Comment on a PREreview of "Nonlinear brain connectivity from neurons to networks: quantification, sources and localization"

This Zenodo record is a permanently preserved version of a comment on a PREreview. You can view the complete PREreview and comments at https://prereview.org/reviews/14286180. We sincerely thank the anonymous reviewers for their thoughtful feedback. While we acknowledge the constraints of this format, we appreciate the opportunity to engage with these points and hope it will lead to a more direct and open exchange. Major Issues We acknowledge that our estimator of MI is not novel; however, it is well-suited for the objectives of this study. As outlined in the paper, we evaluated alternative estimators, including those included in the cited implementation, and found no substantial differences in their outcomes. While valuable, conducting a comprehensive numerical comparison of all potential estimators falls outside the scope of this work and would be more appropriately addressed in a separate, focused publication. Additionally, we observed significantly longer computational times with some alternative methods—often hundreds of times greater—and parameters such as k in KSG and the bandwidth in KDE still require heuristic tuning. The extra-Gaussian information underlying our Relative Non-Linearity measure is grounded in solid information-theoretic principles. In the paper's first section, we further adopted a pragmatic approach by using ratios to facilitate straightforward visualization and comparison. While we recognize the potential for a more formal theoretical framework, such an endeavor—similar to the extensive efforts in Partial Information Decomposition over the past decade—lies beyond the scope of this paper. We welcome and would be thrilled to see this work catalyze further discussion and exploration. The cited studies offer interesting insights into comparing linear and nonlinear coupling metrics across various modalities. While this topic has been explored, it is inherently open-ended, allowing for the potential emergence of additional nonlinear metrics that could surpass existing linear ones. Our claim takes a different perspective: we propose to quantify non-linearity as such and conjecture that given the limited non-linearity observed in some of the modalities analyzed and with current technological capabilities, while there might be statistically detectable differences, no metric can offer a substantial improvement over linear methods. Thank you for sharing these references. They provide helpful context and may be of particular interest to researchers seeking a broader understanding of factors that may influence the apparent linearity of brain activity. As mentioned above, our focus is not on evaluating all available methods for computing pairwise dependence. Instead, we aim to assess the practical benefits of alternative approaches to linear methods, which is why we chose MI, as it captures all possible dependencies highlighted by other approaches. In particular, we strive to reduce variability in analysis techniques and improve reproducibility. Minor Issues Thank you for your suggestion. We have worked to make our explanations more explicit and precise. Competing interests I'm one of the paper's authors, and I write on behalf and with the approval of all the authors.