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FedSPM treats dual heterogeneity as a resource: client-specific latent mixtures plus density-ratio routing improve both query routing and prediction in federated learning.

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2026-07-11 21:47 UTC pith:CHTNGMVH

load-bearing objection Solid methods paper: client-specific DRM-EL mixtures for routing under dual heterogeneity, with a careful federated EM and a convergence transfer that honestly conditions on bridge errors. the 3 major comments →

arxiv 2607.04085 v1 pith:CHTNGMVH submitted 2026-07-05 cs.LG cs.AIcs.DC

FedSPM: Routing-Enabled Federated Learning under Dual Heterogeneity via Semiparametric Mixture

Zijian Wang , Pengfei Li , Guangyu Yang , Qiong Zhang This is my paper
classification cs.LG cs.AIcs.DC
keywords federated learningdual heterogeneityrouting-predictionsemiparametric mixturedensity ratio modelempirical likelihoodfederated EMmedical imaging
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Routing-prediction federated learning turns differences across clients into a strength by sending each new query to the client whose data best match it. Most such methods still treat each client as one homogeneous population, so they miss latent subtypes inside a hospital, device fleet, or clinic. FedSPM models every client as a mixture of latent components; each component has its own predictive head and a feature distribution written as a density ratio against a shared nonparametric baseline estimated by empirical likelihood. A federated EM algorithm optimizes a tractable surrogate while still converging to a stationary point of the exact profiled objective at the usual O(1/√T) rate when surrogate bridge errors stay controlled. On controlled image benchmarks with injected dual heterogeneity and on the real multi-center Fed-ISIC2019 skin-lesion dataset, the method improves both routing accuracy and system-level prediction over strong federated baselines. The result is a practical way to turn unobserved within-client structure into better server-side routing and better client-side predictions.

Core claim

Under dual heterogeneity—simultaneous inter-client distribution shift and latent intra-client subpopulations—representing each client by client-specific semiparametric mixture components (shared embeddings plus client-specific predictive heads, and density-ratio feature models relative to a shared empirical-likelihood baseline) jointly improves server-side routing of external queries and the accuracy of the selected client’s predictions, while a federated EM procedure that optimizes a tractable surrogate still converges for the exact profiled objective at the standard rate when the surrogate errors are controlled.

What carries the argument

FedSPM: a client-specific semiparametric mixture in which each latent component pairs a predictive distribution with a density-ratio model (DRM) of the feature distribution relative to a common nonparametric baseline estimated by empirical likelihood, optimized by federated EM that substitutes a tractable surrogate for the profiled DRM block.

Load-bearing premise

The proof that optimizing the tractable surrogate still drives the exact profiled objective to a stationary point rests on two bridge assumptions that are only checked empirically, not derived from the model: along the training path the surrogate gradients and function values must stay close enough to the true ones that their average errors do not spoil the O(1/√T) rate.

What would settle it

If, on the dual-heterogeneity image suites or Fed-ISIC2019, FedSPM’s system accuracy, average accuracy, and routing accuracy fail to exceed those of the strongest routing baseline (FedDRM) and the strongest mixture baselines once model capacity is equalized, or if the numerically computed bridge errors grow with rounds so that the averaged gradient of the profiled objective stops decreasing, the central claim fails.

Watch this falsifier — get emailed when new claim-graph text bears on it.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The paper proposes FedSPM, a routing-enabled federated learning framework for dual heterogeneity (inter-client plus latent intra-client structure). Each client is modeled as a mixture of client-specific components; each component has a predictive head (shared embeddings, client-specific classifiers) and a feature model given by density ratios relative to a shared nonparametric baseline estimated by empirical likelihood. A federated EM algorithm optimizes a tractable DRM surrogate with analytic Lagrange multipliers at critical points, and Theorem 1 claims an O(1/√T) stationary-point rate for the exact profiled objective under local SGD with momentum when gradient and function-value bridge errors are controlled. Controlled dual-heterogeneity benchmarks (FMNIST, CIFAR-10/100) and a real Fed-ISIC2019 case study report gains in system and average accuracy over global, personalized, mixture, and routing baselines, with code released.

Significance. If the results hold, the work meaningfully extends routing-prediction FL beyond the usual homogeneous-client assumption and gives a concrete semiparametric recipe (client-specific mixtures + DRM-EL) that jointly targets routing and prediction. Strengths include: full derivations of profile EL, EM, and the analytic λ form (App. C); a multi-lemma convergence analysis for local SGD with momentum; explicit 1× vs C× capacity controls; ablations on α_inter, α_intra, C, and μ; a real multi-center medical evaluation with routing accuracy; and public code. The dual-heterogeneity framing and the surrogate-to-profiled transfer are of genuine interest to federated learning and semiparametric statistics audiences.

major comments (3)
  1. [Sec. 2.4, Thm. 1, Assumps. 4–5, Fig. 2, App. C.5–C.6, D.4] Theorem 1 (Sec. 2.4) transfers the O(1/√T) rate from the tractable surrogate êf^(t) to the exact profiled objective F only through Assumptions 4–5 (gradient and function-value bridges). App. C.5 shows that critical points of Q₂ and êQ₂ coincide via λ_ic = n⁻¹∑_j w_ijc, and Lemmas 1–2 give exact EM bridges at the current parameter, but there is no analytic control of gradient alignment or one-step value mismatch away from critical points under the DRM-EL constraints (Eqs. 5–6). The only support is post-hoc numerical estimation of ˆε^(t), ˆδ^(t) on FMNIST (Fig. 2, App. D.4). Because the abstract and Theorem 1 advertise convergence of the exact profiled objective, either (i) multi-dataset bridge diagnostics (CIFAR, Fed-ISIC2019) with reported ¯ε_T, ¯δ_T, or (ii) a clearer scoping of the theorem as conditional on empirically verified bridges with failure modes, is needed before the claim is
  2. [Tables 1–2, Fig. 4, Sec. 3.2] Tables 1–2 report system and average accuracy but not routing accuracy on the controlled benchmarks, even though routing is central to the paradigm and only FedGMM/FedDRM/FedSPM are routing-capable. Fig. 4 reports routing accuracy only for Fed-ISIC2019. Without benchmark routing accuracy (and, ideally, confusion among clients under varying α_inter/α_intra), it is hard to attribute system-accuracy gains to improved routing versus improved local predictors. Adding routing accuracy (and a simple oracle-routing upper bound) to the main tables would make the dual-heterogeneity claim falsifiable.
  3. [Sec. 2.1–2.3, Algorithm 1 (App. B)] In Algorithm 1 and Sec. 2.3, every client optimizes the full coupled DRM block (γ_ic, ξ_ic for all i, plus shared ν) using only local data plus the scalar summaries {τ_ic}, then the server averages all of (θ, γ, ξ, ν). The text calls (γ_ic, ξ_ic) “client-specific,” yet they are treated as globally averaged parameters of a joint objective. This is internally consistent as federated optimization of a global DRM, but it should be stated explicitly: which parameters are truly local (π_i, α_i, β_i) versus globally coupled and averaged, and whether averaging other clients’ tilting parameters can distort client-specific covariate models under severe dual heterogeneity. A short ablation (freeze other clients’ (γ,ξ) vs. joint update) would clarify that the design is intentional rather than an aggregation artifact.
minor comments (6)
  1. [Remark 1, Sec. 3] Remark 1 correctly flags non-identifiability of components; consider adding a short note in the experiments on whether learned responsibilities correlate with the synthetic component labels (even if not required for the method).
  2. [Fig. 1, Introduction] Fig. 1 is referenced as an overview but is not described in text beyond a caption pointer; a one-sentence walk-through of the inference path (route then mixture prediction) would help readers who skip the figure.
  3. [Eq. (10), Sec. 2.3] Notation: ρ_i is sample fraction in routing (Eq. 10) and aggregation; state once that it is treated as known (or estimated from n_i) at inference.
  4. [App. A, Sec. 2.2] Related work on DRM-EL (App. A) is useful; a brief pointer in the main text to the dual-EL equivalence (Keziou & Leoni-Aubin) would help readers who wonder why the surrogate is tractable.
  5. [Throughout] Typos / polish: “App. C.1 for the derivation” style is fine; ensure consistent use of eQ vs êQ / ef vs êf in the main text vs. appendix; arXiv ID and “Code is available here” should match the GitHub URL already given.
  6. [Tables 1–2, Fig. 4] Only three seeds are reported; if space allows, note variance of routing accuracy on Fed-ISIC2019 as well as classification metrics.

Circularity Check

1 steps flagged

No definitional circularity: convergence of F is conditional on explicit bridge assumptions, not equated to the surrogate by construction; mild FedDRM self-lineage is scaffolding only.

specific steps
  1. self citation load bearing [App. A Related Work; Introduction (routing-prediction paradigm)]
    "Recently, Wang et al.[40] first introduced DRM-based EL into FL and established a routing-prediction FL paradigm, thereby enabling explicit client routing together with personalized representation learning. However, this paradigm treats each client as internally homogeneous."

    FedDRM [40] shares authors (Z. Wang, Q. Zhang) with the present paper and supplies the routing-prediction framing that FedSPM extends. This is ordinary prior-work scaffolding, not a uniqueness theorem or the sole support for Theorem 1 or the dual-heterogeneity experiments; it does not force the mixture/EL/EM results by construction. Flagged only as mild self-lineage, not as a load-bearing circular reduction.

full rationale

Walked the load-bearing chain: (i) profile log-EL pℓ and complete-data Q are derived from the DRM-EL mixture (Eqs. 1–6, App. C.1–C.3); (ii) the tractable surrogate êQ₂ is justified by showing critical points of Q₂ and êQ₂ coincide via λ_ic = n⁻¹∑_j w_ijc (App. C.5), not by redefining the objective; (iii) Theorem 1 transfers stationarity rates from êf^(t) to F only under Assumptions 4–5 (gradient/function-value bridges), which are stated as assumptions and checked empirically by numerically solving the true Lagrange system (6) rather than tautologically reusing the surrogate (Fig. 2, App. D.4). Lemmas 1–2 give exact EM bridges at the current iterate, which is standard EM analysis, not circular. Empirical gains are measured against external baselines on constructed dual-heterogeneity benchmarks and Fed-ISIC2019, not by fitting a quantity and renaming it a prediction. The only mild self-lineage is citation of FedDRM [40] (overlapping authors) as the homogeneous-client routing-prediction precursor that FedSPM extends; that citation motivates the problem setting and is not used as a uniqueness theorem or as the sole support for Theorem 1 or the dual-heterogeneity results. No self-definitional loop, no fitted-input-as-prediction, and no ansatz smuggled as external fact. Score 1 only for that non-load-bearing self-citation; central claims remain independent.

Axiom & Free-Parameter Ledger

5 free parameters · 5 axioms · 3 invented entities

The central claim rests on standard FL optimization assumptions, the DRM-EL modeling choice, mixture non-identifiability accepted as approximation, and two paper-specific bridge assumptions that link the optimized surrogate to the exact profiled objective. Free parameters include component count, encoder capacity variants, and heterogeneity construction knobs used in evaluation. Invented entities are modeling constructs (dual heterogeneity framing, client-specific latent components, profiled EL objective) rather than physical objects.

free parameters (5)
  • Number of mixture components C
    Chosen (C=3 for main tables; ablated 1–5 on FMNIST). Directly affects capacity and reported gains under dual heterogeneity.
  • Dirichlet α_inter, α_intra and transform/permutation recipes
    Control synthetic dual heterogeneity on FMNIST/CIFAR; default α_inter=1.0, α_intra=2.0. Evaluation outcomes depend on these design choices.
  • Local SGD hyperparameters (η, E, μ, batch size, rounds)
    Learning rate schedule, local steps (10/15), momentum (0.9/0.95), and communication rounds are hand-set and enter both practice and the η=Θ(1/√T) theory regime.
  • Encoder dimensions and 1× vs C× capacity
    Shared vs per-component encoders and output dims (32/64/256) are design choices that change sample dilution vs capacity trade-offs reported in results.
  • Bridge sequences ε^(t), δ^(t) and constants Γ0,Γ1,Γ2,L,σ²
    Appear in Assumptions 1–5 and Theorem 1; not estimated from first principles—Γ2 is even quantile-estimated post hoc in App. D.4 for plots.
axioms (5)
  • domain assumption Each client distribution is a finite mixture of C latent components with client-specific weights and component laws (Eq. 1).
    Core generative modeling assumption enabling intra-client heterogeneity; components need not be true subgroups (Remark 1).
  • domain assumption Component feature laws follow a density-ratio model vs shared nonparametric G; predictive laws are softmax of shared embeddings plus client heads (Eqs. 2–3).
    Semiparametric structure that enables information sharing and routing scores.
  • standard math L-smoothness, unbiased stochastic gradients with bounded variance, and bounded inter-client gradient heterogeneity (Assumptions 1–3).
    Standard federated optimization assumptions cited as such.
  • ad hoc to paper Gradient and function-value bridges between exact DRM objective and tractable surrogate (Assumptions 4–5).
    Required to transfer descent on êf to stationarity of F; only empirically supported, not proved from the model.
  • domain assumption EM/GEM monotone updates for supervised and mixing-weight blocks inherit guarantees from prior mixture FL analysis.
    Authors restrict new analysis to the DRM block and cite FedEM-style inheritance for the rest.
invented entities (3)
  • Dual heterogeneity no independent evidence
    purpose: Name the joint inter-client and intra-client distribution shift problem that routing-only or mixture-only methods miss.
    Framing device; not a physical entity. Independent evidence is conceptual (medical subtype examples) rather than a new measurable law.
  • FedSPM client-specific semiparametric mixture (profiled EL + DRM surrogate) independent evidence
    purpose: Represent each client for joint routing and prediction while sharing a nonparametric baseline G.
    Primary algorithmic object; falsifiable via held-out routing/prediction metrics and code, but defined inside this framework.
  • Tractable DRM surrogate êQ₂ / êf^(t) with analytic λ = average responsibilities no independent evidence
    purpose: Avoid solving the nonlinear Lagrange system every gradient step while still targeting the profiled objective.
    Derived as sharing critical points with Q₂ under the paper’s first-order conditions (App. C.5); still a paper-specific optimization construct.

pith-pipeline@v1.1.0-grok45 · 30513 in / 3818 out tokens · 39917 ms · 2026-07-11T21:47:33.271487+00:00 · methodology

0 comments
read the original abstract

Routing-prediction federated learning has emerged as a new paradigm that reframes inter-client heterogeneity as a resource for system-level intelligence: at inference time, the server routes each external query to the best-matched client for prediction. Existing approaches, however, typically treat each client as internally homogeneous, overlooking latent subpopulations within local data. For example, patients with the same diagnosis at one hospital may exhibit morphologically distinct disease subtypes. The coexistence of inter-client and intra-client heterogeneity, which we call dual heterogeneity, can impair both routing and prediction. To address this challenge, we propose FedSPM, a routing-enabled semiparametric mixture framework that represents each client using client-specific latent components. Each component combines a predictive distribution for classification with a feature distribution for routing. To flexibly model feature distributions while effectively sharing information across clients, FedSPM models their density ratios relative to a common nonparametric measure estimated via empirical likelihood. We develop a federated expectation-maximization algorithm that optimizes a tractable surrogate and prove convergence of the exact profiled objective at the standard $\mathcal{O}(1/\sqrt{T})$ rate when the surrogate errors are properly controlled. Experiments on controlled benchmarks and real-world medical data demonstrate consistent improvements in routing and prediction under dual heterogeneity. Code is available at https://github.com/zijianwang0510/FedSPM.

Figures

Figures reproduced from arXiv: 2607.04085 by Guangyu Yang, Pengfei Li, Qiong Zhang, Zijian Wang.

Figure 1
Figure 1. Figure 1: Overview of the FedSPM framework. To address this challenge, we propose FedSPM ( [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Impact of momentum µ. From left to right, the panels show the running average of ∥∇ϕF(ζ (t) )∥ 2 and the normalized cumulative sums of εb (t) and δb(t) . Impact of µ. We study the impact of momentum µ under a constant learning rate on FMNIST. To align the empirical evaluation with our theory, we report the running average of ∥∇ϕF(ζ (t) )∥ 2 , together with the normalized cumulative sums of the estimated br… view at source ↗
Figure 3
Figure 3. Figure 3: Impact of C. Impact of C. We study the impact of the number of components C on FMNIST. To largely isolate the effect of varying C from model capacity changes, we employ a shared encoder across all components so that increasing C only adds lightweight component-specific heads. As shown in [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Average, system, and routing accuracies on Fed-ISIC2019 [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Visualization of an FMNIST sample under client- and component-level transformations. [PITH_FULL_IMAGE:figures/full_fig_p023_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Visualization of client label distributions under varying [PITH_FULL_IMAGE:figures/full_fig_p023_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Visualization of client mixing weights under varying [PITH_FULL_IMAGE:figures/full_fig_p023_7.png] view at source ↗

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Reference graph

Works this paper leans on

50 extracted references · 6 linked inside Pith

  1. [1]

    D. A. E. Acar, Y . Zhao, R. Matas, M. Mattina, P. Whatmough, and V . Saligrama. Federated learn- ing based on dynamic regularization. InInternational Conference on Learning Representations, 2021

    2021

  2. [2]

    J. A. Anderson. Multivariate logistic compounds.Biometrika, 66(1):17–26, 1979

    1979

  3. [3]

    M. G. Arivazhagan, V . Aggarwal, A. K. Singh, and S. Choudhary. Federated learning with personalization layers.arXiv preprint arXiv:1912.00818, 2019

    Pith/arXiv arXiv 1912

  4. [4]

    J. C. T. Braga, A. Scope, I. Klaz, P. Mecca, P. Spencer, and A. A. Marghoob. Melanoma mimicking seborrheic keratosis: an error of perception precluding correct dermoscopic diagnosis. Journal of the American Academy of Dermatology, 58(5):875–880, 2008

    2008

  5. [5]

    S. Cai, J. Chen, and J. V . Zidek. Hypothesis testing in the presence of multiple samples under density ratio models.Statistica Sinica, 27(2):761–783, 2017

    2017

  6. [6]

    Carrera, S

    C. Carrera, S. Segura, P. Aguilera, M. Scalvenzi, C. Longo, A. Barreiro, P. Broganelli, S. Cavic- chini, A. Llambrich, P. Zaballos, L. Thomas, J. Malvehy, S. Puig, and I. Zalaudek. Dermoscopic clues for diagnosing melanomas that resemble seborrheic keratosis.JAMA Dermatology, 153 (6):544–551, 2017

    2017

  7. [7]

    Changchien, S

    L. Changchien, S. W. Dusza, A. L. C. Agero, A. J. Korzenko, R. P. Braun, D. Sachs, M. H. U. Usman, A. C. Halpern, and A. A. Marghoob. Age- and site-specific variation in the dermoscopic patterns of congenital melanocytic nevi: an aid to accurate classification and assessment of melanocytic nevi.Archives of Dermatology, 143(8):1007–1014, 2007

    2007

  8. [8]

    Chen and Y

    J. Chen and Y . Liu. Quantile and quantile-function estimations under density ratio model.The Annals of Statistics, 41(3):1669–1692, 2013

    2013

  9. [9]

    C. T. Dinh, N. H. Tran, and T. D. Nguyen. Personalized federated learning with moreau envelopes. InAdvances in Neural Information Processing Systems, 2020

    2020

  10. [10]

    Ghosh, J

    A. Ghosh, J. Chung, D. Yin, and K. Ramchandran. An efficient framework for clustered federated learning. InAdvances in Neural Information Processing Systems, 2020

    2020

  11. [11]

    K. He, X. Zhang, S. Ren, and J. Sun. Deep residual learning for image recognition. InIEEE Conference on Computer Vision and Pattern Recognition, 2016

    2016

  12. [12]

    Ho, C.-Y

    N. Ho, C.-Y . Yang, and M. I. Jordan. Convergence rates for gaussian mixtures of experts. Journal of Machine Learning Research, 23(323):1–81, 2022

    2022

  13. [13]

    H. Hsu, H. Qi, and M. Brown. Measuring the effects of non-identical data distribution for federated visual classification.arXiv preprint arXiv:1909.06335, 2019

    Pith/arXiv arXiv 1909

  14. [14]

    Kairouz, H

    P. Kairouz, H. B. McMahan, B. Avent, A. Bellet, M. Bennis, A. N. Bhagoji, K. Bonawitz, Z. Charles, G. Cormode, R. Cummings, R. G. L. D’Oliveira, H. Eichner, S. E. Rouayheb, D. Evans, J. Gardner, Z. Garrett, A. Gascón, B. Ghazi, P. B. Gibbons, M. Gruteser, Z. Harchaoui, C. He, L. He, Z. Huo, B. Hutchinson, J. Hsu, M. Jaggi, T. Javidi, G. Joshi, M. Khodak, ...

    2021

  15. [15]

    S. P. Karimireddy, S. Kale, M. Mohri, S. J. Reddi, S. U. Stich, and A. T. Suresh. Scaffold: Stochastic controlled averaging for federated learning. InInternational Conference on Machine Learning, 2020

    2020

  16. [16]

    Kay and S

    R. Kay and S. Little. Transformations of the explanatory variables in the logistic regression model for binary data.Biometrika, 74(3):495–501, 1987

    1987

  17. [17]

    Keziou and S

    A. Keziou and S. Leoni-Aubin. On empirical likelihood for semiparametric two-sample density ratio models.Journal of Statistical Planning and Inference, 138(4):915–928, 2008. 10

    2008

  18. [18]

    Krizhevsky

    A. Krizhevsky. Learning multiple layers of features from tiny images. Technical report, University of Toronto, 2009

    2009

  19. [19]

    LeCun, L

    Y . LeCun, L. Bottou, Y . Bengio, and P. Haffner. Gradient-based learning applied to document recognition.Proceedings of the IEEE, 86(11):2278–2324, 1998

    1998

  20. [20]

    L. Li, Y . Fan, M. Tse, and K.-Y . Lin. A review of applications in federated learning.Computers & Industrial Engineering, 149:106854, 2020

    2020

  21. [21]

    T. Li, A. K. Sahu, A. Talwalkar, and V . Smith. Federated learning: Challenges, methods, and future directions.IEEE Signal Processing Magazine, 37(3):50–60, 2020

    2020

  22. [22]

    T. Li, A. K. Sahu, M. Zaheer, M. Sanjabi, A. Talwalkar, and V . Smith. Federated optimization in heterogeneous networks. InProceedings of Machine Learning and Systems, 2020

    2020

  23. [23]

    T. Li, S. Hu, A. Beirami, and V . Smith. Ditto: Fair and robust federated learning through personalization. InInternational Conference on Machine Learning, 2021

    2021

  24. [24]

    X. Li, K. Huang, W. Yang, S. Wang, and Z. Zhang. On the convergence of fedavg on non-iid data. InInternational Conference on Learning Representations, 2020

    2020

  25. [25]

    Z. Li, T. Lin, X. Shang, and C. Wu. Revisiting weighted aggregation in federated learning with neural networks. InInternational Conference on Machine Learning, 2023

    2023

  26. [26]

    Marfoq, G

    O. Marfoq, G. Neglia, A. Bellet, L. Kameni, and R. Vidal. Federated multi-task learning under a mixture of distributions. InAdvances in Neural Information Processing Systems, 2021

    2021

  27. [27]

    McMahan, E

    B. McMahan, E. Moore, D. Ramage, S. Hampson, and B. A. y Arcas. Communication-efficient learning of deep networks from decentralized data. InInternational Conference on Artificial Intelligence and Statistics, 2017

    2017

  28. [28]

    Nguyen, T

    H. Nguyen, T. Nguyen, and N. Ho. Demystifying Softmax gating function in Gaussian mixture of experts. InAdvances in Neural Information Processing Systems, 2023

    2023

  29. [29]

    Ogier du Terrail, S.-S

    J. Ogier du Terrail, S.-S. Ayed, E. Cyffers, F. Grimberg, C. He, R. Loeb, P. Mangold, T. Marc- hand, O. Marfoq, E. Mushtaq, B. Muzellec, C. Philippenko, S. Silva, M. Tele ´nczuk, S. Al- barqouni, S. Avestimehr, A. Bellet, A. Dieuleveut, M. Jaggi, S. P. Karimireddy, M. Lorenzi, G. Neglia, M. Tommasi, and M. Andreux. Flamby: Datasets and benchmarks for cros...

    2022

  30. [30]

    J. Oh, S. Kim, and S.-Y . Yun. Fedbabu: Toward enhanced representation for federated image classification. InInternational Conference on Learning Representations, 2022

    2022

  31. [31]

    A. B. Owen. Empirical likelihood ratio confidence regions.The Annals of Statistics, 18(1): 90–120, 1990

    1990

  32. [32]

    J. Qin. Empirical likelihood in biased sample problems.The Annals of Statistics, 21(3): 1182–1196, 1993

    1993

  33. [33]

    J. Qin. Empirical likelihood ratio based confidence intervals for mixture proportions.The Annals of Statistics, 27(4):1368–1384, 1999

    1999

  34. [34]

    S. J. Reddi, Z. Charles, M. Zaheer, Z. Garrett, K. Rush, J. Koneˇcný, S. Kumar, and H. B. McMa- han. Adaptive federated optimization. InInternational Conference on Learning Representations, 2021

    2021

  35. [35]

    Sattler, K.-R

    F. Sattler, K.-R. Müller, and W. Samek. Clustered federated learning: Model-agnostic distributed multi-task optimization under privacy constraints.IEEE Transactions on Neural Networks and Learning Systems, 32(8):3710–3722, 2021

    2021

  36. [36]

    S. U. Stich. Local SGD converges fast and communicates little. InInternational Conference on Learning Representations, 2019. 11

    2019

  37. [37]

    Y . Tan, C. Chen, W. Zhuang, X. Dong, L. Lyu, and G. Long. Is heterogeneity notorious? taming heterogeneity to handle test-time shift in federated learning. InAdvances in Neural Information Processing Systems, 2023

    2023

  38. [38]

    J. Wang, Q. Liu, H. Liang, G. Joshi, and H. V . Poor. Tackling the objective inconsistency problem in heterogeneous federated optimization. InAdvances in Neural Information Processing Systems, 2020

    2020

  39. [39]

    K. Wang, R. Mathews, C. Kiddon, H. Eichner, F. Beaufays, and D. Ramage. Federated Evaluation of On-device Personalization.arXiv preprint arXiv:1910.10252, 2019

    Pith/arXiv arXiv 1910

  40. [40]

    Z. Wang, X. Zhang, X. Zhang, Y . Liu, and Q. Zhang. Beyond aggregation: Guiding clients in heterogeneous federated learning. InInternational Conference on Learning Representations, 2026

    2026

  41. [41]

    Y . Wu, S. Zhang, W. Yu, Y . Liu, Q. Gu, D. Zhou, H. Chen, and W. Cheng. Personalized federated learning under mixture of distributions. InInternational Conference on Machine Learning, 2023

    2023

  42. [42]

    H. Xiao, K. Rasul, and R. V ollgraf. Fashion-mnist: a novel image dataset for benchmarking machine learning algorithms.arXiv preprint arXiv:1708.07747, 2017

    Pith/arXiv arXiv 2017

  43. [43]

    J. Xu, B. S. Glicksberg, C. Su, P. Walker, J. Bian, and F. Wang. Federated learning for healthcare informatics.Journal of Healthcare Informatics Research, 5(1):1–19, 2021

    2021

  44. [44]

    Q. Yang, Y . Liu, T. Chen, and Y . Tong. Federated machine learning: Concept and applications. ACM Transactions on Intelligent Systems and Technology, 10(2):1–19, 2019

    2019

  45. [45]

    Yurochkin, M

    M. Yurochkin, M. Agarwal, S. Ghosh, K. Greenewald, N. Hoang, and Y . Khazaeni. Bayesian nonparametric federated learning of neural networks. InInternational Conference on Machine Learning, 2019

    2019

  46. [46]

    Zalaudek, S

    I. Zalaudek, S. Grinschgl, G. Argenziano, A. A. Marghoob, A. Blum, E. Richtig, I. H. Wolf, R. Fink-Puches, H. Kerl, H. P. Soyer, and R. Hofmann-Wellenhof. Age-related prevalence of dermoscopy patterns in acquired melanocytic naevi.British Journal of Dermatology, 154(2): 299–304, 2006

    2006

  47. [47]

    B. Zhang. Quantile estimation under a two-sample semi-parametric model.Bernoulli, 6(3): 491–511, 2000

    2000

  48. [48]

    B. Zhang. Assessing goodness-of-fit of generalized logit models based on case-control data. Journal of Multivariate Analysis, 82(1):17–38, 2002

    2002

  49. [49]

    Zhang, Q

    Q. Zhang, Q. Tian, and P. Li. Neyman-pearson multiclass classification under label noise via empirical likelihood.arXiv preprint arXiv:2603.21623, 2026

    Pith/arXiv arXiv 2026

  50. [50]

    Y . Zhao, M. Li, L. Lai, N. Suda, D. Civin, and V . Chandra. Federated learning with Non-IID data.arXiv preprint arXiv:1806.00582, 2018. A Related Work on DRM and EL The DRM, first introduced by Anderson[2], provides a statistical framework for modeling multiple re- lated populations by formulating their densities as ratios with respect to a shared baseli...

    Pith/arXiv arXiv 2018