Title: Support recovery for sparse high dimensional matrices
Authors: Adam Kashlak - University of Alberta (Canada) [presenting]
Linglong Kong - University of Alberta (Canada)
Abstract: The estimation problem for high dimensional covariance matrices and coefficient matrices is considered under the assumption of sparsity, which is qualitatively when most of the matrix entries are zero or negligible. Much past work has gone into such estimation based on approaches such as thresholding and LASSO. Instead, we take a unique and nonasymptotic approach to such estimation by using concentration inequalities to construct confidence sets for matrix estimators guaranteed to hold for finite samples. This is followed by an optimization over the confidence set in order to improve the estimator with respect to the sparsity criterion. In the context of support recovery, this methodology allows for the fixing of a false positive rate--i.e. zero entry claimed to be non-zero--and optimizing the true positive rate.