Excited to share our paper @NeuroImage_EiC by @DavSabbagh with @PierreAblin @GaelVaroquaux @agramfort doi.org/10.1016/j.neur… Nonlinear subject-level regression on M/EEG using linear models without source localization: theory + empirical benchmarks Thread👇 
1/ When regressing outcomes on M/EEG power spectra (f = power; f = log(power), ...), volume conduction creates a nonlinear problem that cannot be addressed with otherwise effective linear models. Source localization can fix this but is not always available. How can we do without?
2/ As long as we consider a single subject we have nearly constant volume conduction. In this case we can show mathematically that source localization can be replaced with spatial filters or with Riemannian geometry.
3/ As multiple subjects induce varying volume conduction, these mathematical guarantees do not hold. Yet, our simulations suggest that spatial filters and Riemannian geometry may be useful. Let’s explore this gap with real M/EEG data.
4/ We performed age-prediction from MEG band-limited covariances with ridge regression on the Cam-CAN dataset. Riemannian embeddings (orange) & spatial filters (red) outperformed “naive” prediction from the diagonal (green) or the entire covariance (blue).
5/ What if we perform the same analysis after source localization? Now the “naive” diagonal model, representing the power in one frequency band, by far performs best, suggesting that Riemannian embeddings in sensor-space partially handle individual volume conduction. But how?
6/ We repeated the analysis on degraded covariances only containing information from leadfields or, in addition, spatially uniform power. It turns out that the leadfiels contained some information on aging and that Riemannian embeddings were most sensitive to this information.
7/ This information was not explained by head positioning, pointing at differences in brain anatomy. It’s conceivable that the Riemannian embedding better exposed this anatomical information, facilitating deconfounding for the ridge model and/or contributing unique information.
8/ Noise may be another source of model violations. Repeating the analysis with no or partial preprocessing, the Riemannian model was robust. Spatial filters or “naive” power were more affected. With minimum processing (SSS) Riemann showed the best performance observed so far.
9/ Well, it’s MEG and it’s got 306 channels. How about clinical EEG? We then repeated the analysis on ~1000 EEGs (22 channels) from the Temple University dataset. We found remarkably similar performance levels, again with the Riemannian embeddings leading to the best performance.
10/ Conclusion: When predicting from M/EEG power spectra is the priority, the capacity of linear models can be extended by Riemannian embeddings & spatial filters despite model violations. Source localization remains a standard. Future research will have to close the gap!
We would like to thank @lucas_c_parra and @wmvanvliet for their invaluable critical feedback on our manuscript.
