Abstract: High-dimensional datasets, where the number of measured variables is larger than the sample size, are not uncommon in modern real-world applications such as brain connectivity modeling using functional Magnetic Resonance Imaging (fMRI) data. Conventional statistical signal processing tools and mathematical models could fail at handling such high-dimensional problems, and developing efficient algorithms for high-dimensional situations are of great importance.
This talk mainly focuses on the following two issues: (1) recovery of sparse regression coefficients in linear systems, here we focus on the Lasso-type sparse linear regression; (2) estimation of high-dimensional covariance matrix and precision matrix, both subject to additional random noise.