Comparison of Trivariate Copula-Based Conditional Quantile Regression Versus Machine Learning Methods for Estimating Copper Recovery

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Journal : Mathematics (ISSN 2227-7390)

Manuscript ID : mathematics-3426363

Type : Article

Title : Comparative analysis of a multivariate copula model versus supervised machine learning models: application case in the estimation of metallurgical copper recovery by flotation

 

******Review******

Dear Authors,

I would like to express how much I enjoyed reviewing your manuscript titled "Comparative analysis of a multivariate copula model versus supervised machine learning models: application case in the estimation of metallurgical copper recovery by flotation" This paper addresses a significant challenge in the field of mineral geology and provides a well-thought-out approach to comparing the performance of a multivariate copula model alongside six machine learning techniques to estimate copper recovery, a crucial metric in mining processes. Your manuscript is one of the few that I found both engaging and well-written.

The overall structure is clear and easy to follow, which made it a pleasure to read. The methodology section is particularly strong, demonstrating a solid understanding of the techniques employed. The flowchart included in the manuscript is a helpful addition, providing clarity. However, I believe more detailed explanations would benefit certain aspects of the methodology. Specifically, I would appreciate additional information on how you selected the model parameters, particularly the marginal distributions used in the copula model. While the explanation you provided is good, a deeper discussion here would enhance the transparency of your approach. Additionally, the decision to use just 5% of the dataset for subsampling is intriguing, but it would be helpful to offer a clearer justification for this choice also if reference is avalable can help readers. A more thorough explanation of why you chose this approach and how it influences the results would help readers better understand your reasoning.

Providing more insight into how the synthetic data was validated would further strengthen the credibility of your findings. This is particularly important given the innovative application of the copula model in the geology. While your paper stands out in its use of the copula model, there are still areas where further exploration could add value. Additionally, integrating geostatistical methods, like Kriging, could provide a promising direction for future research in this area.

In conclusion, I believe your work contributes meaningfully to the field of mineral geology and offers new techniques to address a complex issue in mining operations. Although there are areas where further refinement could be beneficial, your research lays a solid foundation for future studies and potential practical applications in the industry. One suggestion I have is to reconsider the title of the manuscript. A more concise and focused title might better reflect the core of your research. Additionally, expanding the introduction section could help set the stage more clearly for readers.

I also noticed that some of the figures were hard to read; enlarging them could significantly improve readability, especially since this manuscript may be printed on A4 paper, which can make smaller figures difficult to interpret. For Figure 5 (right), I was unsure of the information it conveys—either consider adding color or removing it, as it doesn’t seem to provide meaningful data. Similarly, Figure 2 might require some attention.

I strongly recommend revising the conclusion. It could be made more concise while still summarizing the key results quantitatively. Try to ensure the conclusion provides a brief yet comprehensive overview of your findings so that readers can grasp the essence of the article without needing to revisit other sections. Though the manuscript is quite strong, I suggest refining it further to meet the standards of an excellent article.

Finally, I think the discussion section would benefit from comparing your research with at least five other studies. This would allow you to position your work within the broader context of the field, highlighting both its strengths and weaknesses.

Thank you again for sharing your valuable research with the scientific community. I recognize the effort you've invested, and I believe that with the recommended improvements, your manuscript could be elevated to the next level.

Best regards

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Author Response

Please see the attachment.

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

The author should ensure that the paper clearly defines both the multivariate copula model and the machine learning algorithms being compared. Also, the introduction should provide the context within which the comparison is meaningful, including the applications where such models are relevant.

 

The paper should thoroughly describe the methodology used in the multivariate copula model and the supervised machine learning techniques. This should include any assumptions made, model parameters, and how they were estimated or chosen.

 

The paper should provide a detailed description of the data used for analysis. This should include the source of the data, its characteristics, any preprocessing steps taken, and its suitability for the models under comparison.

 

The author should explains the implementation details for both the copula model and the machine learning models and the paper should define clear performance metrics for the comparison and provide justification for their selection.

 

The author should describe robust validation techniques, such as k-fold cross-validation, holdout validation, or bootstrapping? Are there any out-of-sample tests to evaluate the predictive power of the models?

 

The author should include an analysis of the robustness of the models' performance to changes in their parameters and underlying assumptions. Is there an investigation into how sensitive the results are to different data conditions or parameter values?

 

Does the paper evaluate the practical implications of using one model over the other? This might include computational efficiency, ease of interpretation, ease of deployment, and the applicability of the model to other similar datasets or problems. The author should provide the necessary details about it.

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Dear authors

Thank you very much for your corrections. I think it's ready now.

Best regards