Fair Federated Medical Image Segmentation via Client Contribution Estimation

Meirui JiangHolger R. RothWenqi LiDong YangCan ZhaoVishwesh NathDaguang XuQi DouZiyue Xu

article2023CVPR105 citations

Proposes a federated learning framework, FedCE, that simultaneously optimizes collaboration and performance fairness across heterogeneous medical institutions by estimating client contributions through gradient direction differences and auxiliary model prediction errors.

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Collaborative healthcare research increasingly relies on federated learning, a decentralized machine learning technique that enables multiple hospitals to jointly train artificial intelligence models without sharing sensitive patient data. However, medical consortia struggle to maintain long-term participation because institutions lack fair incentives for their contributions, known as collaboration fairness. Concurrently, wide variations in imaging protocols and patient volume across sites cause standard models to perform poorly on underrepresented institutions, violating performance fairness. While existing research addresses these challenges separately, practical deployment requires solving both simultaneously.

The article develops and demonstrates a novel framework called Federated Training via Contribution Estimation (FedCE). This approach aims to accurately quantify each hospital's true marginal value and directly apply these estimates to dynamically balance model updates, achieving fair reward allocation alongside uniform, high-accuracy diagnostic performance across all participating sites.

The researchers designed an efficient contribution estimation mechanism inspired by cooperative game theory. Rather than computing exhaustive combinations of participants, the method evaluates each site against the collective group across two dimensions: optimization direction differences in gradient space and local validation error on an auxiliary model in data space. These metrics are combined using summation or multiplication to dynamically weight client updates during training without requiring raw data sharing or separate validation sets. The framework was evaluated across two multi-institution medical imaging benchmarks—a 6-site retinal fundus dataset and a 6-institution prostate magnetic resonance imaging dataset—and validated through formal convergence and distribution-shift proofs.

The empirical evaluation revealed four central findings. First, FedCE improved overall segmentation accuracy across institutions by over 2% while reducing client performance variance by up to 5.1 points compared to standard federated averaging. Second, the method significantly boosted accuracy for outlier clients with distinct imaging distributions from roughly 40% under standard baselines to 54–57%. Third, the computed client values closely mirrored empirical benchmark contributions, achieving a 93% to 96% correlation with ground-truth leave-one-out experiments. Finally, the framework successfully exposed simulated free riders—clients attempting to obtain global models using duplicated data—within the first 10 training rounds while maintaining estimation stability within 1% during global distribution shifts.

These findings demonstrate that linking fair credit assignment directly to model aggregation improves both equity and core predictive utility. By allocating greater aggregation weight to clinically unique or rare datasets, consortia can eliminate underrepresentation risks and provide transparent, auditable incentive structures. This reduces the risk of institutional attrition, lowers administrative overhead for multi-center initiatives, and enhances diagnostic safety for patients at smaller or specialized clinics.

Decision-makers establishing medical imaging consortia should deploy contribution-based aggregation methods to automatically govern participation rewards and prevent free riding. Leaders can choose between multiplicative or additive combinations based on heterogeneity levels, with additive variants offering slightly greater stability across uniform datasets. Before widespread clinical deployment, consortia should conduct pilot studies on additional imaging modalities and expand the framework to handle corrupt or adversarial client updates.

The study’s primary limitation lies in its focus on clean, controlled benchmark distributions across six institutions per task, leaving extreme client volumes and corrupted or noisy labels for future investigation. Nonetheless, because the underlying theoretical proofs and empirical results align closely across multiple distinct medical imaging tasks, stakeholders can maintain high confidence in the framework's effectiveness for multi-institutional deployments.

NVIDIA The Chinese University of Hong Kong estimation method medical image segmentation federated learning fair federated medical image segmentation client contribution estimation collaboration fairness

arXiv: 2303.16520 NVIDIA/NVFlare

Paper: Closing the Generalization Gap of Cross-silo Federated Medical Image Segmentation, An Xu et al. (2022). This study articulates the core challenge of client drift and the cross-silo generalization gap in multi-institutional medical image segmentation that FedCE directly aims to solve.
Paper: The future of digital health with federated learning, Nicola Rieke et al. (2020). This foundational review details the collaborative requirements, regulatory dynamics, and data-silo challenges inherent to deploying federated learning across healthcare consortia.
Paper: FedBN: Federated Learning on Non-IID Features via Local Batch Normalization, Xiaoxiao Li et al. (2021). This paper establishes how inter-scanner feature shifts undermine distributed medical imaging models, providing essential context for handling non-IID client distributions.
Paper: Communication-Efficient Learning of Deep Networks from Decentralized Data, H. B. McMahan et al. (2016). This seminal paper introduces the Federated Averaging algorithm, which serves as the fundamental baseline that FedCE adapts and enhances via contribution-weighted aggregation.
Paper: Federated Optimization in Heterogeneous Networks, Tian Li et al. (2018). This work formulates the optimization hurdles and client drift that arise under heterogeneous network settings, framing the performance disparities FedCE addresses.
Paper: Advances and Open Problems in Federated Learning, Peter Kairouz et al. (2019). This comprehensive survey outlines the open problems of performance fairness, collaboration fairness, and incentive allocation across cross-silo federated learning.

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Abstract

How to ensure fairness is an important topic in federated learning (FL). Recent studies have investigated how to reward clients based on their contribution (collaboration fairness), and how to achieve uniformity of performance across clients (performance fairness). Despite achieving progress on either one, we argue that it is critical to consider them together, in order to engage and motivate more diverse clients joining FL to derive a high-quality global model. In this work, we propose a novel method to optimize both types of fairness simultaneously. Specifically, we propose to estimate client contribution in gradient and data space. In gradient space, we monitor the gradient direction differences of each client with respect to others. And in data space, we measure the prediction error on client data using an auxiliary model. Based on this contribution estimation, we propose a FL method, federated training via contribution estimation (FedCE), i.e., using estimation as global model aggregation weights. We have theoretically analyzed our method and empirically evaluated it on two real-world medical datasets. The effectiveness of our approach has been validated with significant performance improvements, better collaboration fairness, better performance fairness, and comprehensive analytical studies. Code is available at https://nvidia.github.io/NVFlare/research/fed-ce

Topics

estimation method medical image segmentation federated learning application servers

Keywords

fair federated medical image segmentation client contribution estimation collaboration fairness agnostic federated learning contribution-based aggregation fundus segmentation prostate MRI segmentation fairness metrics client valuation

1. Introduction
2. Related Works
2.1. Fairness in Federated Learning
2.2. Shapley Value based Client Valuation
3. Methods
3.1. Preliminary
3.2. Client Contribution Estimation
3.3. Federated Training via Contribution Estimation - FedCE
3.4. Theoretical Analysis for FedCE
4. Experiment
4.1. Experimental Settings
4.2. Experimental Results
4.3. Analytical Studies
5. Conclusion
Acknowledgement
References

Knowls

Knowl 1 — Dual-Space Client Contribution Estimation for Federated Learning
model/method
Exact Shapley Value (SV) calculation requires evaluating all $2^N$ client coalitions, which is computationally prohibitive in federated learning (FL). To approximate SV efficiently while capturing both optimization dynamics and generalization, client contribution is approximated by evaluating the marginal value of each client $i \in [N]$ directly against the coalition of all other remaining clients $N \setminus \{i\}$ across gradient space and data space.

In gradient space, the optimization direction difference is measured at communication round $k$ by computing the cosine similarity between local client gradient $\nabla F_i(w_{k,i})$ (the difference between local updated parameter $w_{k,i}^{\kappa_i}$ and received global parameter $w_k$ ) and the aggregated gradient excluding client $i$ , $\nabla F(w_k^{-i})$ :

$\nabla F(w_k^{-i}) = \frac{\nabla F(w_k) - p_i \nabla F(w_{k,i})}{1 - p_i},$

$\Gamma_{k,i}(\text{cos}) = 1 - \cos\left(\nabla F_i(w_{k,i}), \nabla F(w_k^{-i})\right),$

where $\nabla F(w_k) = \sum_{j=1}^N p_j \nabla F_j(w_{k,j})$ , $\sum_{j=1}^N p_j = 1$ , and $p_i \ge 0$ is the baseline importance weight (such as local sample proportion). $\Gamma_{k,i}(\text{cos})$ is normalized across clients to sum to 1. A client with a different gradient direction receives a higher score.

In data space, the aggregated model parameters excluding client $i$ are constructed as $w_k^{-i} = \frac{w_k - p_i w_{k,i}}{1 - p_i}$ and evaluated on client $i$ 's empirical validation distribution $\hat{\mathcal{D}}_i$ :

$\Gamma_{k,i}(\text{err}) = E(\hat{\mathcal{D}}_i; w_k^{-i}) = 1 - \text{Score}(\hat{\mathcal{D}}_i; w_k^{-i}),$

which is also normalized across clients to sum to 1. A higher error indicates that the remaining coalition lacks the representation present in client $i$ 's data.

The combined round-level contribution is computed using either a multiplication-based ( $\Gamma_{k,i}^m$ ) or summation-based ( $\Gamma_{k,i}^s$ ) mechanism:

$\Gamma_{k,i}^m = \Gamma_{k,i}(\text{cos}) \times \Gamma_{k,i}(\text{err}),$

$\Gamma_{k,i}^s = \Gamma_{k,i}(\text{cos}) + \Gamma_{k,i}(\text{err}).$
Knowl 2 — FedCE: Federated Training via Contribution Estimation
algorithm
Federated Training via Contribution Estimation (FedCE) utilizes dynamically accumulated dual-space client contribution estimations as aggregation weights for global model updates, replacing static sample-size-based weighting to simultaneously promote collaboration fairness (rewarding high contributors) and performance fairness (upweighting unique, underrepresented client data distributions).
Input: Communication rounds $K$ , number of clients $N$ , local datasets $\{\hat{\mathcal{D}}_i\}_{i=1}^N$ , learning rate $\eta$ , local update steps $\{\kappa_i\}_{i=1}^N$ .
Output: Final global model $w_K$ , accumulated client contributions $\{\rho_{K,i}\}_{i=1}^N$ .
Initialize server model $w_0$
for $k = 1, \dots, K-1$ do
    Server distributes global model $w_k$ to all clients: $w_{k,i}^0 \leftarrow w_k$
    for Client $i = 1, \dots, N$ in parallel do
        Compute overall previous update $\nabla F(w_k) = w_k - w_{k-1}$
        for $j = 1, \dots, \kappa_i$ do
             $w_{k,i}^{j} \leftarrow w_{k,i}^{j-1} - \eta \nabla F_i(w_{k,i}^{j-1})$
        end for
        Compute local client gradient $\nabla F_i(w_{k,i}) = w_{k,i}^{\kappa_i} - w_{k,i}^0$
        Compute excluded gradient $\nabla F(w_k^{-i}) = \frac{\nabla F(w_k) - \rho_{(k-1,i)} \nabla F_i(w_{k,i})}{1 - \rho_{(k-1,i)}}$
        Compute gradient metric $\Gamma_{k,i}(\text{cos}) = 1 - \cos(\nabla F_i(w_{k,i}), \nabla F(w_k^{-i}))$
        Construct excluded model $w_k^{-i} = \frac{w_k - \rho_{(k-1,i)} w_{k,i}^{\kappa_i}}{1 - \rho_{(k-1,i)}}$
        Compute validation error $\Gamma_{k,i}(\text{err}) = E(\hat{\mathcal{D}}_i; w_k^{-i})$
        Combine metrics into $\Gamma_{k,i} = \Gamma_{k,i}^m$ or $\Gamma_{k,i}^s$
        Compute normalized historical weight $\rho_{k,i} = \frac{\sum_{r=1}^k \Gamma_{r,i}}{\sum_{j=1}^N \sum_{r=1}^k \Gamma_{r,j}}$
        Send local updated model $w_{k,i}^{\kappa_i}$ and contribution $\rho_{k,i}$ to server
    end for
    Server aggregates global model: $w_{k+1} \leftarrow \sum_{i=1}^N \rho_{k,i} w_{k,i}^{\kappa_i}$
eend for
return $w_K, \{\rho_{K,i}\}_{i=1}^N$
Knowl 3 — Robustness Upper Bound of Client Contribution Valuation Under Distribution Shift
theoretical result
Let $\Gamma$ be a $B$ -Lipschitz stable valuation function with respect to sample space $\mathcal{Z} = \mathcal{X} \times \mathcal{Y}$ . Let $\mathcal{D}_s$ and $\mathcal{D}_t$ be two probability distributions supported on $\mathcal{Z}$ . For any number of clients $N \in \mathbb{N}$ and any client $i \in [N]$ , the difference in approximated client contribution valuation $\hat{\nu}$ between distribution $\mathcal{D}_s$ and distribution $\mathcal{D}_t$ satisfies:

$|\hat{\nu}(i; \Gamma, \mathcal{D}_s, N) - \hat{\nu}(i; \Gamma, \mathcal{D}_t, N)| \le 2 N B \cdot W_1(\mathcal{D}_s, \mathcal{D}_t),$

where $W_1(\mathcal{D}_s, \mathcal{D}_t)$ is the first Wasserstein distance between $\mathcal{D}_s$ and $\mathcal{D}_t$ . This confirms that small distributional variations lead to bounded changes in the estimated client contribution.
Knowl 4 — Convergence Descent Bound and Aggregation Weight Condition for FedCE
theoretical result
Assume the federated objective function $F$ is $L$ -Lipschitz smooth and local gradient variances are bounded. At communication round $k \in [0, K-1]$ , with learning rate $\eta$ satisfying $\eta L - 1 < 0$ , local steps $\kappa_{(k,i)}$ , and client variance factors $\beta_{(k,i)}, \delta_{(k,i)}$ , the global objective decrease is bounded by:

$F(w_{k+1}) - F(w_k) \le \left( \frac{\eta}{4} \left(2\eta L + \sum_{i=1}^N p_i \rho_{(k,i)} \eta A_{(k,i)}\right) - \eta \right) \|\nabla F(w_k)\|^2,$

where $A_{(k,i)} = \eta \sqrt{\kappa_{(k,i)}(\kappa_{(k,i)} - 1)} \beta_{(k,i)}^2 \delta_{(k,i)}$ , and $\delta_{(k,i)}$ measures the proportion of local client gradients relative to the global gradient norm:

$\delta_{(k,i)} \approx \frac{\|\sum_{s=0}^{\kappa-1} \nabla F_i(w_{(k,i)}^s)\|^2}{\sum_{s=0}^{\kappa-1} \|\nabla F(w_k)\|^2}.$

Under $A_{(k,i)}$ -dominated convergence, the global model converges when client aggregation weights satisfy:

$\rho_{(k,i)} \le \frac{4 A_{(k,i)}^{1/2}}{A_{(k,i)} - 2L} = \mathcal{O}\left(\frac{1}{\sqrt{A_{(k,i)}}}\right).$

To promote convergence when heterogeneous or boundary clients are under-represented (low $\delta_{(k,i)}$ ), FedCE assigns higher weights $\rho_{(k,i)}$ to clients presenting divergent gradient directions or high local exclusion errors.

Knowl 5 — Medical Image Segmentation Performance and Inter-Client Uniformity

data/table

FedCE was evaluated against standard federated averaging (FedAvg), standalone client training, and fairness-oriented FL baselines (q-FedAvg, CFFL, FedCI, CGSV) across 6-client splits on two multi-center medical segmentation benchmarks: Retinal Fundus Image Segmentation and Prostate MRI Segmentation. Local update epoch was set to 1, Adam optimizer with initial learning rate $1\times 10^{-3}$ , batch size 8, trained for 200 communication rounds using Dice loss. Client 5 in the retinal fundus dataset exhibits severe domain shift compared to other clients.

Task	Retinal Fundus Segmentation								Prostate MRI Segmentation
Client	1	2	3	4	5	6	Avg.	Std.	1	2	3	4	5	6	Avg.	Std.
Standalone	86.69	85.51	86.21	89.91	79.77	90.98	86.51	3.95	91.23	84.59	87.57	87.37	86.70	89.25	87.79	2.26
FedAvg	81.34	85.21	83.28	88.16	40.81	90.79	78.27	18.66	91.10	84.59	89.02	89.09	83.87	89.27	87.82	2.90
q-FedAvg	86.24	86.97	87.37	89.13	44.68	90.72	80.85	17.80	90.94	85.60	89.28	89.18	84.27	88.67	87.99	2.52
CFFL	85.72	86.29	86.96	88.62	41.12	90.16	79.81	19.02	91.01	85.49	89.24	88.98	82.11	88.17	87.50	3.20
FedCI	87.02	86.93	87.35	88.53	40.99	90.22	80.17	19.24	91.21	85.40	89.49	88.37	83.96	88.49	87.82	2.68
CGSV	83.46	85.57	85.47	88.48	33.79	91.01	77.96	21.80	91.15	84.90	89.27	88.09	83.47	89.16	87.67	2.91
FedCE (Multi.)	86.73	87.45	87.51	89.26	57.30	90.25	83.08	12.70	91.43	85.79	89.21	89.13	85.68	88.62	88.31	2.22
FedCE (Sum.)	87.22	87.36	87.93	89.66	54.42	90.92	82.92	14.03	91.18	85.54	89.59	89.22	84.99	88.79	88.22	2.43

On the highly heterogeneous Retinal Fundus task, existing FL methods degrade significantly on the outlier client (Client 5: 33.79%--44.68% Dice, std up to 21.80), while FedCE improves Client 5's performance to 57.30% (Multi.) and 54.42% (Sum.), boosting overall average Dice to 83.08% and lowering standard deviation across clients to 12.70. On Prostate MRI, FedCE achieves the highest overall accuracy (88.31%) and lowest inter-client standard deviation (2.22).

Knowl 6 — Performance Fairness Metrics Comparison Across FL Methods

data/table

Performance fairness evaluates the uniformity and fidelity of federated client performance relative to individual standalone model performance. Pearson correlation ( $\uparrow$ , higher is better) and Euclidean distance ( $\downarrow$ , lower is better) between local test Dice scores of standalone models and federated models quantify performance fairness.

Task	Retinal Fundus Segmentation		Prostate MRI Segmentation
Metric	Pearson Correlation	Euclidean Distance	Pearson Correlation	Euclidean Distance
FedAvg	88.82 ( $1.8 \times 10^{-2}$ )	38.94	88.67 ( $1.9 \times 10^{-2}$ )	3.31
q-FedAvg	87.02 ( $2.4 \times 10^{-2}$ )	38.96	91.69 ( $1.0 \times 10^{-2}$ )	2.61
CFFL	84.53 ( $3.4 \times 10^{-1}$ )	38.96	92.47 ( $8.3 \times 10^{-3}$ )	2.46
FedCI	85.69 ( $2.9 \times 10^{-2}$ )	48.42	93.57 ( $6.1 \times 10^{-3}$ )	2.25
CGSV	87.47 ( $2.3 \times 10^{-2}$ )	49.47	87.71 ( $2.2 \times 10^{-2}$ )	3.45
FedCE (Multi.)	88.94 ( $1.8 \times 10^{-2}$ )	24.57	98.25 ( $4.6 \times 10^{-4}$ )	1.09
FedCE (Sum.)	89.11 ( $1.7 \times 10^{-2}$ )	24.69	97.15 ( $1.2 \times 10^{-3}$ )	1.41

Values in parentheses denote the statistical $p$ -value. FedCE achieves the lowest Euclidean distance to standalone performance on both tasks (24.57 vs. 38.94--49.47 on Retinal Fundus; 1.09 vs. 2.25--3.45 on Prostate MRI) and achieves the highest Pearson correlation on both datasets (89.11 on Retinal Fundus; 98.25 on Prostate MRI, $p < 0.001$ ), confirming improved performance fairness across participating clients.

Knowl 7 — Collaboration Fairness and Contribution Estimation Accuracy

data/table

Collaboration fairness ensures that client reward allocations accurately reflect actual contributions to the global model. Valuation accuracy was benchmarked against leave-one-out data valuation ground truth (measuring performance degradation when a specific client is omitted from training). Dynamic client aggregation weights produced by each FL method were compared to leave-one-out values using Pearson correlation ( $\uparrow$ ), Euclidean distance ( $\downarrow$ ), and Cosine similarity ( $\uparrow$ ).

Task	Retinal Fundus Segmentation			Prostate MRI Segmentation
Metric	Pearson Corr.	Euclidean Dist.	Cosine Sim.	Pearson Corr.	Euclidean Dist.	Cosine Sim.
FedAvg	-39.76 ( $4.4 \times 10^{-1}$ )	0.55	0.26	3.01 ( $9.5 \times 10^{-1}$ )	0.62	0.52
q-FedAvg	63.28 ( $1.8 \times 10^{-1}$ )	0.31	0.57	63.35 ( $1.8 \times 10^{-1}$ )	0.59	0.57
CFFL	0.90 ( $9.9 \times 10^{-1}$ )	0.45	0.47	75.44 ( $8.3 \times 10^{-2}$ )	0.49	0.74
FedCI	-12.36 ( $8.2 \times 10^{-1}$ )	0.37	0.53	-0.31 ( $1.0 \times 10^0$ )	0.61	0.53
CGSV	-44.50 ( $3.8 \times 10^{-1}$ )	0.57	0.22	-1.85 ( $9.7 \times 10^{-1}$ )	0.63	0.50
FedCE (Multi.)	94.93 ( $3.8 \times 10^{-3}$ )	0.17	0.82	93.12 ( $6.9 \times 10^{-3}$ )	0.49	0.75
FedCE (Sum.)	96.34 ( $2.0 \times 10^{-3}$ )	0.22	0.73	93.53 ( $6.1 \times 10^{-3}$ )	0.53	0.69

Values in parentheses denote the $p$ -value. FedCE achieves strong positive correlations ( $>93$ % with $p < 0.01$ ) and high cosine similarities ( $0.73$ -- $0.82$ on Retinal Fundus, $0.69$ -- $0.75$ on Prostate MRI) relative to ground-truth leave-one-out impact, whereas standard FedAvg and baseline valuation methods exhibit poor or negative correlation with true marginal utility.

Knowl 8 — Early Free-Rider Detection in Federated Learning
model/method
A 'free rider' in federated learning is a client that lacks sufficient genuine local data and attempts to obtain the trained consensus model by participating with repeated copies of a single image or low-quality data. In FedCE, free riders are detected at early communication rounds without additional validation data by computing a free-rider detection index from variables generated during local contribution estimation:

$\text{Index}_{\text{free-rider}}(i) = \cos\left(\nabla F_i(w_{k,i}), \nabla F(w_k)\right) \times \left| E(\hat{\mathcal{D}}_i; w_{k,i}) - E(\hat{\mathcal{D}}_i; w_k) \right|.$

Because a free rider's local training on duplicated data fails to produce useful gradient steps while suffering distinct error patterns, the detection value spikes significantly. Empirical testing across 6 clients shows that free riders are detected within the first 10 communication rounds, where the designated free rider exhibits values exceeding genuine clients by over 5 times, enabling early exclusion or penalty assignment before training concludes.
Knowl 9 — Ablation of Contribution Estimation Components
empirical result
An ablation study evaluated the individual and combined effects of the gradient-space metric $\Gamma(\text{cos})$ and data-space validation metric $\Gamma(\text{err})$ on final segmentation performance across the Retinal Fundus and Prostate MRI benchmarks:
1. Retinal Fundus Image Segmentation:
  - $\Gamma(\text{cos})$ only: 81.61% Dice
  - $\Gamma(\text{err})$ only: 82.12% Dice
  - FedCE (Multiplication): 82.62% Dice
  - FedCE (Summation): 83.35% Dice
2. Prostate MRI Segmentation:
  - $\Gamma(\text{cos})$ only: 88.17% Dice
  - $\Gamma(\text{err})$ only: 88.16% Dice
  - FedCE (Multiplication): 88.15% Dice
  - FedCE (Summation): 88.35% Dice
Solely relying on either gradient direction divergence or data space exclusion error results in lower performance than combining both components. The two metrics serve complementary roles: gradient difference monitors update direction uniqueness, while data space error checks whether the client's data distribution is already adequately covered by the remaining client coalition.
Knowl 10 — Empirical Valuation Invariance Under Client Coalition Shift
empirical result
To evaluate the sensitivity of FedCE contribution estimation when the client coalition changes, relative contribution weights were measured on the Retinal Fundus dataset under two setups: the 'original distribution' containing all 6 clients, and the 'distribution excluding Client 5' (the most divergent client) containing the remaining 5 clients.

After re-normalizing the relative weights among the 5 common clients (Client 1, Client 2, Client 3, Client 4, Client 6), the shift in assigned contribution percentages was consistently under 1% for all clients:
- Client 1 shift: $\Delta = 0.61\%$
- Client 2 shift: $\Delta = 0.13\%$
- Client 3 shift: $\Delta = 0.59\%$
- Client 4 shift: $\Delta = 0.005\%$
- Client 6 shift: $\Delta = 0.12\%$
This empirical result confirms the theoretical Wasserstein-distance stability bound, showing that FedCE provides consistent and reliable credit assignment even when participants join or leave the federated coalition.

Coverage note — All major contributions—including dual-space contribution modeling, the FedCE algorithm, stability and convergence theorems, comprehensive empirical comparisons on collaboration and performance fairness, free-rider identification, and ablation studies—are included; intermediate lemma proofs from the appendix are excluded per guidelines.

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Citation

MLA

Jiang, M., et al. “Fair Federated Medical Image Segmentation via Client Contribution Estimation”. arXiv, 2023, http://arxiv.org/abs/2303.16520v1.

APA

Jiang, M., Roth, H. R., Li, W., Yang, D., Zhao, C., Nath, V., Xu, D., Dou, Q., & Xu, Z. (2023). Fair Federated Medical Image Segmentation via Client Contribution Estimation. arXiv. http://arxiv.org/abs/2303.16520v1

Chicago

Jiang, M., H. R. Roth, W. Li, et al. 2023. “Fair Federated Medical Image Segmentation via Client Contribution Estimation”. arXiv. http://arxiv.org/abs/2303.16520v1.

Harvard

Jiang, M. et al. (2023) “Fair Federated Medical Image Segmentation via Client Contribution Estimation”, arXiv [Preprint]. Available at: http://arxiv.org/abs/2303.16520v1.

Vancouver

1. Jiang M, Roth HR, Li W, Yang D, Zhao C, Nath V, Xu D, Dou Q, Xu Z (2023) Fair Federated Medical Image Segmentation via Client Contribution Estimation. arXiv

BibTeX

@article{jiang2023fair,
  title = {Fair Federated Medical Image Segmentation via Client Contribution Estimation},
  author = {Jiang, Meirui and Roth, Holger R and Li, Wenqi and Yang, Dong and Zhao, Can and Nath, Vishwesh and Xu, Daguang and Dou, Qi and Xu, Ziyue},
  year = {2023},
  journal = {arXiv},
  url = {http://arxiv.org/abs/2303.16520v1},
  eprint = {2303.16520}
}

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Fair Federated Medical Image Segmentation via Client Contribution Estimation

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Knowls

Knowl 1 — Dual-Space Client Contribution Estimation for Federated Learning

Knowl 2 — FedCE: Federated Training via Contribution Estimation

Knowl 3 — Robustness Upper Bound of Client Contribution Valuation Under Distribution Shift

Knowl 4 — Convergence Descent Bound and Aggregation Weight Condition for FedCE

Knowl 5 — Medical Image Segmentation Performance and Inter-Client Uniformity

Knowl 6 — Performance Fairness Metrics Comparison Across FL Methods

Knowl 7 — Collaboration Fairness and Contribution Estimation Accuracy

Knowl 8 — Early Free-Rider Detection in Federated Learning

Knowl 9 — Ablation of Contribution Estimation Components

Knowl 10 — Empirical Valuation Invariance Under Client Coalition Shift

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