Minimizing the distortions in electrophysiological source imaging of cortical oscillatory activity via Spectral Structured Sparse Bayesian Learning
Bibliographic record
Abstract
Oscillatory processes at all spatial scales and on all frequencies underpin brain function. Electrophysiological Source Imaging (ESI) is the data-driven brain imaging modality that provides the inverse solutions to the source processes of the EEG, MEG, or ECoG data. This study aimed to carry out an ESI of the source cross-spectrum while controlling common distortions of the estimates. As with all ESI-related problems under realistic settings, the main obstacle we faced is a severely ill-conditioned and high-dimensional inverse problem. Therefore, we opted for Bayesian inverse solutions that posited a priori probabilities on the source process. Indeed, rigorously specifying both the likelihoods and a priori probabilities of the problem leads to the proper Bayesian inverse problem of cross-spectral matrices. These inverse solutions are our formal definition for cross-spectral ESI (cESI), which requires a priori of the source cross-spectrum to counter the severe ill-condition and high-dimensionality of matrices. However, inverse solutions for this problem were NP-hard to tackle or approximated within iterations with bad-conditioned matrices in the standard ESI setup. We introduce cESI with a joint a priori probability upon the source cross-spectrum to avoid these problems. cESI inverse solutions are low-dimensional ones for the set of random vector instances and not random matrices. We achieved cESI inverse solutions through the variational approximations via our Spectral Structured Sparse Bayesian Learning (ssSBL) algorithm https://github.com/CCC-members/Spectral-Structured-Sparse-Bayesian-Learning . We compared low-density EEG (10–20 system) ssSBL inverse solutions with reference cESIs for two experiments: (a) high-density MEG that were used to simulate EEG and (b) high-density macaque ECoG that were recorded simultaneously with EEG. The ssSBL resulted in two orders of magnitude with less distortion than the state-of-the-art ESI methods. Our cESI toolbox, including the ssSBL method, is available at https://github.com/CCC-members/BC-VARETA_Toolbox .
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".