Evaluating Fairness and Mitigating Bias in Machine Learning: A Novel Technique using Tensor Data and Bayesian Regression

Dhavalkumar Thakker; Koorosh Aslansefat; Kuniko Paxton; Yiannis Papadopoulos

REVIEW 4 major objections 7 minor 25 references

Evaluating Fairness and Mitigating Bias in Machine Learning: A Novel Technique using Tensor Data and Bayesian Regression

T0 review · 4 major / 7 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper's central claim is that individual-level skin-tone bias in image classifiers can be detected and mitigated without annotations, using per-pixel skin-tone distributions and a Bayesian-regression-weighted loss.

desk verdict Per-pixel ITA distributions are a promising idea, but Eq. (3) is not a Wasserstein distance and the experimental evidence is too weak; this needs a major revision, not acceptance. read the letter →

arxiv 2506.11627 v1 pith:QXIWYT5H submitted 2025-06-13 cs.CV cs.AIcs.LG

Kuniko Paxton , Koorosh Aslansefat , Dhavalkumar Thakker , Yiannis Papadopoulos This is my paper · ORCID

classification cs.CVcs.AIcs.LG

keywords fairnessskincolorsensitiveattributesIndividualTypologyAngleWassersteindistanceBayesianregressionlossreweightingimageclassification

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 argues that fairness for image classifiers should treat skin color as a continuous, per-pixel tensor rather than a predefined category such as 'light' or 'dark'. It proposes a pipeline that converts the skin pixels in each image into a probability distribution of Individual Typology Angle (ITA) values and measures the signed statistical distance from a baseline image. A Bayesian regression model then predicts how model performance (F1 score or accuracy) varies across that distance, and the training loss is reweighted to penalize skin tones where performance is predicted to be worse. On three image datasets, the method exposes performance differences hidden within a single skin-tone category and, in most tested settings, reduces the correlation between skin-tone nuance and performance. The paper asserts this is the first annotation-free technique to evaluate and mitigate individual-level skin-tone bias in image classification.

What carries the argument

The central mechanism is the signed distance measure of Eq. (3), applied to per-image ITA (Individual Typology Angle) distributions computed from skin pixels: $D(A_0,A_i)=\int_{-\infty}^{\infty}|F(A_0)-F(A_i)|\,dA\cdot\operatorname{sign}(A_i-A_0)$, where ITA is a CIELab-based skin-tone angle. This distance turns a tensor of skin pixels into a one-dimensional directional quantity that says how far and in which direction an individual's skin-tone distribution sits relative to a baseline image. A Bayesian polynomial regression then maps that distance to expected per-batch performance (F1 score or accuracy), and the training loss is reweighted by the softmax of the inverted performance estimate, with the penalty switched on after a chosen epoch. The distance measure, the regression, and the reweighted cross-entropy loss together carry the argument.

What would settle it

Recompute the signed distance $D(A_0,A_i)$ for the same validation images using several different randomly chosen baseline images $x_0$; if the rank ordering of images by distance changes materially across baselines, or if the correlation values in Table 3 no longer reproduce, the reported bias signal is an artifact of baseline choice rather than a stable property of skin tone.

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Extended reading notes

Core claim

The paper's central claim is that latent, individual-level skin-tone bias in image classifiers can be detected and mitigated without annotations, by treating skin color as a tensor of pixel values, converting it into a probability distribution, and measuring a directional statistical distance from a baseline. On this view, conventional group-fairness checks that compare coarse categories like 'light' and 'dark' can report parity while hiding within-category performance differences. The results section reports that biases latent within the same category could be detected, and that weighting the loss function according to nuanced skin-color differences significantly reduced the correlation with the target evaluation metric. The paper also asserts that no prior research has achieved a fair model without annotations using only detected skin color nuances.

Load-bearing premise

The load-bearing premise is that the signed distance in Eq. (3) is a meaningful measure of skin-tone difference, even though it is not the true Wasserstein distance and depends on which image is randomly chosen as the baseline, because if this quantity is meaningless the detected correlations and the reweighted-loss mitigation collapse.

Editorial extensions

If this is right

Group-fairness metrics that coarse-categorize skin tone can certify parity while hidden individual-level bias remains; this method claims to reveal and reduce that within-category bias.
The same signed-distance construction extends Equal Opportunity, Demographic Parity, and Equalized Odds to continuous sensitive attributes.
Fairness evaluation no longer requires human skin-tone annotations, only a skin-pixel detector and a validation set for the Bayesian prior.
In most tested model-dataset combinations, posterior training weakens the correlation between skin-tone distance and F1/accuracy, with the largest reported reductions on the HAM skin-lesion dataset.

Reading between the lines

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

Editorial inference: because Eq. (3) depends on a randomly chosen baseline image, the paper leaves open a natural robustness check: average distances over many baselines and re-run Table 3; material changes in rank order would make the fairness signal baseline-dependent.
Editorial inference: the same distance-plus-Bayesian-reweight pipeline could be extended to other continuous sensitive attributes expressed as images, such as apparent age or body shape, not just skin color.
Editorial inference: the method's applicability is bounded by the quality of the skin-pixel detector, so combining it with learned skin segmentation could extend it to datasets the paper lists as out of scope, such as images with tiny or multiple skin regions.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Quick take: the paper has a genuinely interesting idea—using per-pixel ITA values as a distribution to capture skin-tone nuance without annotation—but the central distance metric is not actually a Wasserstein distance, the cross-entropy formula in Eq. (10) is wrong, and the experiments lack the baselines and error bars needed to support the claims. I would not accept it as is, but I would not dismiss the general direction.

The good part is the conceptual shift: instead of collapsing skin tone to a single average ITA or a category, the authors build a distribution of ITA values over skin pixels and then measure a signed distance between distributions. That is a reasonable way to think about within-group variation, and it seems new to combine this with a Bayesian regression–weighted loss for mitigation. The idea of detecting bias that category-based fairness misses is worth taking seriously.

The problems are load-bearing. Eq. (3) defines the distance as an integral of |F(A0) − F(Ai)| dA times sign(Ai − A0). As written, this is not the Wasserstein distance—the Wasserstein-1 distance between two distributions with CDFs F0 and Fi is ∫|F0(t) − Fi(t)| dt, without a sign factor, and it does not require a reference point. The sign and the arbitrary reference baseline x0 (chosen randomly, no seed reported) mean the correlations in Table 3 and the penalty weights in the mitigation are artifacts of an unreported random draw. A different baseline changes relative orderings, not just a global shift. Eq. (10) is also incorrect: both terms in the cross-entropy use log xn, which is not a valid cross-entropy. The experiments don’t compare to any baseline method, report no error bars or significance tests, and one result (HAM VGG F1) worsened from −0.497 to −0.600 without comment. Appendix C says the code is “available here” but no link appears.

On the citation pattern: the literature review is adequate and the claim of being the first annotation-free method is overstated, since Chiu et al. and others have worked in that direction, but this is a minor sin.

Where does that leave us? The paper is not ready for publication, but it has a seed of a plausible method. A major revision that replaces Eq. (3) with a properly defined distance (e.g., signed W1 with a deterministic baseline or a rank-based measure), fixes the loss, adds baselines and error bars, and reports seeds could make a contribution. The paper is for readers who study algorithmic fairness in computer vision, especially those interested in continuous sensitive attributes and annotation-free evaluation. I’d send it to a serious referee rather than desk-reject, because the flaws are concrete and fixable, and the underlying question matters.

Recommendation: reject the current version, but invite a revise-and-resubmit with a corrected measure and proper experiments.

Referee Report

4 major / 7 minor

Summary. The manuscript proposes an annotation-free pipeline for measuring and mitigating skin-color bias in image classifiers. Skin pixels are converted into per-image ITA distributions; a signed "Wasserstein" distance from a randomly chosen baseline image is computed; a Bayesian polynomial regression predicts validation performance as a function of this distance; and a softmax-weighted cross-entropy loss penalizes samples whose predicted performance is low. Experiments on UTKFace, CelebA, and HAM with EfficientNet, ResNet50, and VGG16 report correlations between the distance and F1/accuracy before and after the proposed reweighting. The paper claims to detect latent within-category bias and to significantly reduce the correlation with the target evaluation metric.

Significance. If the method worked as claimed, it would address a real gap: most fairness work on skin tone uses coarse categories or requires annotations, while this paper models skin tone as a per-image distribution and targets individual-level fairness. The motivation is clear, the distribution-based treatment of skin color is a sensible direction, and the authors explicitly list limitations in Section 6.2. However, the central distance measure is not correctly defined, the loss equation contains an error, and the experimental evidence is not sufficient to support the headline claims. The contribution is therefore not yet established.

major comments (4)

[§3.3.1, Eq. (3)] This is not a Wasserstein distance and is not well defined as written. If F denotes the CDF function of a distribution, then F(A0) and F(Ai) are numbers, the integrand |F(A0) − F(Ai)| is constant in A, and the integral over R diverges; if F(A0) is intended to denote an entire CDF, the notation is undefined. Even interpreting Eq. (3) as W1(A0,Ai)·sign(median(Ai)−median(A0)), the result depends on the randomly selected baseline image x0, and the relative ordering of distances to different references is not preserved under a change of baseline. Since D feeds the Bayesian estimator (§3.4), the loss penalty (§3.5), and all correlations in Table 3, and since no seed or baseline is reported, the experimental results are not reproducible. The authors should define a canonical baseline (or average over baselines) and report sensitivity to that choice.
[§3.5, Eq. (10)] The cross-entropy term is written with the same log xn for both yn and 1−yn, so the displayed formula is not a valid binary cross-entropy loss. Algorithm 2 implements a correct per-sample BCE, but Eq. (10) cannot be used to reproduce the training. Please correct Eq. (10) and state precisely how the softmax penalty σ and scalar α enter the per-sample and per-batch losses.
[§5, Table 3] The evidence for mitigation is statistically weak. Correlations are reported without confidence intervals, significance tests, or repeated runs; the batch size for performance estimation is 1% of validation with no justification. One combination, HAM/VGG F1, moves from −0.497 to −0.600, i.e., it worsens, and this is not commented on. In addition, the Bayesian performance estimator is fit to the base model's validation scores on the same distance D that the loss then penalizes, so the reported reduction in the D–performance correlation is partly an artifact of optimizing the evaluation metric. An independent fairness evaluation (e.g., a held-out test set with a separate estimator, or comparison with standard reweighting and adversarial baselines) is required.
[§3.4 and Tables 2/4] Several free parameters (polynomial degree g, penalty start epoch pe, penalty weight α, batch size, preprocessing thresholds) are tuned per dataset and model without a selection rule or sensitivity analysis. Because the method's generality claim depends on these choices, the authors should report how the results vary with these parameters or provide a principled selection procedure.

minor comments (7)

[§3.2 and §3.3.1] The text refers to the "Washer Stain Distance" in two places; this should be "Wasserstein distance".
[Table 4 caption] The caption contains the typo "Performancce" and should be corrected.
[Table 1] Table 1 includes an ISIC2024 column, but the experimental section lists only three datasets and does not describe ISIC2024.
[Figure 4] The x-axis convention (0 for baseline, positive for lighter, negative for darker) should be stated in the caption or on the axis label, since the current description is not self-contained.
[Tables 2 and 4] In every row of Tables 2 and 4, the validation F1 score equals the validation accuracy; this is unusual and should be explained or checked.
[Appendix C] The source-code link is given as "this GitHub repository" without an actual URL, so the code is not locatable from the manuscript.
[Header] The header contains the placeholder "Editor: My editor"; this should be removed before submission.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the Bayesian estimator is a supervised fit used as a loss weight, not a renamed prediction, and the reported reductions are empirical and partly counterexamples.

full rationale

The derivation chain does not reduce to its inputs. The skin-color distance D in Eq. (3) is constructed from ITA pixel distributions independently of model outputs; the Bayesian regression in Section 3.4 fits validation performance to D as a standard supervised model; and Section 3.5 uses the fitted estimator only to reweight the cross-entropy loss. The mitigation outcome in Table 3 is measured on data and is not forced by construction: for the HAM/VGG combination the F1 correlation actually worsens from -0.497 to -0.600, which would be impossible if the result were a tautology. The paper contains no author self-citations and does not invoke a uniqueness theorem from the authors' own prior work; the load-bearing mathematical references (Hardt et al. 2016, Cai and Lim 2022) are external. The baseline dependence and unseeded random choice of x0 in Eq. (3) are serious reproducibility and validity concerns, and the appended Limitations section acknowledges only the skin-detection scope limit, not this issue; but a flawed or arbitrary distance is a correctness problem, not a circular definition. No fitted parameter is renamed as a prediction, and no equation is equivalent to its own input by construction. Therefore the circularity score is 0.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The central claim rests on a custom distance metric that is not a true metric, a reduction of skin color to ITA distributions, and a performance estimator fitted to the base model's validation scores. The polynomial degree, penalty start epoch, penalty weight, batch size, and preprocessing thresholds are all free choices that influence the reported correlations.

free parameters (5)

Polynomial degree g
Degree of the Bayesian polynomial regression is 'determined from the prior distribution' (Section 3.4) but no criterion or value is given; it affects the performance estimator used for reweighting.
Penalty start epoch pe = 1-18 across runs (Table 2)
Chosen per model/dataset for best mitigation; a tuneable schedule hyperparameter.
Penalty weight alpha = 0.95 or 1.0 (Table 2)
Chosen per model/dataset; scales the fairness penalty.
Batch size for performance estimation = 1% of validation (Section 3.4)
Arbitrary grouping of samples into batches for computing F1/accuracy per distance bin.
Skin preprocessing thresholds and kernel sizes
Hair removal and skin detection parameters are 'heuristics based on the visual perspective of each dataset' (Section 4.2).

assumptions (4)

ad hoc to paper The signed distance D(A0,Ai) in Eq. (3) is a valid statistical distance reflecting skin-tone differences.
The paper calls it Wasserstein distance but the formula uses CDF values at points rather than distributional CDFs and applies an external sign, so it is not a metric; the evaluation and mitigation depend on this quantity.
domain assumption Skin color is adequately represented by the per-pixel ITA distribution, ignoring chroma and texture.
Section 3.3 reduces skin color to ITA values; no validation that this captures the phenotypic diversity relevant to model bias.
domain assumption The Bayesian performance estimator predicts individual performance from distance, enabling effective reweighting.
Section 3.4 fits a polynomial to batched validation F1/accuracy; the loss weighting assumes this estimator generalizes to test samples.
domain assumption Pixel distributions are IID across and within images.
Section 3.3.1 states 'Assuming the distributions are IID' to justify using Wasserstein distance, but this assumption is not tested and likely false for spatially correlated skin pixels.

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Cite this review

Pith. "Pith review of Evaluating Fairness and Mitigating Bias in Machine Learning: A Novel Technique using Tensor Data and Bayesian Regression." pith.science (2026). https://pith.science/paper/QXIWYT5H

@misc{pith2026250611627,
  author       = {Pith},
  title        = {Pith review of: Evaluating Fairness and Mitigating Bias in Machine Learning: A Novel Technique using Tensor Data and Bayesian Regression},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QXIWYT5H}},
  note         = {Machine review of arXiv:2506.11627}
}

read the original abstract

Fairness is a critical component of Trustworthy AI. In this paper, we focus on Machine Learning (ML) and the performance of model predictions when dealing with skin color. Unlike other sensitive attributes, the nature of skin color differs significantly. In computer vision, skin color is represented as tensor data rather than categorical values or single numerical points. However, much of the research on fairness across sensitive groups has focused on categorical features such as gender and race. This paper introduces a new technique for evaluating fairness in ML for image classification tasks, specifically without the use of annotation. To address the limitations of prior work, we handle tensor data, like skin color, without classifying it rigidly. Instead, we convert it into probability distributions and apply statistical distance measures. This novel approach allows us to capture fine-grained nuances in fairness both within and across what would traditionally be considered distinct groups. Additionally, we propose an innovative training method to mitigate the latent biases present in conventional skin tone categorization. This method leverages color distance estimates calculated through Bayesian regression with polynomial functions, ensuring a more nuanced and equitable treatment of skin color in ML models.

Figures

Figures reproduced from arXiv: 2506.11627 by the authors.

**Figure 1.** Difference of Sensitive Attributes The reason GF predomination up to today is the data characteristics of the SA. Many SAs are categorical values. Many SAs are categorical values. For example, giving SA a is gender can only take one of the categorical values in the defined set {male, female}. This can be selected using judgment based on well-defined criteria, such as biological gender. These categorical values fit w… view at source ↗

**Figure 2.** Bias Mitigation Learning Process: The performance estimator for the posterior [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

**Figure 3.** Examples for skin gradation distribution: (A) These are the original image and [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: Bayesian Performance Estimators: This shows the performance prediction of the [PITH_FULL_IMAGE:figures/full_fig_p015_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

Skin deep: Investigating subjectivity in skin tone annotations for computer vision benchmark datasets

Teanna Barrett, Quanze Chen, and Amy Zhang. Skin deep: Investigating subjectivity in skin tone annotations for computer vision benchmark datasets. In Proceedings of the 2023 ACM Conference on Fairness, Accountability, and Transparency, pages 1757–1771,

work page 2023

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Silvia Chiappa and Aldo Pacchiano. Fairness with continuous optimal transport. arXiv preprint arXiv:2101.02084,

arXiv

[3] [8]

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Abigail Z Jacobs and Hanna Wallach. Measurement and fairness. In Proceedings of the 2021 ACM conference on fairness, accountability, and transparency , pages 375–385,

work page 2021

[4] [14]

Estimating and improving fairness with adversarial learning

Xiaoxiao Li, Ziteng Cui, Yifan Wu, Lin Gu, and Tatsuya Harada. Estimating and improving fairness with adversarial learning. arXiv preprint arXiv:2103.04243 ,

arXiv

[5] [16]

General fair empirical risk mini- mization

Luca Oneto, Michele Donini, and Massimiliano Pontil. General fair empirical risk mini- mization. In 2020 International Joint Conference on Neural Networks (IJCNN) , pages 1–8. IEEE,

work page 2020

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Towards Fair Face Verification: An In-depth Analysis of Demographic Biases

Ioannis Sarridis, Christos Koutlis, Symeon Papadopoulos, and Christos Diou. Towards fair face verification: An in-depth analysis of demographic biases. arXiv preprint arXiv:2307.10011,

work page Pith review arXiv

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Very deep convolutional networks for large-scale image recognition

Karen Simonyan and Andrew Zisserman. Very deep convolutional networks for large-scale image recognition. arXiv preprint arXiv:1409.1556 ,

arXiv

[8] [19]

Feature and Label Embedding Spaces Matter in Addressing Image Classifier Bias

William Thong and Cees GM Snoek. Feature and label embedding spaces matter in ad- dressing image classifier bias. arXiv preprint arXiv:2110.14336 ,

work page Pith review arXiv