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Gradient Hard Thresholding Pursuit for Sparsity-Constrained Optimization
Xiao-Tong Yuan XTYUAN 1980@GMAIL .COM
Department of Statistical Science, Cornell University, Ithaca, NY 14853, USA
Dept. of Statistics Biostatistics, Dept. of Computer Science, Rutgers University, Piscataway, NJ 08854, USA
Ping Li PINGLI @STAT.RUTGERS .EDU
Dept. of Statistics Biostatistics, Dept. of Computer Science, Rutgers University, Piscataway, NJ 08854, USA
Tong Zhang TZHANG @STAT.RUTGERS .EDU
Dept. of Statistics Biostatistics, Rutgers University, Piscataway, NJ 08854, USA
Abstract learning (Jalali et al., 2011) where the likelihood of sam-
Hard Thresholding Pursuit (HTP) is an iterative ples drawn from an underlying probabilistic model is used
greedy selection procedure for finding sparse so- to measure data fidelity.
lutions of underdetermined linear systems. This However, due to the non-convex cardinality constraint,
method has been shown to have strong theoreti- the problem ( 1) is generally NP-hard even for quadratic
cal guarantees and impressive numerical perfor- cost functions (Natarajan, 1995). Thus, one must in-
mance. In this paper, we generalize HTP from stead seek approximate solutions. In particular, the spe-
compressed sensing to a generic problem setup cial case of ( 1) in least square regression models has
of sparsity-constrained convex optimization. The gained significant attention in the area of compre
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