Generalized Connectivity Matrix Response Regression with Applications in Brain Connectivity Studies.

Area of Science:

• Neuroscience
• Statistics
• Machine Learning

Background:

• Multiple-subject network data, comprising individual connectivity matrices and subject covariates, are increasingly prevalent.
• Analyzing these complex datasets requires advanced statistical models to capture population-level patterns and individual variations.

Purpose of the Study:

• To propose a generalized matrix response regression model for multiple-subject network data.
• To characterize population connectivity using a low-rank intercept and covariate effects via a sparse slope tensor.
• To develop an efficient algorithm for parameter estimation and analyze its statistical properties.

Main Methods:

• A novel generalized matrix response regression model is formulated.
• An alternating gradient descent algorithm is developed for parameter estimation.
• Non-asymptotic error bounds are established for the estimator.
• Strong consistency for graph community recovery and edge selection are theoretically proven.

Main Results:

• The proposed model effectively estimates population-level connectivity and sparse covariate effects.
• The developed algorithm provides efficient parameter estimation with quantifiable computational and statistical error bounds.
• The method demonstrates strong consistency in recovering graph communities and selecting relevant edges.
• Simulations and real-world brain connectivity studies validate the model's efficacy.

Conclusions:

• The generalized matrix response regression model offers a powerful framework for analyzing multiple-subject network data.
• The proposed estimation algorithm is computationally efficient and statistically sound.
• The method provides reliable graph community recovery and edge selection, advancing brain connectivity research.