CL-NOTEARS: Continuous Optimization Algorithm Based on Curriculum Learning Framework

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This manuscript proposes a novel algorithm, CL-NOTEARS, for learning causal structures. CL-NOTEARS is based on curriculum learning and aims to be robust to the impact of sample data noise and to improve the efficiency and accuracy of causal structure learning. This algorithm adaptively adjusts the model’s sample learning sequence using a curriculum loss function and then optimizes the learning of curriculum samples at different stages to identify the DAG structures for each stage. Then, it updates the weights based on these DAGs to get the final causal structure. Multiple simulations have been conducted to evaluate the performance of CL-NOTEARS. The algorithm demonstrated competitive performance in terms of SHD, TPR, and FDR, particularly in cases with complex structures. The manuscript also justifies the use of curriculum mechanisms in the algorithm and explains the impact of the number of curriculum stages with simulations.

Here are some comments:

1. How many simulations (replicates) were considered to evaluate the performance?
2. How many curriculum stages were used in sections 5.2, 5.3, and 5.4? How was this determined?
3. According to Tables 2 and 3, in some cases, CL-NOTEARS had an FDR of 0 ± 1, which seems quite optimistic. It would be helpful to provide some explanations.
4. Is it possible to show some results using this algorithm with real-world data analysis?

 

Comments on the Quality of English Language

In general, the English writing is fine; however, there are some typos that need to be corrected. For example, the same title is used in Figure 7 (a) and (b), and the citation after SF in section 5.1 is marked as [?]. Also, the flow of the manuscript can be improved to make it smoother.

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

This study presents a continuous optimization technique based on the curriculum learning framework, namely CL-NOTEARS. The paper's organization is commendable. The article is well written. The efficacy of the strategy is illustrated in many cases. This tool would prove beneficial to a wide range of users across many fields since the data and code are provided. This work is highly pertinent to the aim and scope of this journal. Therefore, it is appropriate for publication in this journal.

Author Response

Comments 1: This study presents a continuous optimization technique based on the curriculum learning framework, namely CL-NOTEARS. The paper's organization is commendable. The paper is well written. The efficacy of the strategy is illustrated in many cases. This tool would prove beneficial to a wide range of users across many fields since the data and code are provided. This work is highly pertinent to the aim and scope of this journal. Therefore, it is appropriate for publication in this journal.

Response 1: Thank you very much for taking the time to review our manuscripts. Your evaluation has affirmed our work. We look forward to publishing it in this journal as soon as possible and I hope that our work can further enhance the development and emphasis on causal discovery.

Reviewer 3 Report

Comments and Suggestions for Authors

The typos, errors, and unclear notations in the paper hinder smooth reading. See attached file.

Comments for author File: Comments.pdf

Comments on the Quality of English Language

See attached file.

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Reviewer 4 Report

Comments and Suggestions for Authors

The same article was submitted to another journal, Nuclear Physics B, on May 31, 2024. The submission can be accessed via the following link:

https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4855395

The authors are required to provide a justification for this simultaneous submission.

Comments for author File: Comments.pdf

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

See the attached file.

Comments for author File: Comments.pdf

Comments on the Quality of English Language

See the attached file.

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Reviewer 4 Report

Comments and Suggestions for Authors

The evidence and arguments presented by the authors regarding my comment are convincing. Some observations should be taken into consideration. My observation concerns the linguistic aspect of the article. Please avoid using:
"We employ a curriculum-based..." (line 7, abstract section)
"We explore how to mitigate..." (line 52, introduction section)
"We have constructed a framework..." (line 64, introduction section)
"We adaptively adjust the model’s sample..." (line 67, introduction section)
"We optimize the learning of..." (line 67, introduction section)
Similar expressions can be found throughout the manuscript. It is essential for the authors to carefully review and revise the language used in the article.

Comments on the Quality of English Language

The evidence and arguments presented by the authors regarding my comment are convincing. Some observations should be taken into consideration. My observation concerns the linguistic aspect of the article. Please avoid using:
"We employ a curriculum-based..." (line 7, abstract section)
"We explore how to mitigate..." (line 52, introduction section)
"We have constructed a framework..." (line 64, introduction section)
"We adaptively adjust the model’s sample..." (line 67, introduction section)
"We optimize the learning of..." (line 67, introduction section)
Similar expressions can be found throughout the manuscript. It is essential for the authors to carefully review and revise the language used in the article.

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Round 3

Reviewer 3 Report

Comments and Suggestions for Authors

see the attached file.

Comments for author File: Comments.pdf

Comments on the Quality of English Language

see the attached file.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf