Dear Mr. Johnsen,

Thank you very much for submitting your manuscript "Inferring feature importance with uncertainties with application to high-dimensional genotype data" for consideration at PLOS Computational Biology.

As with all papers reviewed by the journal, your manuscript was reviewed by members of the editorial board and by several independent reviewers. In light of the reviews (below this email), we would like to invite the resubmission of a significantly-revised version that takes into account the reviewers' comments.

We cannot make any decision about publication until we have seen the revised manuscript and your response to the reviewers' comments. Your revised manuscript is also likely to be sent to reviewers for further evaluation.

When you are ready to resubmit, please upload the following:

[1] A letter containing a detailed list of your responses to the review comments and a description of the changes you have made in the manuscript. Please note while forming your response, if your article is accepted, you may have the opportunity to make the peer review history publicly available. The record will include editor decision letters (with reviews) and your responses to reviewer comments. If eligible, we will contact you to opt in or out.

[2] Two versions of the revised manuscript: one with either highlights or tracked changes denoting where the text has been changed; the other a clean version (uploaded as the manuscript file).

Important additional instructions are given below your reviewer comments.

One of the reviewers pointed out that the Github repository linked in your submission contains code for an earlier work and does not contain the subSAGE method described in your manuscript. In your revision, please advise whether an open source code implementation of your method is available to the community, as required by the journal. 

Please prepare and submit your revised manuscript within 60 days. If you anticipate any delay, please let us know the expected resubmission date by replying to this email. Please note that revised manuscripts received after the 60-day due date may require evaluation and peer review similar to newly submitted manuscripts.

Thank you again for your submission. We hope that our editorial process has been constructive so far, and we welcome your feedback at any time. Please don't hesitate to contact us if you have any questions or comments.

Sincerely,

Shaun Mahony

Academic Editor

PLOS Computational Biology

Ilya Ioshikhes

Section Editor

PLOS Computational Biology

***********************

Reviewer's Responses to Questions

Comments to the Authors:

Please note here if the review is uploaded as an attachment.

Reviewer #1: In this work, Johnsen and colleagues build on SAGE to estimate feature importance with uncertainties. While SAGE has the advantage (compared to SHAP values) of providing a global estimate of feature importance via a loss function, it is ultimately an estimate, and as such, the authors argue, we should be interested in quantifying the uncertainty associated with this estimate. They propose sub-SAGE as an approach to do this in a computationally efficient manner, by using a reduced number of subsets/features and providing bootstrapped confidence intervals. To demonstrate their approach, they provide a proof-of-concept example using a small synthetic dataset, as well as a further example with a tree ensemble model using genotype data from the UK Biobank to infer importance for genetic and non-genetic features in an obesity phenotype. As noted by the authors themselves, there are some potential limitations to this approach, namely: using a limited number of subsets results in sub-SAGE values which no longer satisfy the efficiency axiom, the use of independent test data is required, and the accuracy of percentile confidence intervals may vary depending on number of bootstraps (although admittedly this variance may be relatively minor).

General comment:

Overall, the manuscript is well-written, providing rigorous detail on the methodological approach taken. Improving the interpretability of machine learning algorithms as applied to high-dimensional biological data (as well as more generally) is an important area of research, and understanding the uncertainty associated with SAGE estimates should prove of interest and benefit to the field.

Specific comments:

- The high-dimensional example provided is still a relatively small dataset given the current size of GWAS studies - can the authors provide an indication of run-time to estimate the sub-SAGE values?

- the authors propose selecting the reduced number of features based on either domain knowledge or by "selecting the top tier". In the case of the former, might this limit the ability for discovery of novel genetic relationships? For the latter, there is no indication as to what this entails - some further details would be helpful.

For the UKBiobank example:

- Have the XGBoost hyperparameters mentioned been optimised?

- Is there any attempt to account for correlation in SNP importance, based on e.g. LD structure and if not, how does this affect importance estimates?

- Recently published work (https://www.nature.com/articles/s42003-022-03812-z) has shown the benefit of including both non-linear contributions and interactions between SNPS (ascertained via XGBoost) as well as simple additive PRS when explaining heritability in complex phenotypes - do the authors see any potential benefit to such a combined approach with sub-SAGE estimates?

Reviewer #2: The authors introduce a novel method for feature selection. Although the method and concept is interesting, the methodology and application of this method bears many limitations as outlined below:

The results from synthetic data are not very convincing that the method identifies the most important variables with high confidence. The interpretation of score is difficult and no understanding of the range of the score is provided. The testing dataset helps understand the confidence a bit but in real world identifying a testing data every-time is a big task.

The simulations are only performed on a sample size of 16,000 which is a moderate samples size but would not be considered large dataset. Authors should show power, sensitivity and specificity of the method on a large set of simulations to represent real world datasets. Variables for simulations should include combinations of:

Sample sizes

Minor allele frequencies

Noise to Signal Ratio

Penetrance and prevalence of the disease

Real world data application: UKBB dataset consists of >400K samples, however authors only used 64000 samples. It is unclear why they chose only this subset. If the point of the method is to perform GWAS, then the new proposed method should be able to run GWAS on as large of dataset as the conventional methods. It would be imperative to run the analyses on all samples and all variants (possibly an imputed GWAS dataset).

Non-genetic features such as age, sex, ancestry are among the most important features in the real world analyses. However, no interpretation is provided on the significance of known SNPs while adjusting for these confounders. A standard GWAS analyses would include adjusting for any covariates, how does this method account for covariates?

Standard GWAS methods assume an additive model and are most powered at identifying additive effects. An improvement over existing GWAS methods would be to identify non-additive effects. Is this method able to identify only known signals or any novel signals as well for BMI that might help elucidate the genetic underpinnings of obesity more than standard GWAS fro UKBB? The previous method published in BMC Bioinformatics focussed on GXG and GXE, does this method also identify those effects, unclear from the manuscript?

Reviewer #3: Johnsen et al. consider the problem of computing global feature importance in high-dimensional datasets. Prior work on computing global feature importance such as SAGE do not scale with the number of features (even when using Monte Carlo approximations). This work proposes a modified measure of feature importance, sub-SAGE, that only considers the importance of a feature based on its marginal and pairwise interactions. This definition has the advantage of enabling efficient computation especially when used to explain tree-based models. Further, the authors propose the use of Bootstrap resampling to compute the uncertainty of the sub-SAGE estimates. While there has been increasing attention paid to estimating feature importance, the notion of uncertainty in these estimates has not been adequately studied (beyond the notion of uncertainty due to Monte Carlo sampling). This is the first work that attempts to provide uncertainty estimates to their estimates of sub-Sage values which is an important step to interpret and trust feature importance measures. Nevertheless, there are several major comments that the

Limitations:

Major:

1. The assumption of feature independence is quite strong, especially if the target application is genetic data, as the authors also pointed out. The authors need to better justify the target application given the assumptions underlying their method. When the authors consider SNPs that are associated with obesity in the UK Biobank, many of these SNPs are likely to be highly correlated due to linkage disequilibrium. Do the authors prune SNPs that are in strong LD?

2. The title refers to high-dimensional genotype data which might suggest that these methods are being applied in the setting where the number of SNPs exceeds the number of individuals/samples. However this is not the case from the UK Biobank application (< 3,000 SNPs and 64,000 samples). The authors might want to reword the title to be more accurate.

3. The ability to scale the algorithm to high-dimensional data relies on considering the pair-wise feature interaction and marginal feature contribution in sub-SAGE. While this is a reasonable choice, a systematic analysis of the loss of power due to such an approximation is missing. The comparison of sub-SAGE and SAGE in Table 2 is done under a simulation that assumes only pair-wise feature interactions.

4. One contribution the paper claims is the development of an efficient algorithm for global feature importance uncertainty estimation under the tree structure. An alternative approach to achieve the same goal is to instead estimate instance-wise feature attribution values using Tree-SHAP, approximate the global feature importance using the expectation of individual feature attribution estimates, and then use the bootstrap similarly to estimate uncertainty. (Covert et al. have justified the equivalency between these two approaches). The authors should clearly state the advantage of computing global feature importance directly compared to calculating it with the aggregated instance-wise feature importance.

5. A more general question for the authors is to demonstrate the usefulness of the uncertainty estimates. One natural application is to perform feature selection. If the intention of the uncertainty estimation is for feature selection purposes, it would be valuable to compare it with some commonly used feature selection techniques in the area. Additional analyses and discussion of the utility of uncertainty estimates would strengthen the manuscript.

Minor:

1. What does the notation y(x) in Equation 5 refer to?

2. There is a sign missing in front of the second line of Equation (19).

**********

Have the authors made all data and (if applicable) computational code underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data and code underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data and code should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data or code —e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: No: The link leads to GitHub page for previously published method in BMC Bioinformatics.

Reviewer #3: Yes

**********

PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No

Reviewer #3: No

Figure Files:

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email us at figures@plos.org.

Data Requirements:

Please note that, as a condition of publication, PLOS' data policy requires that you make available all data used to draw the conclusions outlined in your manuscript. Data must be deposited in an appropriate repository, included within the body of the manuscript, or uploaded as supporting information. This includes all numerical values that were used to generate graphs, histograms etc.. For an example in PLOS Biology see here: http://www.plosbiology.org/article/info%3Adoi%2F10.1371%2Fjournal.pbio.1001908#s5.

Reproducibility:

To enhance the reproducibility of your results, we recommend that you deposit your laboratory protocols in protocols.io, where a protocol can be assigned its own identifier (DOI) such that it can be cited independently in the future. Additionally, PLOS ONE offers an option to publish peer-reviewed clinical study protocols. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols

Dear Mr. Johnsen,

Thank you very much for submitting your manuscript "Inferring feature importance with uncertainties with application to large genotype data" for consideration at PLOS Computational Biology. As with all papers reviewed by the journal, your manuscript was reviewed by members of the editorial board and by several independent reviewers. The reviewers appreciated the attention to an important topic. Based on the reviews, we are likely to accept this manuscript for publication, providing that you modify the manuscript according to the review recommendations.

Please prepare and submit your revised manuscript within 30 days. If you anticipate any delay, please let us know the expected resubmission date by replying to this email.

When you are ready to resubmit, please upload the following:

[1] A letter containing a detailed list of your responses to all review comments, and a description of the changes you have made in the manuscript. Please note while forming your response, if your article is accepted, you may have the opportunity to make the peer review history publicly available. The record will include editor decision letters (with reviews) and your responses to reviewer comments. If eligible, we will contact you to opt in or out

[2] Two versions of the revised manuscript: one with either highlights or tracked changes denoting where the text has been changed; the other a clean version (uploaded as the manuscript file).

Important additional instructions are given below your reviewer comments.

Thank you again for your submission to our journal. We hope that our editorial process has been constructive so far, and we welcome your feedback at any time. Please don't hesitate to contact us if you have any questions or comments.

Sincerely,

Shaun Mahony

Academic Editor

PLOS Computational Biology

Ilya Ioshikhes

Section Editor

PLOS Computational Biology

***********************

A link appears below if there are any accompanying review attachments. If you believe any reviews to be missing, please contact ploscompbiol@plos.org immediately:

Reviewer's Responses to Questions

Comments to the Authors:

Please note here if the review is uploaded as an attachment.

Reviewer #1: I thank the authors for their detailed response to comments and for the additional text added to the manuscript.

Reviewer #3: In the revised version, the authors addressed most of the previous comments in the following aspects:

1. Conceptual advantage of sub-SAGE compared to linear approach of feature selection

2. The advantage of sub-SAGE uncertainty calculating compared to SHAP.

3. Discussion of the advantage and limitations of sub-SAGE approximation compared to SAGE.

Here are some additional comments:

1. In lines 472-475, the authors discussed that the threshold and multiple testing procedure is needed to control the false positive rate. The authors should further expand this part since how to set the threshold and demonstrate calibration is not directly clear from the estimated uncertainty computed using the sub-SAGE approach, but a crucial step in GWAS.

2. In table 3, it would be good to run linear models on the selected feature, compute their feature coefficient and the corresponding p-values and discuss how much benefit we gain from computing feature importance in a nonlinear way using sub-SAGE.

3. In line 398, the SNP rs2820312 exclusively detected by sub-SAGE need further analysis. For example, have any other SNPs in the LD block of SNP rs2820312 been previously detected to be associated with obesity ?

4. In lines 450-454, the authors described several sources of the uncertainty of the Sub-SAGE uncertainty estimate. However, another important source of uncertainty, the model uncertainty, needs to be mentioned. I suggest the authors add it to the text.

Overall, the proposed algorithm is novel and could potentially benefit the understanding of large-genetic dataset. However, the advantage of sub-SAGE on actual genetic applications still has room for improvement.

**********

Have the authors made all data and (if applicable) computational code underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data and code underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data and code should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data or code —e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #3: Yes

**********

PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #3: No

Figure Files:

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email us at figures@plos.org.

Data Requirements:

Please note that, as a condition of publication, PLOS' data policy requires that you make available all data used to draw the conclusions outlined in your manuscript. Data must be deposited in an appropriate repository, included within the body of the manuscript, or uploaded as supporting information. This includes all numerical values that were used to generate graphs, histograms etc.. For an example in PLOS Biology see here: http://www.plosbiology.org/article/info%3Adoi%2F10.1371%2Fjournal.pbio.1001908#s5.

Reproducibility:

To enhance the reproducibility of your results, we recommend that you deposit your laboratory protocols in protocols.io, where a protocol can be assigned its own identifier (DOI) such that it can be cited independently in the future. Additionally, PLOS ONE offers an option to publish peer-reviewed clinical study protocols. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols

References:

Review your reference list to ensure that it is complete and correct. If you have cited papers that have been retracted, please include the rationale for doing so in the manuscript text, or remove these references and replace them with relevant current references. Any changes to the reference list should be mentioned in the rebuttal letter that accompanies your revised manuscript.

If you need to cite a retracted article, indicate the article’s retracted status in the References list and also include a citation and full reference for the retraction notice.

Dear Mr. Johnsen,

We are pleased to inform you that your manuscript 'Inferring feature importance with uncertainties with application to large genotype data' has been provisionally accepted for publication in PLOS Computational Biology.

Before your manuscript can be formally accepted you will need to complete some formatting changes, which you will receive in a follow up email. A member of our team will be in touch with a set of requests.

Please note that your manuscript will not be scheduled for publication until you have made the required changes, so a swift response is appreciated.

IMPORTANT: The editorial review process is now complete. PLOS will only permit corrections to spelling, formatting or significant scientific errors from this point onwards. Requests for major changes, or any which affect the scientific understanding of your work, will cause delays to the publication date of your manuscript.

Should you, your institution's press office or the journal office choose to press release your paper, you will automatically be opted out of early publication. We ask that you notify us now if you or your institution is planning to press release the article. All press must be co-ordinated with PLOS.

Thank you again for supporting Open Access publishing; we are looking forward to publishing your work in PLOS Computational Biology. 

Best regards,

Shaun Mahony

Academic Editor

PLOS Computational Biology

Ilya Ioshikhes

Section Editor

PLOS Computational Biology

***********************************************************

Reviewer's Responses to Questions

Comments to the Authors:

Please note here if the review is uploaded as an attachment.

Reviewer #3: The authors have addressed major concerns from the previous revision. Overall, this work presents an innovative algorithm that will motivate additional work in the community.

**********

Have the authors made all data and (if applicable) computational code underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data and code underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data and code should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data or code —e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #3: Yes

**********

PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #3: No