A General Aggregation Federated Learning Intervention Algorithm based on $do$-Calculus

Thanks for your valuable suggestions!

Weaknesses

1. We will further clarify this in the revision. The causal perspective helps accurately quantify the contribution of different clients to tail data, avoiding the blind allocation of client weights seen in traditional methods, thus improving performance on tail categories. We have added results from medical datasets in the experimental section, demonstrating performance improvements on tail data (such as rare diseases) and showcasing the key role of causal methods in real-world applications. For details, please refer to Appendix E in the revised manuscript.

2. We have adjusted the structure of the introduction to ensure better logic and coherence. We first discuss data heterogeneity and the long-tail problem in federated learning, followed by an analysis of the limitations of existing research, such as inadequate solutions to the long-tail problem, the lack of a causal perspective, and communication cost issues. Then, we introduce the research motivation and briefly present the innovations of the CRePA and FedLT-CI methods, ensuring that the content is more organized and cohesive. Furthermore, we recognize that providing overly detailed descriptions of the method in the contributions section may lead to excessive length and inconsistencies with the earlier parts of the introduction. During the revision, we have modified and optimized the contributions section to ensure that it is concise, highlights the key points, and aligns with the content presented earlier. Please refer to the revised manuscript's Introduction.

3. In response to your feedback, we have incorporated the AUC-ROC metric into our experiments on the PTB-XL dataset to provide a more comprehensive evaluation of the model's performance. Additionally, we have updated the baselines by including the latest models from 2024. For more details, please refer to Appendix E in the revised manuscript.

Questions:

1. We believe that causal effects play a crucial role in addressing data heterogeneity and long-tail distribution problems, which is currently a gap in the existing research, as reflected in the following aspects: (1) Causal effect analysis quantifies the contribution of different clients to the global model, particularly for tail classes. This helps dynamically adjust the aggregation strategy by excluding clients with minimal impact on the tail performance, thereby enhancing the model's adaptability to tail data. (2) The causal perspective provides a new analytical framework that explains the reasons for model performance improvements and optimizes existing federated learning frameworks by embedding intervention mechanisms.

2. Thank you for the reviewer’s suggestion! We have conducted a theoretical analysis of the communication cost of the proposed method in the revised version. Since our FedLT-CI method selectively prevents certain clients from uploading their updated models or gradients during each communication round, compared to traditional aggregation algorithms that require all selected clients to upload their models, this approach effectively reduces the communication burden. Please refer to the newly added Figure 1 in the Introduction section for further details.

We hope our response will satisfy your questions about adjusting the ranking.

Thank you for your suggestions!

Motivation:

1. Our motivation is to enhance the performance of current FL methods on long-tail (LT) data by introducing interventions and calculating clients' causal effects using gradient information. This has been further emphasized in the Introduction of the revised version.

2. Our model evaluates the impact of clients on the tail performance of the aggregation model by calculating causal effects. This process can be likened to treating the tail performance of the aggregation model as a disease, where client participation in aggregation is considered as treatment, and the treatment effects are assessed. By removing clients with small or negative causal effects, we improve performance and enhance explainability. This has been further elaborated in the Introduction.

3. We will highlight the limitations of existing methods and the improvements made by FedLT-CI in the text. The revised paper includes a comparison of steps when Fed-CI is integrated into general FL, with further clarification of our innovations. Please refer to Fig. 1 for details.

4. Fed-CI enhances tail performance by removing clients with small or negative causal effects, based on causal analysis. Afterward, a weighted aggregation algorithm, such as CRePA, can be applied. We have added a diagram in Fig. 1 to clearly illustrate the relationship between the methods and their application.

Methods and Experiments

1.We highly value the timeliness of citations and have re-examined and updated the relevant literature. In the revision, we have included recent research on data heterogeneity and its solutions in federated learning, providing a more comprehensive discussion in the context of Fed-LT. Thank you for your helpful suggestions!

2.We updated the experimental baselines with 2024 models and used the PTB-XL ECG dataset with simulated data from 40 hospitals. Our results show significant improvements in recognizing tail classes (rare diseases) across algorithms, with AUC-ROC evaluations included. Detailed results are in Appendix E, strengthening the experimental validation.

3.Our model does not change the clients' computational cost but increases the servers' computational cost. We will show more details if it is necessary.

4.Due to word limit, please refer to the response to question 5

Writing: We have polished our manuscript following your advices.

1.We will further clarify the logical connection before and after "therefore" in the revised manuscript to ensure the coherence and readability of the content.

2.Some methods rely on statistical information from the data, such as sample counts or feature distributions. However, this approach is not suitable for FL as it may expose sensitive client information. We have provided further clarification in the revised paper.

3.In Section 5.1, we provide a detailed explanation of the dataset splitting method, including the use of IF (the ratio of training samples in the largest class to the smallest class) to represent the long-tail distribution degree and the parameter $\alpha$ to quantify data heterogeneity (i.e., the Non-IID degree).

4. In experimental design, researchers often subdivide the head data into head and middle categories, which may lead to inconsistencies in the description. We have added an explanation of the "many, middle, few" classification in the experimental section.

Questions

1. The core of the FedLT-CI model lies in using do-Calculus to intervene in the FL aggregation process. It evaluates the impact of client participation or non-participation on the global model's tail performance through causal inference and intervenes in the aggregation of clients. This process is illustrated with a figure in the Introduction of the revised manuscript.

2. We believe the causal perspective offers a new modeling framework that explains performance improvements and optimizes aggregation by embedding an intervention mechanism. This enhances adaptability and tail performance in long-tail scenarios. By quantifying client contributions to the tail performance and dynamically adjusting participating clients, we aim to propose a general method that improves the algorithm's performance on tail classes.

3. Ignoring the impact of clients on tail data and the lack of flexibility in aggregation strategies makes the approach difficult to generalize and lacking in interpretability.

4. CRePA is a weighted aggregation method similar to FedAvg. FedLT-CI enhances the performance of CRePA or other baselines on tail data by excluding clients that negatively impact tail performance. Please refer to Fig. 1 added in the Introduction.

5. In FL, head data dominates and converges quickly, while tail data gradients are often overshadowed. CRePA increases the weight of tail gradients, while Fed-CI improves tail performance by removing clients with minimal causal effect using causal inference.

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We appreciated your advice and modified our manuscript.

Weaknesses & Questions:

1. Our motivation is to improve the performance of current FL algorithms on long-tail data by introducing interventions in traditional FL and calculating the causal effects of clients using gradient information. We have further strengthened the motivation statement in the Introduction. In FL, data heterogeneity and long-tail distribution are interrelated. Heterogeneity manifests as differences in data distribution across clients, such as how patient characteristics may vary between hospitals due to geographic and medical factors. Long-tail distribution refers to the scarcity of samples for certain categories in the global dataset, such as rare diseases in healthcare scenarios. We will further strengthen the description of these two issues in the text. We hope our response meets your satisfaction.
2. CRePA treats client weights as a distribution, similar to traditional federated learning methods. Fed-CI is the core innovation of this paper, optimizing the aggregation process through causal intervention by dynamically removing certain clients to improve tail data performance. Fed-CI can be seen as a plugin for federated learning, significantly enhancing the performance of any algorithm on tail data (details can be found in Figure 1 of the revised version). The introduction of these two algorithms not only demonstrates the versatility of Fed-CI but also shows that existing weighting methods can infer the weight distribution and achieve better results.
3. Fed-CI can seamlessly integrate with other federated learning algorithms (including CRePA). Its core objective is to improve tail performance by using causal analysis to remove clients that have minimal or negative effects on the tail. After removing such clients, a weighted aggregation method can be directly applied to the remaining clients. In the revised version of the paper, we have added a diagram (Figure 1) to clearly illustrate the logical relationship and application scenarios of the two methods, further enhancing the reader's understanding of this section.
4. We design a causal model using client gradients to evaluate their causal effects in the aggregation process, where a larger effect indicates a more significant contribution. Causal analysis is applied to intervene in the aggregation process to improve the algorithm's performance on tail data, which is a novel approach in the current literature. We have added experiments on real medical datasets, included a new 2024 baseline, and incorporated ROC curve evaluation (see Appendix E) to validate the effectiveness of the method.
5. We simulated the data distribution from 40 hospitals on the publicly available electrocardiogram dataset PTB-XL and conducted experimental validation in the revised version. By evaluating the model with various metrics, the results show that our method significantly improves the recognition accuracy of tail categories (such as rare diseases) compared to all baselines. This further validates the effectiveness and broad applicability of the method in real-world healthcare scenarios, particularly in the presence of data heterogeneity and long-tail distributions. Detailed information about the experiment can be found in Appendix E of the revised manuscript.

We hope our response will satisfy your questions about adjusting the ranking.