Pith. sign in

REVIEW 2 major objections 6 minor 49 references

Tackling Algorithmic Bias in Neural-Network Classifiers using Wasserstein-2 Regularization

T0 review · 2 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A Wasserstein-2 penalty on the training loss can temper algorithmic bias in any neural-network classifier while preserving most of its accuracy.

desk verdict Original batch-computable gradient for W2-regularized fair NN training, with honest experiments; the claimed chain-rule inversion in Proposition 2 is a misreading. read the letter →

arxiv 1908.05783 v3 pith:D4ZVBPLD submitted 2019-08-15 stat.ML cs.LG

Laurent Risser , Alberto Gonzalez Sanz , Quentin Vincenot , Jean-Michel Loubes This is my paper · ORCID
classification stat.MLcs.LG MSC 68T0762H30
keywords algorithmicbiasWasserstein-2regularizationneuralnetworkclassifiersfairnessdisparateimpactequalizedoddsstochasticgradientdescentimageclassification
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 algorithmic bias in neural-network classifiers can be tempered by adding a Wasserstein-2 penalty to the training loss, and that the resulting method works for any architecture and for large image datasets. The authors derive approximate gradient formulas for this penalty, so it can be used with standard stochastic gradient descent. They demonstrate on Adult, MNIST, and CelebA that the penalty raises the Disparate Impact toward 1 and balances per-group error rates while preserving most of the prediction accuracy. A second variant targets equalized odds by regularizing the distribution of squared errors instead of raw scores. If the claims hold, fairness correction becomes a drop-in modification of the loss rather than a redesign of the network.

What carries the argument

The central object is the empirical Wasserstein-2 distance $W^2_2(\mu_{\theta,0},\mu_{\theta,1})$ between score distributions of the two sensitive groups, computed via the quantile functions of discretized cumulative distributions $H_0,H_1$. Its gradient is approximated by the identity in Proposition 1, Eq. (12), whose per-sample factor is roughly $\frac{f_\theta(X_i)-\mathrm{cor}_1(f_\theta(X_i))}{n_0(H_0^{j_i+1}-H_0^{j_i})}$ for group 0, with $\mathrm{cor}$ denoting linear interpolation of quantile matching. The argument treats only the histogram bin containing $f_\theta(X_i)$ as changing, so the derivative of the inverse CDF reduces to a reciprocal bin height. This object is what makes the penalty computable in a batch and backpropagatable through an arbitrary network. The batch-training procedure in Algorithm 1 precomputes the histograms once per batch and then applies Eq. (12) (or Eq. (18) for error rates) before the standard gradient update.

What would settle it

On a small synthetic two-group dataset, compute the exact gradient of the discretized Wasserstein-2 penalty, for example by automatic differentiation through the histogram and quantile operations, and compare it with Eq. (12); if the two directions consistently disagree or the SGD trajectory with the approximate gradient fails to decrease the true penalty while increasing accuracy, the central claim would fail.

Watch

Extended reading notes

Core claim

The paper's central claim is that the Wasserstein-2 distance between score distributions for two protected groups can be used as a differentiable, architecture-agnostic regularizer, provided one replaces its gradient by a carefully chosen finite-difference approximation. Proposition 1 gives that approximation: for each observation in a batch, the gradient contribution is proportional to the signed difference between the observation's score and the quantile-mapped score of the opposite group, divided by the empirical bin height of the discretized cumulative distribution. Proposition 2 extends the same idea to the distributions of squared errors, which favors similar true-positive and false-positive rates rather than merely similar positive-prediction rates. The paper presents this as a strategy that scales to massive image training sets because the per-batch cost is dominated by precomputing histograms and cheap linear interpolation.

Load-bearing premise

The method rests on the assumption that the finite-difference gradient, which supposes only one histogram bin changes when a single output moves by the discretization step, points the stochastic-descent optimizer in essentially the right direction even though no error bound is provided.

Editorial extensions

If this is right

  • The regularizer can be appended to any neural-network classifier whose loss is differentiable in the output scores, including convolutional and residual architectures.
  • On the Adult census data, the regularized network reaches Disparate Impact 0.68 with accuracy 0.78, a better fairness-accuracy balance than the compared hard-constraint and Wasserstein-1 baselines.
  • On MNIST with artificially injected label bias, the regularized model improves test Disparate Impact from 0.86 to 0.96 without losing prediction accuracy.
  • On CelebA, a Disparate Impact around 0.6 is reached with little predictive loss; the error-rate variant keeps the per-group good-prediction ratio near 1 even when score parity saturates.

Reading between the lines

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

  • The same quantile-matching gradient formula should transfer to multi-class outputs via one-hot score distributions, since the Wasserstein-2 distance on product measures is separable per coordinate.
  • Because the penalty only aligns conditional distributions along the sensitive variable, it may also serve as a domain-adaptation regularizer by treating source and target distributions as the two groups.
  • The finite-difference derivation suggests a testable sensitivity: the method should be most affected by the choice of bin count $J$; implementations on very different score scales may require re-tuning, which the automatic $\lambda$ scaling of Appendix C.3 does not explicitly address.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 6 minor

Summary. The manuscript proposes a fairness regularizer for neural-network classifiers that penalizes the Wasserstein-2 distance between the conditional distributions of network scores (Reg. Prediction) or of squared errors (Reg. Error) across two sensitive groups. The authors derive approximate gradient formulas (Propositions 1 and 2, Eqs. (12) and (18)) based on finite differences over discretized empirical CDFs, integrate them into a batch SGD loop (Algorithm 1), and evaluate the method on Adult, MNIST, and CelebA. The central claim is that the regularizer is architecture-agnostic, computationally reasonable, and can temper algorithmic bias with limited accuracy loss.

Significance. If the gradient estimator is faithful and the experiments are reproducible, the paper offers a practical, architecture-agnostic fairness tool for image classifiers, with explicit gradient formulas and a demonstration on a 200k-image dataset. The authors are transparent about the approximate nature of the derivation. That said, the method's empirical support is currently limited: on image data the comparison is only against a lambda=0 self-baseline, and the hyperparameters of the approximation are not reported. The claimed scalability and the identification of the regularized objective with a Wasserstein-2 penalty rest on an unvalidated stochastic-gradient approximation.

major comments (2)
  1. [3.4.1 / Eq. (11)] The estimator in Eq. (11) replaces the expectation of the full-data derivative by a batch average of per-sample derivatives while treating H0 and H1 as fixed. Since the regularizer W2^2(mu^n_{theta,0}, mu^n_{theta,1}) is a functional of the whole sample, the derivative for sample i depends on all n (or n_sub) observations through the empirical CDFs; the resulting direction is not a standard unbiased stochastic gradient, and the paper provides no bias, variance, or consistency analysis. Because Algorithm 1 uses this estimator at every SGD step, the claim that the method can be used with 'standard stochastic gradient-descent strategies' needs either a theoretical justification or a direct numerical validation (e.g., comparing the approximate batch gradient with the full-batch finite-difference gradient on a small problem).
  2. [Appendix A / Eq. (23)] The finite-difference derivation in Appendix A, summarized in Eq. (23), assumes that perturbing f_theta(X_i) by J^{-1} only changes the single bin containing f_theta(X_i), and it divides by the bin height H^{j_i+1}_{S_i}-H^{j_i}_{S_i}. For finite subsample sizes n_sub and moderate J, empty bins are common, making the denominator in Eqs. (12), (18), (25), and (28) zero; no clipping, jitter, or smoothing is described, and no error bound in J, Delta_tau, or n_sub is given. The experiments never report the values of J, Delta_tau, and n_sub, so the stability of the proposed gradient computation cannot be checked. At minimum, the authors should report these values and provide a sensitivity analysis.
minor comments (6)
  1. [3.5.2 / Eqs. (18) and (28)] The alleged inversion of the chain rule in Proposition 2 is not present in the manuscript as written: the factor (f_theta(X_i)-Y_i)^{-1} appears in the denominator, so the summand is equivalent to multiplying by (f_theta(X_i)-Y_i), which matches Eq. (27). The notation is nevertheless very easy to misread, and I recommend rewriting Eq. (18) (and Eq. (28)) with the factor (f_theta(X_i)-Y_i) explicitly in the numerator.
  2. [3.5.1 / Eq. (14)] In Eq. (14), the identity (g_theta(X_i)-Y_i)^2 = 1_{Y_i = g_theta(X_i)} is backwards: the indicator should be 1_{Y_i != g_theta(X_i)} (the squared error equals one on misclassified examples and zero on correctly classified ones).
  3. [Algorithm 1 / Sec. 3.6] In Algorithm 1, line 3 precomputes H0 and H1 before the batch B is drawn and before the outputs f_theta(X_i), i in B, are computed in line 5; the algorithm should clarify which data are used for these CDFs (full set, fixed subsample, or batch), at which current parameters they are evaluated, and how the required forward passes are scheduled.
  4. [Sections 4.1-4.3] The hyperparameters J, Delta_tau, n_sub (and alpha in Appendix C.3) are never specified for any of the experiments, and most results appear to be single runs; reporting these values and multiple-seed statistics is necessary for reproducibility and for assessing the stability of the method.
  5. [Abstract / Section 5] The claim that the method 'scales well to massive training sets' is supported only indirectly; the paper reports no wall-clock time or memory overhead compared with plain training, and the implementation is promised only after acceptance, so the algorithmic-cost claim in the abstract is not quantified or verifiable.
  6. [Sections 4.2-4.3] On MNIST and CelebA the evaluation is only against a lambda=0 self-baseline; adding at least one existing fair-training baseline or a post-hoc thresholding baseline on these image tasks would help position the method relative to the literature.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the Wasserstein-2 gradient derivations are self-contained, and the Appendix B chain-rule inversion is an algebraic error rather than a circular reduction.

full rationale

The derivation chain is self-contained. Proposition 1 (Eq. 12) is obtained in Appendix A by finite-difference approximations of the inverse empirical cumulative distribution functions (Eqs. 19-25); its inputs are the empirical histograms H0 and H1 and the discretization grid, not the fairness metrics being evaluated. Proposition 2's derivation similarly starts from the W2 distance between squared-error distributions, and Eq. (27) states the correct chain rule; the fact that Eq. (28) then places (f_theta(X_i)-Y_i)^{-1} in the denominator instead of multiplying by (f_theta(X_i)-Y_i) is an internal algebraic inconsistency, which is a correctness or validity concern rather than a circular reduction of the result to its inputs. The empirical evaluation is against standard external benchmarks (Adult, MNIST, CelebA) and compares with baselines; reporting DI, DMSE, or accuracy after training is not circular because those metrics are not fitted parameters renamed as predictions. The automatic lambda tuning of Appendix C.3 uses DI and accuracy heuristically, but the reported Adult DI of 0.68 does not match the 0.85 threshold used in the heuristic, so the outcome is not merely a fitted artifact. Self-citations, such as [3], [8], [9], and [33], provide background analysis or external mathematical results about optimal transport and fairness; none is invoked as a uniqueness theorem or as the sole justification of the gradient formulas. Consequently, no load-bearing step reduces by construction to its own inputs.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The method introduces no new physical entities. It does introduce several tunable numerical parameters (lambda, J, Delta_tau, n_sub, alpha) whose values are not fully reported. The most consequential unproven premise is the empirical link between W2 regularization and the fairness metrics, which the authors explicitly defer to future work in Section C.3.

free parameters (5)
  • lambda (regularization weight) = 2.0e-5 on MNIST; 4e-3 on CelebA; tuned via C.3 on Adult
    Controls the trade-off between prediction accuracy and the W2 penalty. Values are chosen per dataset by inspecting test-set curves (Fig. 3, 4) or by the heuristic in C.3, and the results depend strongly on this choice.
  • J (number of CDF discretization steps) = not reported
    Used to build the discrete cumulative distributions in Eq. (9); determines fidelity of the gradient approximation. The paper never states J in the experiments.
  • Delta_tau (integration step in gradient formulas) = not reported
    Scales the approximate gradients in Eqs. (12) and (18); the paper only says 'for Delta_tau small enough' and does not give its value.
  • n_sub (subsample size for CDF precomputation) = not reported
    Mentioned in Section 3.4.2 for the case where n is extremely large; no value or sensitivity analysis is given.
  • alpha (scale factor for auto-tuning lambda in C.3) = not reported
    Used in the Adult experiments to update lambda based on accuracy and DI; the initial value and update constants are not fully specified.
assumptions (6)
  • domain assumption The sensitive attribute S is binary and observed for every training sample.
    Section 3.1 defines S in {0,1} and the method splits groups accordingly; extensions to multiple attributes are left to future work.
  • domain assumption Fairness is adequately measured by Disparate Impact (Eq. 2) and equalized-odds probabilities (Eq. 5).
    Section 2.1 adopts these standard metrics; the paper acknowledges that purely random classifiers score well on them, so it also requires accuracy to stay high.
  • ad hoc to paper Reducing the W2 distance between group score distributions improves DI and output-parity metrics.
    Section C.3 states the effect on thresholded prediction differences was 'empirically verified' and that a formal causal relation is future work; this is the main unproven link for the statistical-parity variant.
  • ad hoc to paper Reducing W2 between squared-error distributions improves error-rate parity (DMSE / equalized odds).
    Section 3.5.1 introduces DMSE and then regularizes the squared-error distributions; the paper gives no proof that W2 on squared errors implies equalized odds.
  • ad hoc to paper The batch approximation of the derivative expectation (Eq. 11) is a valid stochastic gradient estimator.
    Section 3.4.1 asserts this is a 'good trade-off' without bias/variance analysis; the whole SGD training procedure rests on it.
  • standard math Standard SGD/Adam convergence assumptions hold for the regularized objective.
    The training procedure (Algorithm 1) uses Adam as in standard deep-learning practice; no convergence analysis is given.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Tackling Algorithmic Bias in Neural-Network Classifiers using Wasserstein-2 Regularization." pith.science (2026). https://pith.science/paper/D4ZVBPLD

@misc{pith2026190805783,
  author       = {Pith},
  title        = {Pith review of: Tackling Algorithmic Bias in Neural-Network Classifiers using Wasserstein-2 Regularization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/D4ZVBPLD}},
  note         = {Machine review of arXiv:1908.05783}
}
read the original abstract

The increasingly common use of neural network classifiers in industrial and social applications of image analysis has allowed impressive progress these last years. Such methods are however sensitive to algorithmic bias, i.e. to an under- or an over-representation of positive predictions or to higher prediction errors in specific subgroups of images. We then introduce in this paper a new method to temper the algorithmic bias in Neural-Network based classifiers. Our method is Neural-Network architecture agnostic and scales well to massive training sets of images. It indeed only overloads the loss function with a Wasserstein-2 based regularization term for which we back-propagate the impact of specific output predictions using a new model, based on the Gateaux derivatives of the predictions distribution. This model is algorithmically reasonable and makes it possible to use our regularized loss with standard stochastic gradient-descent strategies. Its good behavior is assessed on the reference Adult census, MNIST, CelebA datasets.

Figures

Figures reproduced from arXiv: 1908.05783 by the authors.

Figure 1
Figure 1. Cumulative distributions H0 and H1 of simulated predictions fθ(Xi |Si = s) in two groups s = 0 and s = 1. Using this distance as a regularizer ensures that the cumulative distributions fθ(Xi |Si = 0) and fθ(Xi |Si = 1) remain reasonably close to each-other. The training problem is then: ˆθ = arg min θ∈Θ  R(θ) + λW2 2 (µ n θ,0 , µn θ,1 ) [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Notations used to efficiently approximate the gradients of Wasserstein-2 distances between the discrete [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Results obtained on the MNIST dataset by following the SR and ST experimental protocols. Both for SR and [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Results obtained on the CelebA dataset by favoring [PITH_FULL_IMAGE:figures/full_fig_p013_4.png]
Figure 5
Figure 5. Figure 5: Observations with the highest differences of predictions with or without regularization. We recall that [PITH_FULL_IMAGE:figures/full_fig_p014_5.png]
Figure 6
Figure 6. Figure 6: Extension of Fig. 2 with specific notations to A. [PITH_FULL_IMAGE:figures/full_fig_p017_6.png]
Figure 7
Figure 7. Figure 7: Impact on a discrete cumulative distribution [PITH_FULL_IMAGE:figures/full_fig_p018_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

49 extracted references · 42 canonical work pages

  1. [1]

    IEEE Trans

    Bengio, Y ., Courville, A., Vincent, P.: Representation learning: A review and new perspectives. IEEE Trans. Pattern Anal. Mach. Intell. 35(8), 1798–1828 (2013)

    work page 2013

  2. [2]

    Springer-Verlag, Berlin, Heidelberg (1990)

    Benveniste, A., Priouret, P., Métivier, M.: Adaptive Algorithms and Stochastic Approximations. Springer-Verlag, Berlin, Heidelberg (1990)

    work page 1990

  3. [3]

    A survey of bias in Machine Learning through the prism of Statistical Parity for the Adult Data Set

    Besse, P., Del Barrio, E., Gordaliza, P., Loubes, J., Risser, L.: A survey of bias in machine learning through the prism of statistical parity for the adult data set. arXiv preprint arXiv:2003.14263 (2020)

    work page Pith review arXiv 2020

  4. [4]

    Bottou, L.: Online learning and stochastic approximations (1998)

    work page 1998

  5. [5]

    In: Proceedings of the 1st Conference on Fairness, Accountability and Transparency, Proceedings of Machine Learning Research, vol

    Buolamwini, J., Gebru, T.: Gender shades: Intersectional accuracy disparities in commercial gender classification. In: Proceedings of the 1st Conference on Fairness, Accountability and Transparency, Proceedings of Machine Learning Research, vol. 81, pp. 77–91 (2018)

    work page 2018

  6. [6]

    Big data 5, 153–163 (2017) 14 Tackling Algorithmic Bias in Neural-Network Classifiers using Wasserstein-2 RegularizationA PREPRINT

    Chouldechova, A.: Fair prediction with disparate impact: A study of bias in recidivism prediction instruments. Big data 5, 153–163 (2017) 14 Tackling Algorithmic Bias in Neural-Network Classifiers using Wasserstein-2 RegularizationA PREPRINT

    work page 2017

  7. [7]

    In: Proceedings of the 27th International Conference on Neural Information Processing Systems - V olume 2, p

    Dauphin, Y .N., Pascanu, R., Gulcehre, C., Cho, K., Ganguli, S., Bengio, Y .: Identifying and attacking the saddle point problem in high-dimensional non-convex optimization. In: Proceedings of the 27th International Conference on Neural Information Processing Systems - V olume 2, p. 2933–2941 (2014)

    work page 2014

  8. [8]

    arXiv preprint arXiv:1806.03195 (2018)

    Del Barrio, E., Gamboa, F., Gordaliza, P., Loubes, J.M.: Obtaining fairness using optimal transport theory. arXiv preprint arXiv:1806.03195 (2018)

    arXiv 2018

Show all 49 references
  1. [9]

    Information and Inference: A Journal of the IMA (2018)

    Del Barrio, E., Gordaliza, P., J.M., L.: A central limit theorem for transportation cost on the real line with application to fairness assessment in machine learning. Information and Inference: A Journal of the IMA (2018)

    2018

  2. [10]

    arXiv preprint arXiv:2005.13755 (2020)

    Del Barrio, E., Gordaliza, P., Loubes, J.M.: Review of mathematical frameworks for fairness in machine learning. arXiv preprint arXiv:2005.13755 (2020)

    2020 arXiv

  3. [11]

    Duchi, J., Hazan, E., Singer, Y .: Adaptive subgradient methods for online learning and stochastic optimization. J. Mach. Learn. Res. 12, 2121–2159 (2011)

    2011

  4. [12]

    In: Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp

    Feldman, M., Friedler, S.A., Moeller, J., Scheidegger, C., Venkatasubramanian, S.: Certifying and removing disparate impact. In: Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 259–268. ACM (2015)

    2015

  5. [13]

    In: Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, p

    Feldman, M., Friedler, S.A., Moeller, J., Scheidegger, C., Venkatasubramanian, S.: Certifying and removing disparate impact. In: Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, p. 259–268 (2015)

    2015

  6. [14]

    In: International Conference on Machine Learning, pp

    Gordaliza, P., Del Barrio, E., Gamboa, F., Loubes, J.M.: Obtaining fairness using optimal transport theory. In: International Conference on Machine Learning, pp. 2357–2365 (2019)

    2019

  7. [15]

    Hardt, M., Price, E., ecprice, Srebro, N.: Equality of opportunity in supervised learning. In: D.D. Lee, M. Sugiyama, U.V . Luxburg, I. Guyon, R. Garnett (eds.) Advances in Neural Information Processing Systems 29, pp. 3315–3323 (2016)

    2016

  8. [16]

    In: Advances in neural information processing systems, pp

    Hardt, M., Price, E., Srebro, N.: Equality of opportunity in supervised learning. In: Advances in neural information processing systems, pp. 3315–3323 (2016)

    2016

  9. [17]

    In: 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp

    He, K., Zhang, X., Ren, S., Sun, J.: Deep residual learning for image recognition. In: 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 770–778 (2016)

    2016

  10. [18]

    2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) pp

    He, K., Zhang, X., Ren, S., Sun, J.: Deep residual learning for image recognition. 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) pp. 770–778 (2016)

    2016

  11. [19]

    In: International Conference on Machine Learning, pp

    Hébert-Johnson, U., Kim, M.P., Reingold, O., Rothblum, G.N.: Calibration for the (computationally-identifiable) masses. In: International Conference on Machine Learning, pp. 1939–1948 (2018)

    2018

  12. [20]

    In: Proc

    Jiang, R., Pacchiano, A., Stepleton, T., Jiang, H., Chiappa, S.: Wasserstein fair classification. In: Proc. Conf. U.A.I. (2019)

    2019

  13. [21]

    In: Proceedings Conference on Uncertainty in Artificial Intelligence (UAI) (2019)

    Jiang, R., Pacchiano, A., Stepleton, T., Jiang, H., Chiappa, S.: Wasserstein fair classification. In: Proceedings Conference on Uncertainty in Artificial Intelligence (UAI) (2019)

    2019

  14. [22]

    Johndrow, J., Lum, K.: An algorithm for removing sensitive information: application to race-independent recidivism prediction. Ann. App. Stat. 13(1) (2019)

    2019

  15. [23]

    In: Proceedings of the 2012th European Conference on Machine Learning and Knowledge Discovery in Databases - V olume Part II, p

    Kamishima, T., Akaho, S., Asoh, H., Sakuma, J.: Fairness-aware classifier with prejudice remover regularizer. In: Proceedings of the 2012th European Conference on Machine Learning and Knowledge Discovery in Databases - V olume Part II, p. 35–50 (2012)

    2012

  16. [24]

    In: International Conference on Machine Learning, pp

    Kearns, M., Neel, S., Roth, A., Wu, Z.S.: Preventing fairness gerrymandering: Auditing and learning for subgroup fairness. In: International Conference on Machine Learning, pp. 2564–2572 (2018)

    2018

  17. [25]

    International Conference on Learning Representations (2014)

    Kingma, D., Ba, J.: Adam: A method for stochastic optimization. International Conference on Learning Representations (2014)

    2014

  18. [26]

    CoRR abs/1412.6980 (2014)

    Kingma, D.P., Ba, J.: Adam: A method for stochastic optimization. CoRR abs/1412.6980 (2014)

    2014 arXiv

  19. [27]

    Komiyama, J., Shimao, H.: Two-stage algorithm for fairness-aware machine learning (2017)

    2017

  20. [28]

    In: Advances in Neural Information Processing Systems 25, pp

    Krizhevsky, A., Sutskever, I., Hinton, G.E.: Imagenet classification with deep convolutional neural networks. In: Advances in Neural Information Processing Systems 25, pp. 1097–1105 (2012)

    2012

  21. [29]

    Kusner, M.J., Loftus, J., Russell, C., Silva, R.: Counterfactual fairness. In: I. Guyon, U.V . Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, R. Garnett (eds.) Advances in Neural Information Processing Systems 30, pp. 4066–4076 (2017) 15 Tackling Algorithmic Bias ...

    2017

  22. [30]

    Neural Comput

    LeCun, Y ., Boser, B., Denker, J.S., Henderson, D., Howard, R.E., Hubbard, W., Jackel, L.D.: Backpropagation applied to handwritten zip code recognition. Neural Comput. 1(4), 541–551 (1989)

    1989

  23. [31]

    In: Proceedings of the IEEE, vol

    LeCun, Y ., Bottou, L., Bengio, Y ., Haffner, P.: Gradient-based learning applied to document recognition. In: Proceedings of the IEEE, vol. 86, pp. 2278–2324 (1998)

    1998

  24. [32]

    In: Proceedings of International Conference on Computer Vision (ICCV) (2015)

    Liu, Z., Luo, P., Wang, X., Tang, X.: Deep learning face attributes in the wild. In: Proceedings of International Conference on Computer Vision (ICCV) (2015)

    2015

  25. [33]

    Information and Inference: A Journal of the IMA (2019)

    Loubes, J.M., Del Barrio, E., Gordaliza, P.: A central limit theorem forlp transportation cost on the real line with application to fairness assessment in machine learning. Information and Inference: A Journal of the IMA (2019)

    2019

  26. [34]

    arXiv preprint arXiv:1811.00247 (2018)

    Manisha, P., Gujar, S.: A neural network framework for fair classifier. arXiv preprint arXiv:1811.00247 (2018)

    2018 arXiv

  27. [35]

    In: Proceedings of the 36th International Conference on Machine Learning, vol

    Mary, J., Calauzènes, C., Karoui, N.E.: Fairness-aware learning for continuous attributes and treatments. In: Proceedings of the 36th International Conference on Machine Learning, vol. 97, pp. 4382–4391 (2019)

    2019

  28. [36]

    University of California Press (2016)

    Mercat-Bruns, M.: Discrimination at Work. University of California Press (2016)

    2016

  29. [37]

    arXiv preprint arXiv:1907.11569 (2019)

    Nguyen, A., Weller, T., Sure-Vetter, Y .: Making neural networks fair. arXiv preprint arXiv:1907.11569 (2019)

    2019 arXiv

  30. [38]

    In: Recent Trends in Learning From Data, pp

    Oneto, L., Chiappa, S.: Fairness in machine learning. In: Recent Trends in Learning From Data, pp. 155–196. Springer (2020)

    2020

  31. [39]

    In: ECML/PKDD (1), pp

    Pérez-Suay, A., Laparra, V ., Mateo-Garcia, G., Muñoz-Marí, J., Gómez-Chova, L., Camps-Valls, G.: Fair kernel learning. In: ECML/PKDD (1), pp. 339–355 (2017)

    2017

  32. [40]

    In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2019)

    Quadrianto, N., Sharmanska, V ., Thomas, O.: Discovering fair representations in the data domain. In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2019)

    2019

  33. [41]

    Raff, E., Sylvester, J.: Gradient reversal against discrimination: A fair neural network learning approach. In: I. Guyon, U.V . Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, R. Garnett (eds.) Proc. IEEE International Conference on Data Science and Advanced Analyt...

    2018

  34. [42]

    In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp

    Ribeiro, M.T., Singh, S., Guestrin, C.: Why Should I Trust You?: Explaining the predictions of any classifier. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1135–1144 (2016)

    2016

  35. [43]

    arXiv preprint arXiv:1801.06229 (2018)

    Rothenhäusler, D., Meinshausen, N., Bühlmann, P., Peters, J.: Anchor regression: heterogeneous data meets causality. arXiv preprint arXiv:1801.06229 (2018)

    2018 arXiv

  36. [44]

    Rumelhart, D.E., Hinton, G.E., Williams, R.J.: Neurocomputing: Foundations of research. chap. Learning Representations by Back-propagating Errors, pp. 696–699 (1988)

    1988

  37. [45]

    Williamson, R., Menon, A.: Fairness risk measures. In: K. Chaudhuri, R. Salakhutdinov (eds.) Proceedings of the 36th International Conference on Machine Learning, vol. 97, pp. 6786–6797 (2019)

    2019

  38. [46]

    arXiv preprint arXiv:1805.08380 (2019)

    Yifan, C., Wuchen, L.: Wasserstein natural gradient in statistical manifolds with continuous sample space. arXiv preprint arXiv:1805.08380 (2019)

    2019 arXiv

  39. [47]

    In: Proceedings of the 26th International Conference on World Wide Web, pp

    Zafar, M.B., Valera, I., Gomez Rodriguez, M., Gummadi, K.P.: Fairness beyond disparate treatment & disparate impact: Learning classification without disparate mistreatment. In: Proceedings of the 26th International Conference on World Wide Web, pp. 1171–1180. International Worl...

    2017

  40. [48]

    In: Proceedings of the 26th International Conference on World Wide Web, pp

    Zafar, M.B., Valera, I., Gomez Rodriguez, M., Gummadi, K.P.: Fairness beyond disparate treatment and dis- parate impact: learning classification without disparate mistreatment. In: Proceedings of the 26th International Conference on World Wide Web, pp. 1171–1180 (2017)

    2017

  41. [49]

    In: Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, vol

    Zafar, M.B., Valera, I., Rogriguez, M.G., Gummadi, K.P.: Fairness Constraints: Mechanisms for Fair Classification. In: Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, vol. 54, pp. 962–970 (2017) 16 Tackling Algorithmic Bias in Neural-N...

    2017

Pith tools

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