On Iterative Hard Thresholding Methods for High-dimensional M-Estimation

The use of M-estimators in generalized linear regression models in high dimensional settings requires risk minimization with hard L_0 constraints. Of the known methods, the class of projected gradient descent (also known as iterative hard thresholding (IHT)) methods is known to offer the fastest and most scalable solutions. However, the current state-of-the-art is only able to analyze these methods in extremely restrictive settings which do not hold in high dimensional statistical models.