of this submission and make suggestions for improvement:
Strengths - The authors provide a useful extension to existing work on VAEs, which appears to be well-suited for the target application they have in mind. - The authors include both synthetic and empirical data as test cases for their method and compare it to a range of related approaches. - I especially appreciated, that the authors validated their method on the empirical data and also provide an assessment of face validity using established psychological questionnaires (BDI and AQ). - I also appreciated the ethics statement pointing out that the method requires additional validation, before it may enter the clinic. - The paper is to a great extend clearly written.
Weaknesses - In Figure 2 it seems that Manner-1 use of diagnostic information is more important than Manner-2 use of this information, which calls your choice into question to set lambda = 0.5 in equation 3. Are you able to learn this parameter from the data? - Also in Figure 2, when applying your full model to the synthetic data, it appears to me that inverting your model seems to underestimate the within-cluster variance (compared to the ground truth). Could it be that your manner-1 use of information introduces constraints that are too strong, as they do not allow for this variance? - It would strengthen your claims of “superiority” of your approach over others, if you could provide a statistical test that shows that your approach is indeed better at recovering the true relationship compared to others. Please, provide such tests. - There are important information about the empirical study missing that should be mentioned in the supplement, such as recording parameters for the MRI, preprocessing steps, was the resting-state recorded under eyes-open or eyes-closed condition? A brief explanation of the harmonization technique would also be appreciated. It would also be helpful to mention the number of regions in the parcellation in the main text. - The validation scheme using the second study is not clear to me. Were the models trained on dataset A and then directly applied to dataset B or did you simply repeat the training in dataset B. If the latter is the case, I would refer to this as a replication dataset and not a validation dataset (which would require applying the same model on a new dataset, without retraining). - Have you applied multiple testing correction for the FID comparisons across diagnoses. If so which? If not, you should apply it and please, state that clearly in the main manuscript. - It is somewhat surprising that the distance between SCZ and MDD is shorter than between SCZ and ASD as often the latter two are viewed as closely related. It might be helpful to discuss, why that may be the case in more detail. - The third ethics statement is not clear to me. Could you clarify? - The font size in the figures is too small. Please, increase it to improve readability.
- There are important information about the empirical study missing that should be mentioned in the supplement, such as recording parameters for the MRI, preprocessing steps, was the resting-state recorded under eyes-open or eyes-closed condition? A brief explanation of the harmonization technique would also be appreciated. It would also be helpful to mention the number of regions in the parcellation in the main text.