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Algorithms & Randomness Center (ARC)
Xiaoming Huo
Monday, November 11, 2019
Klaus 1116 East- 11:00 am
Title: Homotopic methods can significantly speed up the Computation of the Lasso-type of estimators
Abstract: In optimization, it is well known that when the objective functions are strictly convex, gradient based approaches can be extremely effective, and most likely achieve the exponential rate in convergence. At the same time, the Lasso-type of estimator in general cannot achieve the optimal rate due to the undesirable behavior of the absolute function at the origin. The homotopic approach is to use a sequence of surrogate functions to approximate the L1 penalty in the Lasso-type of estimators. The approximating functions will converge to the L1 penalty in the Lasso estimator. At the same time, each approximating function is strictly convex and facilitates efficient numerical convergence. We demonstrate that by meticulously defined the surrogate functions, one can approve faster numerical convergence rate than any existing methods in computing for the Lasso-type of estimators. Our numerical simulations validate the above claim. We demonstrate the applications of the proposed methods in some cases.
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