Pith. sign in

REVIEW 3 major objections 5 minor 42 references

Risk-averse Fair Multi-class Classification

T0 review · 3 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

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

Pith's one-line read This paper claims that replacing expected misclassification error with a systemic coherent risk measure in multi-class classification yields classifiers that generalize better on noisy, scarce, or mislabeled data and can enforce fairness ac

desk verdict A novel risk-averse multi-class framework with a plausible fairness mechanism, but the kernel dual derivation has a load-bearing sign error and an invalid WLOG, so the kernel experiments don't support the claims. read the letter →

arxiv 2509.05771 v2 pith:MDWX5IC4 submitted 2025-09-06 stat.ML cs.LGmath.OC

Darinka Dentcheva , Xiangyu Tian This is my paper · ORCID
classification stat.MLcs.LGmath.OC MSC 68T0590C1562H30
keywords coherentriskmeasuressystemicmulti-classclassificationmean-upper-semi-deviationfairnesskernelmethodsstochasticprogrammingregularizeddecomposition
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 tries to establish that multi-class classification should minimize a systemic coherent risk measure of the class errors rather than their expectation. It argues that when data are noisy, scarce, or mislabeled, the risk-averse objective produces classifiers with lower out-of-sample risk and better F1/AUC performance than the standard multi-class method, and that the advantage grows with the number of classes. A second claim is that choosing a mean-semi-deviation aggregation of per-class risks puts a penalty on classes whose risk exceeds the average, which enforces fairness across classes and across sensitive groups without the usual performance trade-off. If true, this gives a single training objective that combines robustness and fairness in multi-class problems.

What carries the argument

The systemic coherent risk measure for random vectors, defined by axioms A1-A4 and represented as ϱ[X] = sup_{ζ∈A_ϱ} ⟨ζ, X⟩, with the mean-upper-semi-deviation aggregation ϱ_sys[Z] = Σ p_i ϱ[Z_i] + κ (Σ p_i (ϱ[Z_i] − Σ p_j ϱ[Z_j])_+^p)^{1/p}. The semi-deviation term is the fairness mechanism: it is small only when all class risks are close to the average. The numerical workhorse is a regularized risk-averse multi-cut decomposition method for the resulting two-stage stochastic program, and for kernels, the dual problem and decision rule express the classifier only through kernel evaluations with training points.

What would settle it

Train the proposed kernel risk-averse method and the linear risk-averse method with intercepts on a synthetic linearly separable multi-class problem whose optimal separating hyperplanes have nonzero intercepts, for instance classes separated by a line not through the origin. If the kernel implementation with a linear kernel cannot reproduce the linear method's accuracy, or if deriving the dual without the γ_i = 0 assumption changes the decision rule, the assumption is load-bearing.

Watch

Extended reading notes

Core claim

The central claim is that replacing the expected misclassification error in a multi-class SVM-style objective with a coherent systemic risk measure changes the learned classifier in a way that helps exactly when the training environment is unreliable. The paper proposes two risk-averse versions of the benchmark method: one with linear aggregation of per-class risk measures, and a two-stage formulation where an outer coherent risk measure aggregates class-level risks, for example the mean-upper-semi-deviation. The outer mean-semi-deviation term penalizes any class whose risk is above the average of all classes, which the paper identifies as a fairness-forcing mechanism. The paper supports the

Load-bearing premise

The load-bearing premise is that setting the intercepts γ_i to zero in the kernel formulation is a harmless normalization; the paper does not augment the feature map with a constant coordinate, so if that premise fails, the derived kernel classifier is a restricted model and the kernel method's theoretical guarantee and experimental results are not accounted for.

Editorial extensions

If this is right

  • Lower test risk despite higher training risk: the risk-averse classifier is claimed to generalize better to unknown data when training data are mislabeled or features are missing.
  • The robustness gap widens as the number of classes grows, making the method more suitable for high-risk many-class problems.
  • Using mean-semi-deviation as the outer risk measure forces per-class risks toward their average, providing fairness across classes and, via contextual risk measures, across sensitive groups without a separate fairness constraint.
  • The kernel extension keeps the kernel trick intact: prediction uses only kernel evaluations with training points, so nonlinear decision boundaries are available in the risk-averse setting.
  • The proposed regularized decomposition method converges to an optimal solution of the two-stage risk-averse problem under the stated assumptions.

Reading between the lines

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

  • The kernel derivation's 'without loss of generality, γ_i = 0' is not a free normalization: unless the feature map is augmented with a constant coordinate, the derived dual and decision rule restrict the classifier to separating hyperplanes through the origin, a different hypothesis class from the intended multiclass problem. Locating Section 3 before Eq. (9), this gap needs repair before the kerne
  • The paper acknowledges that the two-stage formulation ideally requires the constraints ∥v_i∥ = 1 but the implemented method drops them; the effect of that relaxation on the fairness interpretation of the semi-deviation risk is left unanalyzed.
  • The no-trade-off claim is demonstrated under corrupted-data conditions; the paper's own clean-data results show the fairness baseline enforcing fairness more strongly, so the trade-off likely reappears when data are reliable.
  • The fairness section refers to a modified objective function with an unresolved '(??)' marker, so the exact formulation for those results cannot be independently reconstructed from the paper alone.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper proposes a risk-averse framework for multi-class classification based on systemic coherent risk measures. The authors extend the Crammer-Singer multi-class SVM by replacing the expected misclassification error with mean-upper-semideviation risk measures, first under linear aggregation (Section 2) and then in a kernel setting (Section 3). A two-stage stochastic programming formulation with nonlinear risk aggregation is introduced in Section 4, together with a regularized multi-cut decomposition method and a convergence claim (Theorem 1). Section 5 argues that the mean-semi-deviation term forces fairness, and Section 6 reports experiments on MNIST, Electrical Fault detection, and Drug Consumption datasets claiming that the risk-averse methods are more robust to noisy/mislabeled data and generalize better to unknown data than the risk-neutral baseline.

Significance. If the technical derivations were correct, the paper would offer a unified training objective that couples robustness to noisy data with fairness enforcement, and it would extend the Crammer-Singer method to kernels in a risk-averse way. The axiomatic embedding of fairness into a coherent systemic risk measure is conceptually appealing, and the numerical study is extensive, with paired comparisons and stochastic-dominance analysis. However, the central kernel derivation is mathematically invalid, and the convergence theorem does not cover the problem that is actually solved. These issues undermine the paper's core claims, including the advertised better generalization of the kernel method in Section 6.4 and the theoretical support for the two-stage method.

major comments (3)
  1. [Section 3, before Eq. (9)] The statement 'without loss of generality, we may assume that γ_i=0' is false for the Crammer-Singer problem (6)/(8). Only a common additive shift of all γ_i can be removed; the per-class intercepts remain essential. Dropping γ_i forces every separating hyperplane to pass through the origin of the feature space, and the paper never augments φ with a constant coordinate. Consequently, the kernel decision rule in Eq. (19) and Proposition 1 do not implement the risk-averse analogue of the original Crammer-Singer classifier. The kernel experiments in Section 6.4 are therefore testing a different, restricted model.
  2. [Section 3, Eq. (18)] The displayed 'dual' problem (18) is stated as a minimization of a concave quadratic (negative semidefinite quadratic form plus linear terms) over a polyhedron. For the convex primal (9), the Lagrangian dual is a concave function that should be maximized. A concave minimization is not equivalent to the Lagrangian dual; it is a nonconvex QP and is not what a standard convex solver would solve. Thus Proposition 1 and the numerical kernel results in Section 6.4 cannot be regarded as validating the method. The sign error or misstatement of the dual problem is load-bearing for the kernel contribution.
  3. [Section 4, Theorem 1 and master problem (28)] The text states that a proper evaluation requires the non-convex constraints ∥v_i∥=1, but then says the proposed method 'ignores them.' The regularized master problem (28) and the convergence proof in Theorem 1 concern the unconstrained soft-margin problem, not problem (21) with the unit-norm constraints. The proof asserts convergence to an optimal solution of (21) without addressing this discrepancy. As written, the convergence claim does not apply to the problem whose properties motivated the regularization, leaving the two-stage method without a valid theoretical guarantee.
minor comments (5)
  1. [Section 2, Eq. (6)] The constraint 'Zi ≥0 i=0,...,N' appears to be a typo; it should be i=1,...,N. The same indexing issue appears in Eq. (8).
  2. [Section 3, Eq. (16)] In the expansion of ∥v_i∥², the cross term is missing the factor 2: the last term should be '-2(∑ M_i^j)^T K_ij (∑ M_j^i)' to be consistent with Eq. (17).
  3. [Section 6.3] The text refers to 'TPR and NPR' when discussing ROC curves; the second quantity should presumably be FPR. Also, 'Guassian' is a typo in Section 6.4.
  4. [Section 6.5] The reference to 'the modified objective function (??)' is unresolved. The reader cannot identify which formulation replaces the original two-stage objective.
  5. [Section 6.4 / Figure 6] The kernel experiment reports only CDF plots without quantitative F1 values or error bars; the claim that the risk-averse kernel method 'produces a remarkable classification result' would be stronger with concrete numbers and hyperparameter settings.

Circularity Check

1 steps flagged · score 2.0 of 10

Minor self-definitional circularity in the fairness claim; the robustness and generalization claims are empirical and not circular.

  1. self definitional [Section 2, Eq. (5) and Section 5 (Risk-averse classification and fairness)]
    "This representation shows that this risk measure is an aggregation of the individual risk of the components, which puts an additional penalty on the deviation of the individual risks from that average. This property is crucial to our treatment of fairness in classification. ... We can call it a fairness term since it prevents any class from being overlooked and having a risk too much higher than other classes. We argue that this is a very attractive property that can force fairness in classification."

    The 'fairness' the model is said to 'force' is the same quantity as the mean-semi-deviation term in Eq. (5), which penalizes class-risk deviations by construction. Calling this explicit penalty a 'fairness term' and concluding that it 'can force fairness in classification' restates the objective's definition rather than deriving a consequence: if fairness is defined as closeness of class risks, then a loss containing that penalty enforces it by definition. The later fairness experiments do use an external metric (statistical parity), so the circularity is partial and localized; it does not infect the held-out generalization claims.

full rationale

The paper's main derivation chain—risk-averse multi-class SVM, kernel dual, and the two-stage decomposition method—is not circular in the sense of a prediction being forced by its own fitted inputs. The systemic-risk representation (1) and the claim that composition (3) satisfies the axioms are imported from prior work [1,11]; these are self-citations but they state a published representation theorem and do not by themselves force the paper's empirical generalization results. The kernel section contains a false 'without loss of generality' assumption (γ_i=0) and a dual written as concave minimization, but these are mathematical-correctness flaws, not circularity. The one genuinely definitional step is the fairness claim: the mean-semi-deviation term is introduced as a penalty on deviation from average class risk and then relabeled as 'fairness,' so the assertion that the formulation 'forces fairness' is true by construction. However, the paper's strongest advertised result—better performance on unknown data—is supported by held-out test comparisons and is not an artifact of the risk-measure definition. Hence the overall circularity score is low.

Assumptions & free parameters 4 free parameters · 5 assumptions · 1 invented entities

The central claims rest on standard risk-measure theory (dual representations, composition properties) imported from self-cited prior work, plus several experiment-specific free parameters (risk level, regularization, class weights, kernel bandwidth) and an invalid intercept-dropping assumption in the kernel derivation. No new physical entities are introduced; the contextual risk measure is a formal composition of existing constructs.

free parameters (4)
  • risk level c_i = 0.05, 0.35, 0.65, 0.95 in experiments
    Coefficient of the mean-upper-semideviation penalty in the class risk measures; performance of the method is highly sensitive to its value and no principled selection rule is given (Section 6.1).
  • regularization parameter sigma = not reported
    Appears in primal objectives (6), (8), (9) and dual (18); experiment setup does not state how it was selected or whether it was tuned per method.
  • class weights lambda_i / probabilities p_i = uniform in experiments
    Weights in the linear risk aggregation (8) and outer measure (4); paper chooses uniform mass without loss of generality but acknowledges weights matter.
  • kernel hyperparameters (RBF/Laplacian gamma) = not stated in text; Figure 6 uses different parameter values
    Kernel width parameters in Section 6.4 influence results; no selection procedure reported.
assumptions (5)
  • standard math Coherent risk measures admit the dual representation ϱ[X]=sup_{ζ∈Aϱ} ⟨ζ,X⟩
    Invoked in Eq. (1), from [1, 11]; standard result.
  • standard math The systemic risk measure defined by (3) satisfies axioms A1-A4
    Stated in Section 2, proven in [1]; used as foundation for the formulations.
  • standard math The regularized decomposition method of Ruszczyński [36] converges and applies to the proposed two-stage problem
    Basis of Theorem 1; the paper only partly verifies the assumptions.
  • ad hoc to paper The intercept gamma_i can be set to zero without loss of generality in the kernel classifier
    Section 3 before Eq. (9); actually a real restriction unless the feature map is augmented with a constant feature.
  • domain assumption Empirical distributions on training sets correctly represent the loss distribution for the risk measure
    Implicit in using empirical risk estimates of coherent risk measures on finite samples.
invented entities (1)
  • contextual risk-measure ϱ_c composition
    purpose: Enforce fairness across groups defined by a sensitive feature by composing conditional risk measures.
    New construction in Section 5; no external validation of the construct itself; acts as a modeling device.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Risk-averse Fair Multi-class Classification." pith.science (2026). https://pith.science/paper/MDWX5IC4

@misc{pith2026250905771,
  author       = {Pith},
  title        = {Pith review of: Risk-averse Fair Multi-class Classification},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MDWX5IC4}},
  note         = {Machine review of arXiv:2509.05771}
}
read the original abstract

We develop a new classification framework based on the theory of coherent risk measures and systemic risk. The proposed approach is suitable for multi-class problems when the data is noisy, scarce (relative to the dimension of the problem), and the labeling might be unreliable. In the first part of our paper, we provide the foundation of the use of systemic risk models and show how to apply it in the context of linear and kernel-based multi-class problems. More advanced formulation via a system-theoretic approach with non-linear aggregation is proposed, which leads to a two-stage stochastic programming problem. A risk-averse regularized decomposition method is designed to solve the problem. We use a popular multi-class method as a benchmark in the performance analysis of the proposed classification methods. We illustrate our ideas by proposing several generalization of that method by the use of coherent measures of risk. The viability of the proposed risk-averse methods are supported theoretically and numerically. Additionally, we demonstrate that the application of systemic risk measures facilitates enforcing fairness in classification. Analysis and experiments regarding the fairness of the proposed models are carefully conducted. For all methods, our numerical experiments demonstrate that they are robust in the presence of unreliable training data and perform better on unknown data than the methods minimizing expected classification errors. Furthermore, the performance improves when the number of classes increases.

Figures

Figures reproduced from arXiv: 2509.05771 by the authors.

Figure 1
Figure 1. CDF of the average F1 scores of the risk-neutral baseline and the risk-averse method with different risk levels [PITH_FULL_IMAGE:figures/full_fig_p013_1.png] view at source ↗
Figure 2
Figure 2. CDF of the average F1 scores of the risk-neutral baseline and the risk-averse method with different risk levels [PITH_FULL_IMAGE:figures/full_fig_p015_2.png] view at source ↗
Figure 3
Figure 3. CDF of the average F1 scores of the risk-neutral baseline and the risk-averse method with different risk [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: CDF of the average F1 scores of the risk-neutral baseline and the risk-averse method with different risk levels [PITH_FULL_IMAGE:figures/full_fig_p018_4.png]
Figure 5
Figure 5. Figure 5: For the 10-class experiment, we show the results of the best and the worst class based on the difference [PITH_FULL_IMAGE:figures/full_fig_p020_5.png]
Figure 6
Figure 6. Figure 6: Results of RBF and Laplacian kernels. 24 [PITH_FULL_IMAGE:figures/full_fig_p024_6.png]
Figure 7
Figure 7. Figure 7: Comparison of fairness results without data pollution. [PITH_FULL_IMAGE:figures/full_fig_p025_7.png]
Figure 8
Figure 8. Figure 8: Comparison of fairness results with data pollution. [PITH_FULL_IMAGE:figures/full_fig_p025_8.png]
Figure 9
Figure 9. Figure 9: Comparison of fairness results with modified risk function. [PITH_FULL_IMAGE:figures/full_fig_p026_9.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

42 extracted references · 34 canonical work pages

  1. [1]

    On risk evaluation and control of distributed multi-agent systems.Journal of Optimization Theory and Applications, pages 1–30, 2024

    Aray Almen and Darinka Dentcheva. On risk evaluation and control of distributed multi-agent systems.Journal of Optimization Theory and Applications, pages 1–30, 2024

    work page 2024

  2. [2]

    Coherent measures of risk.Mathematical finance, 9(3):203–228, 1999

    Philippe Artzner, Freddy Delbaen, Jean-Marc Eber, and David Heath. Coherent measures of risk.Mathematical finance, 9(3):203–228, 1999

    work page 1999

  3. [3]

    A general and adaptive robust loss function

    Jonathan T Barron. A general and adaptive robust loss function. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 4331–4339, 2019

    work page 2019

  4. [4]

    Ben-Tal, S

    A. Ben-Tal, S. Bhadra, C. Bhattacharyya, et al. Chance constrained uncertain classification via robust optimiza- tion.Mathematical Programming, 127:145–173, 2011

    work page 2011

  5. [5]

    Robust classification.Journal on Optimization, 1:2–34, 2018

    Dimitris Bertsimas, Jack Dunn, Colin Pawlowski, and Ying Daisy Zhuo. Robust classification.Journal on Optimization, 1:2–34, 2018

    work page 2018

  6. [6]

    Support vector classification with input data uncertainty

    Jinbo Bi and Tong Zhang. Support vector classification with input data uncertainty. InAdvances in Neural Information Processing Systems, pages 161–168, Cambridge, 2005. MIT Press

    work page 2005

  7. [7]

    Random forests.Machine learning, 45:5–32, 2001

    Leo Breiman. Random forests.Machine learning, 45:5–32, 2001

    2001

  8. [8]

    Fair regression with wasserstein barycenters.Advances in Neural Information Processing Systems, 33:7321–7331, 2020

    Evgenii Chzhen, Christophe Denis, Mohamed Hebiri, Luca Oneto, and Massimiliano Pontil. Fair regression with wasserstein barycenters.Advances in Neural Information Processing Systems, 33:7321–7331, 2020

    work page 2020

Show all 42 references
  1. [9]

    Crammer and Y

    K. Crammer and Y . Singer. On the algorithmic implementation of multiclass kernel-based vector machines. Journal of Machine Learning Research, 2:265–292, 2001

    2001

  2. [10]

    Coherent risk measures on general probability spaces.Advances in Finance and Stochastics, pages 1–37, March 2000

    Freddy Delbaen. Coherent risk measures on general probability spaces.Advances in Finance and Stochastics, pages 1–37, March 2000

    2000

  3. [11]

    Springer Series in Operations Research and Financial Engineering

    Darinka Dentcheva and Andrzej Ruszczynski.Risk-Averse Optimization and Control Theory and Methods. Springer Series in Operations Research and Financial Engineering. Springer Cham, 2024

    2024

  4. [12]

    Empirical risk minimization under fairness constraints.Advances in neural information processing systems, 31, 2018

    Michele Donini, Luca Oneto, Shai Ben-David, John S Shawe-Taylor, and Massimiliano Pontil. Empirical risk minimization under fairness constraints.Advances in neural information processing systems, 31, 2018

    2018

  5. [13]

    UCI machine learning repository, 2019

    Dheeru Dua and Casey Graff. UCI machine learning repository, 2019. University of California, Irvine, School of Information and Computer Sciences

    2019

  6. [14]

    Electrical fault detection and classification

    Sathya Prakash E. Electrical fault detection and classification

  7. [15]

    Cer- tifying and removing disparate impact

    Michael Feldman, Sorelle A Friedler, John Moeller, Carlos Scheidegger, and Suresh Venkatasubramanian. Cer- tifying and removing disparate impact. Inproceedings of the 21th ACM SIGKDD international conference on knowledge discovery and data mining, pages 259–268, 2015

    2015

  8. [16]

    A confidence-based approach for balancing fairness and accuracy

    Benjamin Fish, Jeremy Kun, and Ádám D Lelkes. A confidence-based approach for balancing fairness and accuracy. InProceedings of the 2016 SIAM international conference on data mining, pages 144–152. SIAM, 2016

    2016

  9. [17]

    Walter De Gruyter, 2011

    Hans Föllmer and Alexander Schied.Stochastic Finance: An Introduction in Discrete Time, 3rd Edition. Walter De Gruyter, 2011

    2011

  10. [18]

    A decision-theoretic generalization of on-line learning and an application to boosting.Journal of computer and system sciences, 55(1):119–139, 1997

    Yoav Freund and Robert E Schapire. A decision-theoretic generalization of on-line learning and an application to boosting.Journal of computer and system sciences, 55(1):119–139, 1997

    1997

  11. [19]

    Greedy function approximation: a gradient boosting machine.Annals of statistics, pages 1189–1232, 2001

    Jerome H Friedman. Greedy function approximation: a gradient boosting machine.Annals of statistics, pages 1189–1232, 2001

    2001

  12. [20]

    Ghaoui and H

    L.E. Ghaoui and H. Lebret. Robust solutions to least-squares problems with uncertain data.SIAM Journal on Matrix Analysis and Applications, 18:1035–1064, 1997

    1997

  13. [21]

    Robust loss functions under label noise for deep neural networks

    Aritra Ghosh, Himanshu Kumar, and P Shanti Sastry. Robust loss functions under label noise for deep neural networks. InProceedings of the AAAI conference on artificial intelligence, volume 31, 2017

    2017

  14. [22]

    Support vector machines based on convex risk functions and general norms

    Jun-ya Gotoh and Stan Uryasev. Support vector machines based on convex risk functions and general norms. Annals of Operations Research, 249:301–328, 2017. 22 Risk-averse Fair Multi-class Classification

    2017

  15. [23]

    Two-stage portfolio optimization with higher-order conditional measures of risk.Annals of Operations Research, 229:409–427, 2015

    Sıtkı Gülten and Andrzej Ruszczy ´nski. Two-stage portfolio optimization with higher-order conditional measures of risk.Annals of Operations Research, 229:409–427, 2015

    2015

  16. [24]

    Data preprocessing techniques for classification without discrimination

    Faisal Kamiran and Toon Calders. Data preprocessing techniques for classification without discrimination. Knowledge and information systems, 33(1):1–33, 2012

    2012

  17. [25]

    Gert R. G. Lanckriet, Laurent El Ghaoui, Chiranjib Bhattacharyya, and Michael I. Jordan. A robust minimax approach to classification.Journal of Machine Learning Research, 3:555–582, 2002

    2002

  18. [26]

    Robust classification via mom minimization.Ma- chine learning, 109:1635–1665, 2020

    Guillaume Lecué, Matthieu Lerasle, and Timlothée Mathieu. Robust classification via mom minimization.Ma- chine learning, 109:1635–1665, 2020

    2020

  19. [27]

    Y . Lee, Y . Lin, and G. Wahba. Multicategory support vector machines: Theory and application to the classifica- tion of microarray data and satellite radiance data.Journal of the American Statistical Association, 99(465):67– 81, 2004

    2004

  20. [28]

    Learning with confident examples: Rank pruning for robust classification with noisy labels.arXiv preprint arXiv:1705.01936, 2017

    Curtis G Northcutt, Tailin Wu, and Isaac L Chuang. Learning with confident examples: Rank pruning for robust classification with noisy labels.arXiv preprint arXiv:1705.01936, 2017

    2017 arXiv

  21. [29]

    Norton, A

    M. Norton, A. Mafusalov, and S. Uryasev. Soft margin support vector classification as buffered probability minimization.Journal of Machine Learning Research, 18:1–43, 2017

    2017

  22. [30]

    Making deep neural networks robust to label noise: A loss correction approach

    Giorgio Patrini, Alessandro Rozza, Aditya Krishna Menon, Richard Nock, and Lizhen Qu. Making deep neural networks robust to label noise: A loss correction approach. InProceedings of the IEEE conference on computer vision and pattern recognition, pages 1944–1952, 2017

    1944

  23. [31]

    Pflug and W

    G.Ch. Pflug and W. Römisch.Modeling, Measuring and Managing Risk. World Scientific, Singapore, 2007

    2007

  24. [32]

    On fairness and calibration

    Geoff Pleiss, Manish Raghavan, Felix Wu, Jon Kleinberg, and Kilian Q Weinberger. On fairness and calibration. Advances in neural information processing systems, 30, 2017

    2017

  25. [33]

    Fairbatch: Batch selection for model fairness.arXiv preprint arXiv:2012.01696, 2020

    Yuji Roh, Kangwook Lee, Steven Euijong Whang, and Changho Suh. Fairbatch: Batch selection for model fairness.arXiv preprint arXiv:2012.01696, 2020

    2012 arXiv

  26. [34]

    Ruszczy ´nski and A

    A. Ruszczy ´nski and A. Shapiro. Optimization of risk measures. In G. Calafiore and F. Dabbene, editors,Prob- abilistic and Randomized Methods for Design under Uncertainty, pages 117–158. Springer-Verlag, London, 2005

    2005

  27. [35]

    Ruszczy ´nski and A

    A. Ruszczy ´nski and A. Shapiro. Optimization of convex risk functions.Mathematics of Operations Research, 31:433–452, 2006

    2006

  28. [36]

    A regularized decomposition method for minimizing a sum of polyhedral functions

    Andrzej Ruszczy ´nski. A regularized decomposition method for minimizing a sum of polyhedral functions. Mathematical programming, 35:309–333, 1986

    1986

  29. [37]

    Metrizing fairness.arXiv preprint arXiv:2205.15049, 2022

    Yves Rychener, Bahar Taskesen, and Daniel Kuhn. Metrizing fairness.arXiv preprint arXiv:2205.15049, 2022

    2022 arXiv

  30. [38]

    Generalised dice overlap as a deep learning loss function for highly unbalanced segmentations

    Carole H Sudre, Wenqi Li, Tom Vercauteren, Sebastien Ourselin, and M Jorge Cardoso. Generalised dice overlap as a deep learning loss function for highly unbalanced segmentations. InDeep Learning in Medical Image Analysis and Multimodal Learning for Clinical Decision Support: T...

    2017

  31. [39]

    A tun- able loss function for robust classification: Calibration, landscape, and generalization.IEEE Transactions on Information Theory, 68(9):6021–6051, 2022

    Tyler Sypherd, Mario Diaz, John Kevin Cava, Gautam Dasarathy, Peter Kairouz, and Lalitha Sankar. A tun- able loss function for robust classification: Calibration, landscape, and generalization.IEEE Transactions on Information Theory, 68(9):6021–6051, 2022

    2022

  32. [40]

    C. A. Vitt, D. Dentcheva, and H. Xiong. Risk-averse classification.Annals of Operations Research, pages 1–35, 2019

    2019

  33. [41]

    Weston and C

    J. Weston and C. Watkins. Support vector machines for multi-class pattern recognition. InProceedings of the Seventh European Symposium On Artificial Neural Networks, pages 219–224, 1999

    1999

  34. [42]

    Learning fair representations

    Rich Zemel, Yu Wu, Kevin Swersky, Toni Pitassi, and Cynthia Dwork. Learning fair representations. InInter- national conference on machine learning, pages 325–333. PMLR, 2013. 23 Risk-averse Fair Multi-class Classification Figure 6: Results of RBF and Laplacian kernels. 24 Risk...

    2013

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.