Congratulations, Josh!!! 🎉🎊🙌

(end) Regarding (4), we already have a discussion point that speaks to this. You can constrain Dxy to a value other than 0, so if there is a known correlation r in your data, you can define your constraining space as wx’*Dxy*wy = r

(1) Hi @ar0mcintosh.bsky.social I think a tensor version of CRM should be feasible; similar work has been done with CCA (arxiv.org/abs/1502.02330). @schottdorflab.bsky.social what are your thoughts on this?

(7) I would say that partial correlation is a closer analogy to CRM than semi-partial because we find weights for both sides. Technically, CRM is rather steering the solution away from variance shared with the confound than regressing it out.

(6) It is true that CRM would find a lower bound of maximal correlation because the max includes the confound and should be higher.

(5) There are many other situations where the strongest correlations are *not* of interest. E.g., ERPs have typical shapes; if you wanted to find a condition specific waveform, you could estimate Cxy between ERPs from the same condition and compute Dxy from ERPs belonging to different conditions.

(4) Another straightforward choice for Dxy is to recompute the same cross-covariance matrix as in Cxy but on data bandpass filtered around the line-noise band (we use this in example 3 in the paper).

(3) The key to using CRM is to find a useful Dxy. This can be different data (e.g., from a baseline period), or the same pseudo-randomized data where only the association of interest is eliminated.