Functional group bridge for simultaneous regression and support estimation.

Area of Science:

• Neuroscience
• Biostatistics
• Signal Processing

Background:

• Intracranial electroencephalography (iEEG) experiments involve analyzing differential brain activities across multiple experimental conditions.
• Identifying localized brain regions with significant responses is crucial, presenting a function-on-scalar regression challenge.
• Existing methods may not simultaneously estimate complex functional patterns and pinpoint precise active brain areas.

Purpose of the Study:

• To develop a method for simultaneous estimation and support recovery of functional brain activity in iEEG data.
• To address the challenge of locally sparse functions in brain activity analysis.
• To account for data heterogeneity in function-on-scalar mixed effect models.

Main Methods:

• Proposed a weighted group bridge approach for simultaneous function estimation and support recovery within function-on-scalar mixed effect models.
• Utilized B-splines to convert function sparsity into a sparse vector representation.
• Developed a fast nonconvex optimization algorithm employing nested alternative direction method of multipliers (ADMM) for efficient estimation.

Main Results:

• Established large sample properties for the proposed method, demonstrating rate-optimal estimation under the L2 norm.
• Observed a phase transition phenomenon in the estimated coefficient functions.
• Derived convergence rates for support estimation, achieving selection consistency under delta-sparsity and strict sparsity conditions.

Conclusions:

• The weighted group bridge approach provides a robust framework for analyzing iEEG data, enabling simultaneous functional estimation and precise localization of brain activity.
• The method's theoretical properties ensure reliable performance in identifying neural responses.
• Demonstrated efficacy through simulations and application to a novel iEEG dataset for multisensory integration studies.