Kati8/ICLR_2023_2025 huggingface dataset:
authors: Peng Wu
authors: Tales Imbiriba
authors: Pau Closas
reviews: 
Comments: This paper proposes a Bayesian framework for clients in a federated setup, which motivates their clustering algorithm. Since, the Bayes optimal assignment is computationally intractable, the paper proposes several heuristics, and empirically compares each with baseline WeCFL on CIFAR10 and FMNIST.
Strengths: 1. The authors provide rigorous (albeit hard-to-parse) derivations for a Bayesian framework in clustered federated learning, that can be applied over a large class of priors.  
2. The main benefit of the above framework is that it models inter-cluster relationships, and seems to be less sensitive (at least in theory) to the choice of number of clusters K. This can be seen as a more principled form of soft-clustering. 
3. Section 3 motivates the need for having approximate association strategies, which the authors investigate in Section 4. The datasets and baselines chosen for the exposition are satisfactory.
Weaknesses: 1. Overall, there is a significant concern over the clarity of writing throughout Sections 3 and 4. For example, even though the authors tabulate their notations in Appendix A, it was pretty hard to follow the arguments in Section 3 because of notation overload. Possibly, some of them can be removed, or some of the derivations can be written down by dropping unnecessary indexing wherever possible. 
2. Since the different possible associations of clients can be combinatorially very large to evaluate, the authors propose approximations in Section 4. But, it is unclear if BCFL-G/C is helpful in practice, compared to WeCFL. In fact, BCFL-G which does greedy association at each round is quite similar to WeCFL. 
3. From point 2, the main contribution I see is BCFL-MH, but this method is computationally heavier given that it requires computing densities in Sec 3.1 and 3.2, and I could not see a computational cost / performance benefit tradeoff to justify BCFL-MH. 
4. The authors claim "new theoretical insights" in their introduction, but the paper does not have any formal guarantees for the proposed approximations. 
5. The authors do not provide any ablations on the choice of number of clusters K, which can be quite critical for some of the proposed approximations like BCFL-MH.
Recommendation: 5: marginally below the acceptance threshold
Reviewer confidence: 3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.
Soundness/correctness: 2 fair
Clarity: 1 poor