Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: In this paper, the authors propose a method called amortized mixing coupling processes for clustering (AMCP). ACMP learns the relationship between samples and reference distribution with intra-cluster mixing (IntraCM); while assigning samples to clusters and generating new clusters with inter-cluster coupling (InterCC). The ACMP method is tested on synthetic and real-world datasets in the experiments.
strengths_and_weaknesses: Strengths:

The authors propose a new clustering method called AMCP.

The method outperforms its competitors in terms of clustering performance and computational efficiency.

Weaknesses:

The contributions of the paper are not clear. The authors do not introduce the related work in detail, and it is not clear how the proposed method differs from the existing methods. How is the InterCC related other amortized clustering methods? Is the paper the first one that makes use of optimal transport for solving a clustering problem? 

The authors might need to briefly introduce an optimal transport plan, entropic regularized Kantorovich relaxation, and how these concepts are related to a clustering problem. The assumption behind the proposed clustering method is also not apparent. Why is the relationship between the samples and reference distribution a proper way to define clusters?

I am not sure whether the proposed optimization procedure converges. It looks like in Equation (11), $b_{i,j}^{(k)}$ and $C_k$ are dependent. Therefore, dividing the optimization process into IntraCM and InterCC might not guarantee the convergence of the algorithm. 

questions: 1. What are the contributions of this paper?
2. What is the assumption of the proposed clustering method? How is it different from existing amortized methods?
3. Is the objective function defined in Equation (11) guaranteed to converge?
4. In Table 1, does the time mean training time?

limitations: The authors did not address the limitations and potential negative social impact of their work.
review_title: null

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: The paper proposes an amortised clustering process model, where the clustering prior is learnt in a meta-learning setting. 

Inference is performed cluster-wise sequentially, involving inter- and intra-cluster similarities. To avoid calculations involving distances between all pairs of clusters, the authors use a linear optimal transport strategy. 

The method is demonstrated on synthetic gaussian mixture models as well as meta-learnt clustering in MNIST, Tiny-ImageNet and CIFAR-10. 
strengths_and_weaknesses: The paper is well-written and quite clear, though some parts (sections 3.2.1 and 3.2.2) are quite dense with equations. Minor suggestion: For easier readability, it might make sense to merge Figures 1 and 2. 

The idea to make use of optimal transport within the inference scheme is interesting and novel, and the authors demonstrate that it's beneficial over the standard EM algorithm. I also liked how the connection between their OT-based approach and ISAB was outlined in the appendix. 

The authors emphasise that their approach is sequential per cluster and not per data point. While true, it seems to me that a clusterwise approach has been previously presented in [Pakman et al, 2020]?

I believe the significance of this type of work will remain relatively limited (In fact, I haven't seen _any_ of the existing work in amortised clustering processes being used for any non-toy tasks yet. On the other hand, one could argue that developing better models/inference algorithms can have the potential to change it -- in that case, ideally, it would be desirable to see convincing qualitative improvements over previous results, or a non-toy application example). 

I have some questions about the experiments, I have outlined them below. 
questions: * In section 4.1, I am confused by the statement "In this case, the training set contains 200 samples belonging to 4 clusters". I thought that amortised clustering methods would be trained on multiple datasets by repeated sampling from the CRP prior, with a variable number of clusters. Could you please clarify what is this "training set" refers to?

* Are results in Tables 1 and 2 based on a single test set case, or averaged over multiple (potentially varying-sized) test sets? For example, for MNIST visualisation, a subset is used, but what about the results in Table 2? 

Minor: 

* The results show that the proposed method outperforms other amortised methods at test time. It could be interesting to see whether this is the case throughout training (e.g. how the training/test curves look like as a function of iterations)?

* Right now, experiments are only presented as summary statistics. While this is common, it could be more insightful to see a qualitative toy example, e.g. some visualisation where the proposed OT-based methodology behaves differently to an existing model (say NCP). 
limitations: No concerns
review_title: null

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: This paper proposes a novel amortized clustering framework coupled with two key strategies named Intra-Cluster Mixing and Inter-Cluster Coupling. Intra-Cluster Mixing utilizes optimal transport to learn the plan for distributing the mass of data to differential reference vectors. Inter-Cluster then resorts to this plan to form the next cluster and update existing clusters. According to the results on both synthetic and real-world datasets, the proposed method enjoys superior performance and computational efficiency.
strengths_and_weaknesses: Strengths:
The proposed method is novel and practical. In contrast to previous point-wise amortized clustering methods, the proposed framework directly models the cluster generative process. Introducing optimal transport in the E step to optimize the ELBO of mixing likelihood is also a highlight. Besides, this paper is well-organized and easy to follow. The proposed method is technically sound.

Weaknesses: The explanation of Figure 2 seems too concise. It would be better if more details are provided to make the proposed learning procedure more understandable. Besides, the difference between the proposed method and the literature [23] is not clear. The authors are encouraged to provide more details on the differences.  

questions: The settings of prior distribution are directly given in experiments, e.g., $l_{1,K}\\sim U(0,9)$ in line 302. I wonder whether the performance is sensitive to the choice of prior.
limitations: Limitations of this work are presented in the conclusion. This work is a technical clustering approach and has few social impacts.
review_title: null

Meta-review: metareview: In this paper. the authors propose a novel amortized clustering method in which intra-cluster mixing and inter-cluster coupling are introduced. The optimal transport is used to learn the relationship between samles and reference distribution with intra-cluster mixing. The inter-cluster coupling assign samples to clusters and generates new clusters. The proposed method is novel in the sense that optimal transport is first introduced to amortized clustering, and its effectiveness is shown though synthetic and real datasets. 
Many readers would be interested in this novel approach. 
confidence: Certain
Decision: Accept