Automated regularization of M/EEG sensor covariance using cross- validation.

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Automated regularization of M/EEG sensor covariance using cross- validation. Based on: Engemann, D.A., Gramfort, A. (2014). Automated model selection in covariance estimation and spatial whitening of MEG and EEG signals. NeuroImage, ISSN 1053-8119 Alexandre Gramfort ParisTech, CEA/INSERM Neurospin, Paris, France Denis A. Engemann CEA/INSERM Neurospin, Gif-sur-Yvette, France ICM, Paris, France https://github.com/mne-tools/mne-python http://www.sciencedirect.com/science/article/pii/S1053811914010325

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- The problem of estimating the M/EEG noise covariance - A statistical learning solution to the problem - Impact on M/EEG inverse solutions - Implementation and API in MNE- Python Plat du jour

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M/EEG inverse solutions take into account the spatial structure of the sensor noise

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M inimum N orm E stimates aka Tikhonov Regularization aka Ridge Regression M = R0GT (GR0GT + C) 1 •constraint linear model (cf. beamformer, S-LORETA, ...) •Gaussian, uncorrelated noise •whitening via covariance (C) ˆ X = RGt(GRGt + C) 1Y ˆ X = R ˜ Gt( ˜ GR ˜ Gt + I) 1 ˜ Y unwhitened whitened 98.749% M/EEG users used whitening

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With whitened data the covariance would be diagonal C = 1 T Y Y t

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No content

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Woolrich, 2011, Neuroimage 10s 80s True sources VS LCMV Beamformer given C

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Regularize your covariance! but let the data tell you how.

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Model selection: Log-likelihood Given my model C how likely are unseen data Y? Higher log likelihood = superior C ➡ better whitening L ( Y |C ) = 1 2 T Trace( Y Y tC 1 ) 1 2 log((2 ⇡ ) N det( C )) .

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Cross-validation -1234.3 -1324.7 -1467.0 -1178.9 average log likelihood and select the best model

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1. Hand-set (REG) 2. Ledoit-Wolf (LW) 3. Cross-validated shrinkage (SC) 4. Probabilistic PCA (PPCA) 5. Factor Analysis (FA) We compared 5 strategies: simple, fast complex, slow C0 = C + ↵I, ↵ > 0 CF A = HHt + diag( 1 , . . . , D) CPPCA = HHt + 2IN CLW = (1 ↵)C + ↵µI CSC = (1 ↵)C + ↵µI

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Which model crashes, which one ﬂies?

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variable noise, true rank 10 300 500 700 900 1100 1300 1500 1700 1900 1uPber of saPSles −49 −48 −47 −46 −45 −44 −43 −42 Log-lLNelLhood (D) heWerosFedasWLF - Wrue ranN 10 33CA FA LW 6C Factor Analysis wins

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Factor Analysis recovers true rank variable noise, true rank 10

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300 500 700 900 1100 1300 1500 1700 1900 1uPber of saPSles −73.0 −72.5 −72.0 −71.5 −71.0 −70.5 −70.0 −69.5 −69.0 Log-lLNelLhood (D) heWerosFedasWLF - Wrue ranN 40 33CA FA LW 6C variable noise, true rank 40 Shrinkage Estimators win!

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Any estimator can be the best.

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MEG and EEG data

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Inspect models, apply model selection, whiten data.

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whitened Global Field Power ( 2) Expected value of 1 during baseline, if appropriately whitened

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select model based on log likelihood score (bigger = closer to zero is better)

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Text whitening based on best C 95 % of the signals expected to assume values betwwen -1.96 and 1.96 during baseline

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Our best models: SC Shrinkage Estimator - 71% Factor Analysis - 21% Hand-set regularization - 8% Only FA won on combined sensors, even with small N PPCA was never better than FA

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Inspect models, apply model selection, whiten data. Impact validation on MNE source estimates

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faces > scrambled SPM faces dataset, Henson (2003) 20 epochs 40 epochs 60 epochs worst best std

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The regularized covariance stabilizes dSPM source amplitudes

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What have we learned? M/EEG sensor noise is not homoscedastic Cross-validated covariance estimates yield spatial whitening without manual tuning The best model depends on system, data rank and noise The best model stabilizes source estimates

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NEW in # Authors: Denis A. Engemann   # Alexandre Gramfort   #  # License: BSD (3-clause)    import mne    data_path = mne.datasets.sample.data_path()  raw_fname = data_path + '/MEG/sample/sample_audvis_filt-0-40_raw.fif'  event_fname = data_path + '/MEG/sample/sample_audvis_filt-0-40_raw-eve.fif'    raw = mne.io.Raw(raw_fname, preload=True)  raw.info['bads'] += ['MEG 2443']  raw.filter(1, 30)    epochs = mne.Epochs(  raw, events=mne.read_events(event_fname), event_id=1, tmin=-.2, tmax=0.5,  picks=mne.pick_types(raw.info, meg=True, eeg=True, exclude='bads'),  baseline=None, reject=dict(mag=4e-12, grad=4000e-13, eeg=80e-6))    ###############################################################################  # Compute covariance using automated regularization and show whitening  noise_covs = mne.cov.compute_covariance(epochs[:20], tmax=0, method='auto',  return_estimators=True)    evoked = epochs.average()  evoked.plot() # plot evoked response  evoked.plot_white(noise_covs) # compare estimators 