[Paper Review] Statistical control for spatio-temporal MEG/EEG source imaging with desparsified multi-task Lasso

Jérôme-Alexis Chevalier, Alexandre Gramfort+2 more|arXiv (Cornell University)|Sep 29, 2020

Photoacoustic and Ultrasonic Imaging48 references4 citations

TL;DR

This paper proposes ecd-MTLasso, an ensemble of clustered desparsified multi-task Lasso estimators for spatio-temporal MEG/EEG source imaging that provides statistical guarantees for false discovery control. By integrating desparsified Lasso with spatial clustering and ensembling, it enables principled thresholding of source maps while balancing spatial specificity and sensitivity.

ABSTRACT

Detecting where and when brain regions activate in a cognitive task or in a given clinical condition is the promise of non-invasive techniques like magnetoencephalography (MEG) or electroencephalography (EEG). This problem, referred to as source localization, or source imaging, poses however a high-dimensional statistical inference challenge. While sparsity promoting regularizations have been proposed to address the regression problem, it remains unclear how to ensure statistical control of false detections. Moreover, M/EEG source imaging requires to work with spatio-temporal data and autocorrelated noise. To deal with this, we adapt the desparsified Lasso estimator -- an estimator tailored for high dimensional linear model that asymptotically follows a Gaussian distribution under sparsity and moderate feature correlation assumptions -- to temporal data corrupted with autocorrelated noise. We call it the desparsified multi-task Lasso (d-MTLasso). We combine d-MTLasso with spatially constrained clustering to reduce data dimension and with ensembling to mitigate the arbitrary choice of clustering; the resulting estimator is called ensemble of clustered desparsified multi-task Lasso (ecd-MTLasso). With respect to the current procedures, the two advantages of ecd-MTLasso are that i)it offers statistical guarantees and ii)it allows to trade spatial specificity for sensitivity, leading to a powerful adaptive method. Extensive simulations on realistic head geometries, as well as empirical results on various MEG datasets, demonstrate the high recovery performance of ecd-MTLasso and its primary practical benefit: offer a statistically principled way to threshold MEG/EEG source maps.

Motivation & Objective

• Address the lack of statistical control in sparse MEG/EEG source imaging methods, particularly for false positive detection.
• Overcome the high-dimensional, ill-posed inverse problem in spatio-temporal MEG/EEG data with autocorrelated noise.
• Develop a method that offers statistical inference guarantees (e.g., p-values, FWER control) for sparse, high-dimensional regression in neuroimaging.
• Enable a trade-off between spatial specificity and detection sensitivity through adaptive clustering and ensembling.
• Provide a practical, computationally efficient method usable on standard hardware for real-world MEG/EEG datasets.

Proposed method

• Adapt the desparsified Lasso estimator to a multi-task setting (d-MTLasso) to handle temporal correlations and improve statistical power.
• Introduce spatially constrained clustering using Ward’s criterion to reduce data dimension and mitigate ill-posedness in the design matrix.
• Apply ensembling across multiple clustering solutions to reduce sensitivity to arbitrary cluster choices and improve robustness.
• Use a desparsified estimator to obtain asymptotically Gaussian-distributed test statistics for each source location, enabling p-value computation.
• Incorporate auto-correlated noise modeling via an AR(1) process in the time domain to improve inference validity.
• Implement a thresholding strategy based on false discovery rate (FDR) or family-wise error rate (FWER) control using estimated p-values.

Experimental results

Research questions

• RQ1 Can a desparsified multi-task Lasso estimator provide valid statistical inference (e.g., p-values, confidence intervals) in high-dimensional, autocorrelated spatio-temporal MEG/EEG data?
• RQ2 How can spatial clustering and ensembling improve the robustness and sensitivity of sparse source imaging while preserving statistical validity?
• RQ3 To what extent can the method balance spatial specificity and detection power through adjustable clustering tolerance?
• RQ4 Does the proposed ecd-MTLasso method achieve better source recovery and false positive control than existing sparse or non-sparse MEG/EEG methods?
• RQ5 Can the method be efficiently deployed on standard hardware for real-world neuroimaging applications?

Key findings

• The ecd-MTLasso method achieves reliable statistical control of the family-wise error rate (FWER) under appropriate assumptions, including sparsity and moderate correlation.
• Extensive simulations on realistic head models show that ecd-MTLasso recovers true sources with high sensitivity and low false positive rates.
• Empirical results on multiple MEG datasets demonstrate that ecd-MTLasso outperforms standard methods like dSPM and sLORETA in source localization accuracy.
• The method enables principled thresholding of source maps using p-values, offering a statistically valid alternative to heuristic thresholding.
• With a recommended configuration (C=1000, 20–50 ms windows, 5–10 ms sampling), ecd-MTLasso runs in under 10 minutes on standard hardware.
• The method is adaptive: increasing spatial tolerance (C) improves sensitivity at the cost of reduced spatial specificity, allowing users to tune the trade-off based on data quality.