An exact penalty removed all disjoint graphical lasso edges in bipolar SEEG paths with positive finite contact variances and zero covariance between contacts

We tested when graphical lasso removes montage edges from consecutive bipolar SEEG paths. Distinct source contacts had zero covariance. Their variances were positive and finite. The input had unit diagonal, and the diagonal had no penalty. We proved a necessary and sufficient clearing penalty and a sharp general upper bound of 0.2287884. We calibrated the model with 48 public samples from eight patients in OpenNeuro ds004473, version 1.0.2. At penalty 0.05, the mean patient median retained fraction was 43.02% for disjoint edges within a path. The mean patient median clearing penalty was 0.17811. All 48 raw range conversions matched the archived spectra. An offline repeat matched nine analysis files. A separate optimizer had the same edge support in 1,419 fits at a 0.00001 cutoff. The package preserves the proof, diagnostic, source code, spectra, provenance, results, and reproduction instructions. These findings concern a constructed covariance model. They do not establish independence or neural interaction in recorded signals.

graphical lasso · bipolar SEEG · sparse precision matrix · partial correlation · contact variance · exact penalty threshold · covariance model · stereoelectroencephalography