core premise of Algorithm 1, stated in Section 3.2. The XOR operation assumes that after enough iterations, only aleatoric regions remain in the uncertainty map. The paper provides no formal justification.
  • domain assumption Multiplying total uncertainty maps across outputs identifies regions that are commonly uncertain, which are more likely to be data-driven rather than due to local misfitting.
    Section 3.2 introduces this heuristic without a derivation or evidence. It is needed to focus sampling on regions shared across outputs.
  • domain assumption Ensemble quantile regression with pinball loss provides reliable aleatoric uncertainty estimates even in low-data regions.
    The paper claims pinball loss is stable and accurate for quantile estimation, but provides no experiments supporting this in the sparse-data regime where the method is applied.

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Cite this review

Pith. "Pith review of Uncertainty separation via ensemble quantile regression." pith.science (2026). https://pith.science/paper/FRPGSO3R

@misc{pith2026241213738,
  author       = {Pith},
  title        = {Pith review of: Uncertainty separation via ensemble quantile regression},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FRPGSO3R}},
  note         = {Machine review of arXiv:2412.13738}
}
read the original abstract

This paper introduces a novel and scalable framework for uncertainty estimation and separation with applications in data driven modeling in science and engineering tasks where reliable uncertainty quantification is critical. Leveraging an ensemble of quantile regression (E-QR) models, our approach enhances aleatoric uncertainty estimation while preserving the quality of epistemic uncertainty, surpassing competing methods, such as Deep Ensembles (DE) and Monte Carlo (MC) dropout. To address challenges in separating uncertainty types, we propose an algorithm that iteratively improves separation through progressive sampling in regions of high uncertainty. Our framework is scalable to large datasets and demonstrates superior performance on synthetic benchmarks, offering a robust tool for uncertainty quantification in data-driven applications.

Figures

Figures reproduced from arXiv: 2412.13738 by the authors.

Figure 1
Figure 1. On the left figure, we observe how the lack of [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Multi joint robotic arm with a moving base and 4 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. This experiment highlights the leakage of epis [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

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Reference graph

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