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The paper studies score function recovery from partially observed data under Missing Completely at Random (MCAR, ~30% missing). It compares marginal Importance-Weighted (Marg-IW) and marginal Variational (Marg-Var) schemes and introduces a 'meta-learning prompt generator' that adaptively selects key hyperparameters (e.g., r ∈ {5,10,50}, L ∈ {1,5,10}, learning rates, truncation τ, and projection count) to stabilize training. The score model is Gaussian s_θ(x) = −P_θ(x − μ_θ) with P_θ = L_θ L_θ^T (diagonal exp for PD), optimized using a surrogate MSE to the true score s_true(x) = −P_true(x − μ_true), restricted to observed entries via masks M (e.g., Eqns. L_obs(θ) and L_IW(θ)). Stabilization uses log-sum-exp and gradient clipping; GGM experiments add an L1 penalty on off-diagonal precision entries. Experiments on synthetic Gaussians and a 10D GGM star-graph (MCAR 30%) report decreasing surrogate loss (9.687→0.094) and AUC improvements (0.219→0.972).
Cross‑Modal Consistency: 28/50
Textual Logical Soundness: 18/30
Visual Aesthetics & Clarity: 16/20
Overall Score: 62/100
Detailed Evaluation (≤500 words):
Image‑First Understanding (visual ground truth)
• Figure 1/(a): Line plot with legend “Score Matching Loss” (blue) and “Parameter Error” (orange), y-axis “Loss/Error”, x-axis “Iteration” (0–300). Both curves monotonically decrease; orange appears near zero by the end.
• Figure 1/(b): Dual‑axis plot. Blue left‑axis “GGM Score Matching Loss” rapidly decays; red right‑axis “ROC AUC” shows markers at ~50, 100, 150, 200 iterations increasing to ≈0.95.
• Figure‑level synopsis: (a) Gaussian training convergence; (b) GGM training and structure‑recovery metric; complementary quantitative views across two settings.
1. Cross‑Modal Consistency
• Major 1: Table mismatch – text says it summarizes missingness mechanisms but shows hyperparameters. Evidence: Sec 1 “Table below summarizes various missingness mechanisms” vs hyperparameter table.
• Major 2: Parameter‑error numbers conflict with Fig. 1(a). Evidence: Sec 5 “parameter error… 3.033… to about 2.030” vs Fig. 1(a) orange approaches ~0 by 300.
• Major 3: Claimed ROC AUC at 250/300 not visible in figure. Evidence: Sec 5 “0.972 at both iterations 250 and 300” vs Fig. 1(b) shows red markers only at 50,100,150,200.
• Major 4: CIFAR‑10 dataset listed but no corresponding results. Evidence: Sec 4 describes CIFAR‑10 (3072‑d) yet no figure/table reports CIFAR outcomes.
• Minor 1: Duplicate comparison tables (Abstract, Sec 2) with slightly different attributions (Schwank vs Givens). Evidence: Sec 2 table header vs References.
• Minor 2: Sub‑figure labels (a)/(b) are in text, not on panels. Evidence: Figure 1 panels lack internal (a)/(b) tags.
2. Text Logic
• Major 1: Use of s_true with real CIFAR data is unclear (true P_true, μ_true unknown). Evidence: Sec 4 includes CIFAR but s_true defined via ground‑truth parameters (Sec 1/3).
• Minor 1: Claim that formulation “inherently accounts for missingness” conflicts with later zero‑imputation note. Evidence: Sec 2 “inherently accounts…” vs Sec 4 “use of zero‑imputation”.
• Minor 2: Author misattribution across sections (Schwank vs Givens). Evidence: Sec 2 vs References.
3. Figure Quality
• Minor 1: Fig. 1(b) dual‑axis is clear but lacks tick labels for ROC AUC points beyond 200; add markers for 250/300. Evidence: Fig. 1(b).
• Minor 2: Embed (a)/(b) tags on panels and add numeric callouts at iteration 50 and 300 for easier verification. Evidence: Figure 1.
Key strengths:
• Clear, modular method description; positive‑definite parameterization and stabilization choices are reasonable.
• GGM plot conveys simultaneous loss and ROC AUC trends effectively.
Key weaknesses:
• Multiple figure–text inconsistencies on key quantitative claims.
• Missing CIFAR results despite being a core dataset.
• Ambiguity about ground‑truth scores on real data; table mislabeling reduces trust.
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The paper proposes a method to learn score functions from data with missing entries, using a meta-learning prompt generator to dynamically select key hyperparameters. The method is evaluated on synthetic datasets, including sparse Gaussian Graphical Models (GGMs), and shows improved performance in parameter estimation and structure recovery compared to traditional methods.
**Soundness:** 2.0
**Presentation:** 1.0
**Contribution:** 1.67
The paper addresses a significant and relevant problem in machine learning: the challenge of learning score functions from partially observed data. This is a crucial issue in many real-world applications where data is often incomplete. The core idea of using a meta-learning prompt generator to dynamically select hyperparameters is innovative and has the potential to improve the performance and robustness of score matching methods. The authors' attempt to adapt score matching to handle missing data, particularly through the use of marginal importance-weighted and marginal variational approaches, is a valuable contribution. The experimental results, while limited to synthetic data, do show promising improvements in surrogate loss reduction, parameter estimation accuracy, and structural recovery, particularly in the Gaussian Graphical Model setting. The inclusion of an L1 penalty for sparsity in the GGM experiments is a sensible choice and contributes to the improved performance. The paper also attempts to address the numerical stability of the method through the use of log-sum-exp stabilization and gradient clipping, which are important considerations when dealing with score matching. The authors' recognition of the limitations of existing methods for handling missing data and their attempt to address these limitations through an adaptive approach is a positive aspect of the work. The paper also highlights the potential for future work, such as extending the method to handle more complex missing data mechanisms and integrating diffusion-based denoising models. These potential extensions suggest that the proposed method could be a valuable contribution to the field if further developed and refined.
After a thorough review of the paper and the reviewer comments, I've identified several significant weaknesses that undermine the paper's current presentation and conclusions. First and foremost, the paper suffers from a lack of clarity and precision in its writing. The abstract introduces notation, such as μ and P, without prior definition, making it difficult to understand for readers unfamiliar with the specific context. This issue extends throughout the paper, with undefined terms and inconsistent notation, creating a barrier to comprehension. For example, the term 'prompt' is used extensively without a clear definition, leaving the reader to guess at its meaning and implementation. This lack of clarity is particularly problematic given the central role of the meta-learning prompt generator in the proposed method. The paper also lacks a clear explanation of the meta-learning process. The architecture and training procedure of the prompt generator are not described in sufficient detail, making it difficult to understand how it functions and how it contributes to the overall performance of the method. The paper mentions that the prompt generator selects hyperparameters from a predefined set, but the criteria for selection and the mechanism of the generator are not explained. This lack of transparency makes it difficult to assess the novelty and effectiveness of the proposed approach. Furthermore, the experimental section is not well-structured and lacks sufficient detail. The experimental setup is described in a way that combines the setup for all experiments, making it difficult to distinguish between the different experimental scenarios. The results are presented in a dense and somewhat confusing manner, with tables and text interwoven. The paper also lacks a clear explanation of the baselines used for comparison. While the authors state that they compare against classical score matching methods and naive imputation techniques, these baselines are not explicitly defined or described, making it difficult to evaluate the relative performance of the proposed method. The paper also lacks a thorough analysis of the experimental results. The discussion of the results is primarily descriptive, focusing on the observed improvements without delving into the underlying reasons for these improvements. The paper also lacks a discussion of the limitations of the proposed method and the potential for future work. While the discussion section touches on future directions, it does not explicitly address the limitations of the current approach. Finally, the paper lacks a rigorous theoretical analysis of the proposed method. The paper does not provide any theoretical guarantees or analysis of the method's properties, such as convergence rates or generalization bounds. This lack of theoretical justification makes it difficult to assess the reliability and robustness of the method. The paper also does not adequately address the potential bias introduced by the zero-imputation strategy used for handling missing data. While the authors acknowledge the use of zero-imputation, they do not discuss its potential impact on the accuracy of the estimated score function. The paper also lacks a clear explanation of the role of the L1 penalty in the Gaussian Graphical Model experiments. While the authors state that the L1 penalty is used to enforce sparsity, they do not provide a detailed explanation of how it contributes to the improved performance. In summary, the paper suffers from a lack of clarity, insufficient methodological detail, inadequate experimental validation, and a lack of rigorous theoretical justification. These weaknesses significantly undermine the paper's current presentation and conclusions, making it difficult to assess the practical utility and generalizability of the proposed method. The confidence level for these weaknesses is high, as they are consistently supported by the paper's content and the reviewers' comments.
To address the identified weaknesses, I recommend several concrete and actionable improvements. First, the authors must significantly improve the clarity and precision of their writing. This includes providing clear definitions for all terms and notations, especially in the abstract and when introducing new concepts. The authors should also ensure consistent notation throughout the paper and avoid using undefined terms. The explanation of the meta-learning prompt generator needs to be significantly enhanced. The authors should provide a detailed description of its architecture, including the type of model used (e.g., neural network, gradient-based method), the input and output spaces, and the training procedure. The paper should also clearly explain the mechanism by which the prompt generator selects hyperparameters and the criteria used for selection. The experimental section needs to be restructured and clarified. The authors should separate the experimental setup for each dataset and clearly state the experimental objectives. The results should be presented in a clear and concise manner, with tables and figures that are easy to understand. The baselines used for comparison should be explicitly defined and described, and the authors should provide a detailed analysis of the experimental results, explaining the reasons for the observed improvements and discussing the limitations of the proposed method. The authors should also include a more thorough theoretical analysis of the proposed method. This should include an analysis of the method's properties, such as convergence rates and generalization bounds. The authors should also address the potential bias introduced by the zero-imputation strategy and discuss alternative imputation techniques. The role of the L1 penalty in the Gaussian Graphical Model experiments should also be clarified, with a detailed explanation of how it contributes to the improved performance. The authors should also consider including more complex datasets in their experiments, such as CIFAR-10 or ImageNet, to demonstrate the generalizability of their method. The paper should also include a more thorough discussion of the limitations of the proposed method and the potential for future work. This should include a discussion of the assumptions made by the method and the potential for extending it to handle more complex missing data mechanisms and more complex data distributions. Finally, the authors should carefully proofread the paper to correct any grammatical errors and ensure that the paper is well-organized and easy to follow. By addressing these issues, the authors can significantly improve the quality and impact of their work. These suggestions are directly tied to the identified weaknesses and aim to provide concrete steps for improvement. The scope of these changes is realistic and achievable within the context of a revised paper.
Several key uncertainties and methodological choices remain unclear after my review of the paper. First, I am curious about the specific architecture and training procedure of the meta-learning prompt generator. What type of model is used for the generator? How is it trained, and what is the loss function used for training? How does the generator explore the hyperparameter space, and what criteria are used to select the optimal hyperparameters? Second, I am interested in the theoretical properties of the proposed method. What are the convergence rates of the method, and what are the conditions under which it is guaranteed to converge to the true score function? What is the impact of the missing data mechanism on the convergence of the method? Third, I would like to understand the limitations of the zero-imputation strategy used for handling missing data. How does this strategy affect the accuracy of the estimated score function, and what are the potential biases introduced by this approach? Are there alternative imputation techniques that could be used to mitigate these biases? Fourth, I am curious about the role of the L1 penalty in the Gaussian Graphical Model experiments. How does the L1 penalty contribute to the improved performance, and what is the impact of the regularization parameter on the results? Fifth, I would like to know more about the generalizability of the proposed method. How does the method perform on more complex datasets, such as CIFAR-10 or ImageNet? What are the challenges of applying the method to these datasets, and how can these challenges be addressed? Finally, I am interested in the potential for extending the proposed method to handle more complex missing data mechanisms, such as MAR or MNAR. What are the challenges of extending the method to these mechanisms, and what are the potential solutions? These questions target core methodological choices and seek clarification of critical assumptions, aiming to provide a deeper understanding of the proposed method and its limitations.