Summary
The paper presents a method for learning the structure of discrete Bayesian networks from potentially corrupted data. It utilizes distributionally robust optimization and regression, optimizing the worst-case risk over a set of distributions. The approach works with general categorical variables without assuming specific conditions and provides efficient algorithms. Non-asymptotic guarantees for successful structure learning are derived, and numerical experiments validate its effectiveness.
Strengths
Originality:
The paper addresses the challenge of missing data in distributionally robust skeleton learning. This aspect adds a unique and valuable contribution to the field.
Quality:
The quality of writing in the paper is commendable. The ideas and concepts are presented effectively, and the paper demonstrates a strong grasp of the subject matter.
Clarity:
The paper's clarity is notable, as it is organized in a logical manner where each section builds upon the previous ones. The flow of information is well-structured, making it easy for readers to follow the paper's content.
Significance:
The task of building discrete Bayesian networks from potentially corrupted data holds significant importance, as it has wide-ranging applications in various fields. By addressing the challenge of distributionally robust skeleton learning, the paper contributes to the advancement of techniques that can handle data uncertainties and enable more accurate modeling and inference in real-world scenarios. The significance of this research lies in its potential to enhance decision-making processes, predictive modeling, and knowledge discovery across diverse domains.
Weaknesses
- The author's assertion that they had limited space to relate their work to the existing literature is understandable. However, it is crucial to provide a clear positioning of their own work within the broader research landscape. Emphasizing the novelty and distinguishing features of their approach will strengthen the paper's contribution and demonstrate its unique value.
- The paper lacks clarity on whether cross-validation or hyperparameter tuning was performed during the experiments. It would be beneficial to address this issue explicitly to ensure the robustness of the results. Additionally, to further improve the reliability of the findings, it is recommended to conduct a rigorous statistical test, such as the corrected Student's t-test proposed by Nadeau and Bengio [1], using 15 hold-out folds. Incorporating such statistical analyses will enhance the credibility and validity of the experimental results.
[1] https://link.springer.com/article/10.1023/A:1024068626366
Questions
l 105: How is T defined in A_{ST}?
Rating
7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
Confidence
2: You are willing to defend your assessment, but it is quite likely that you did not understand the central parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.
Limitations
- The proposed method accounts for the effect of outliers by optimizing the worst-case risk over a family of distributions within bounded Wasserstein distance or KL divergence. However, the extent to which the method can effectively handle outliers and their impact on the learned network structure should be further explored and evaluated.
- The proposed approach is designed for general categorical random variables without assuming faithfulness, an ordinal relationship, or a specific form of conditional distribution. While this makes the approach flexible, it may also limit its applicability to certain domains or types of data. Investigating the generalizability of the approach to a broader range of variable types or distributions could be a potential limitation.