Dynamic Matching Utilizing Latent Factor Modeling

1.The manuscript lacks a cohesive overview of related work. 2.There are inconsistencies in the use of nouns and variables throughout the manuscript. For instance, in Section 4.1, "MULTI-CENTROID GROUPING PENALTY," A denotes collections of latent factors for jobs, whereas in Section 3, "A MODEL OF MATCHING WHILE LEARNING," ai refers to the latent factor for the i-th worker. Additionally, Section 3 alternates between the terms "benefit matrix" and "reward matrix." These discrepancies diminish the clarity of the manuscript and may confuse readers. 3.The manuscript contains several minor spelling and indentation errors. Further review and revision would enhance the overall readability of the paper.

1. [Scalability to large scales]: In the simulations, only a limited number of worker types (|I∣=4) and job types (∣J∣=3) are tested (Section 6.1). The statistics of the kidney exchange dataset is missing in the paper. Real-world platforms (e.g., gig economy platforms, online job recommender systems) would require handling significantly more types of jobs and workers. Without evidence of scalability tests with larger worker-job type spaces, it’s uncertain if the model can handle the complexity of diverse real-world data effectively, particularly as computation time could increase exponentially with more latent factors.

2. [Lack of comprehensive comparison]: In Section 6.3, the authors describe the point process model as an alternative but do not provide direct performance comparisons such as AUC, accuracy, or computational efficiency on the same kidney dataset. Additionally, there is limited analysis on how each model performs with temporal data, given that point process models are often preferred for event-driven, time-sensitive scenarios.

3. [Data noise and imbalance]: The model assumes labeled data for training latent factors and matching, but in practical applications, data is often noisy or imbalanced, as seen in fields like crowdsourcing and organ donation w here certain worker types or job types (e.g., rare blood types in kidney exchanges) are underrepresented. The lack of strategy for handling label noise or class imbalance may lead to reduced performance or biased matching results, especially for minority classes.

The paper lacks a comprehensive review of related literature, resulting in weak research motivation. Without placing this work within the context of existing studies, it fails to highlight the specific challenges and significance of the problem. Additionally, only one real-world dataset (kidney exchange) is used in the experiments, which limits the demonstration of the model's generalizability and its relevance to the defined problem. The context gap between the problem statement and the dataset also raises questions about applicability. Furthermore, the paper does not compare with recent baseline models, which could have substantiated the effectiveness and robustness of the proposed modules and strategies.

• While the earlier parts of the paper are well-written, the later sections feel somewhat rushed and confusing at parts. See below for my specific comments.
• The notation used throughout the paper is somewhat difficult to understand, and there are inconsistencies. For example, the sets associated with the group membership of workers and jobs are introduced as $\mathbf{V}$ and $\mathbf{U}$, but then subsequently referred to using $V$ and $U$, respectively. Fixing these and any other inconsistencies (e.g., $A \leftrightarrow \mathbf{A}$, $B \leftrightarrow \mathbf{B}$, $L \leftrightarrow \mathcal{L}$, $G \leftrightarrow \mathcal{G}$) would help with the paper’s readability. Streamlining notation wherever possible would also be appreciated.
• While I did not spend a large amount of time looking at them, the proofs in the Appendix seem to skip several steps. E.g., on line 655, the proof of Theorems 1 and 3 claims “With the choice of $\lambda_n$ as mentioned, we can show: $\Vert \hat{\Theta} - \Theta^\star \Vert = O_p (n^{-1/2})$”, which implies the theorem statement. However, $\Vert \hat{\Theta} - \Theta^\star \Vert$ was not mentioned anywhere before this statement in the proof, so it is a little unclear where this is coming from. Similarly, on line 692, the proof claims that “And as $n$ approaches positive infinity, $R(\hat{V}, \hat{U})$ goes to $1$”. The justification for this claim is not clear from the preceding lines.
• The experimental evaluation in Section 6.1 feels somewhat lacking to me — see specific comments below:
  • The last sentence of Section 6.1 states “We found that the LFGP model performs well in handling binary labels, but its accuracy decreases when dealing with more label types.” I appreciate the acknowledgement of the model’s limitations, but I do not see the corresponding evidence for this claim? In the setup, I do not see any characterizations of the label types considered that would suggest how this comparison and conclusion was reached.
  • The setting considered seems small and somewhat arbitrary when compared with a real application to matching markets.
• In Section 6.2, I appreciate the increased detail in the setup description for the real-world data. Including evaluations on this data set somewhat addresses my concerns with the experiment in Section 6.1.
  • However, I am a little confused about the amount of detail dedicated to evaluating the LFGP model on this task — as far as I can tell, the only reported performance metric for LFGP on the kidney exchange task is in the sentence “We applied the processed dataset to the model and obtained an accuracy of 60% for matching prediction”.
  • The remainder of Section 6 describes an application of the point process model to the same problem as a comparison with LFGP. The explanation of this implementation seems lengthy, and could be relegated to an Appendix.
  • In contrast, the comparison between the point process model and LFGP is isolated to a single paragraph, namely lines 506-516. Since the performance of the point process model is reported as a ROC curve, and the performance of LFGP is reported as a single accuracy number (60%), this comparison is confusing and inconclusive.
• I would expect to see significantly more results in a quantitative sense (e.g., figures, performance metrics that are the same for the proposed model and the comparison model) to support the claims made in the abstract and introduction.
• It seems that [Xu et al., 2023 (10.1080/01621459.2023.2178925)] use the multi-centroid grouping penalty as part of a two-stage model for multi-categorical crowdsourcing in the context of a platform such as Amazon MTurk, where the first stage is to fit the observed labels with a latent factor model, and the second stage is to identify high-quality workers and to make predictions. It is unclear to me how much of the current work is a new contribution with respect to this paper.

• The contribution of the approach is not sufficiently clear. What is the difference between this paper and existing work? The paper even does not include related work section.
• The approach is straightforward and lacks novelty. The latent factor learning is straightforward and sort of trivial.
• The writing could be better. The paper should add adequate contents to clarify the difference between this work and the existing literature.