  


Consistency Bounds and Support Recovery of Dstationary Solutions of Sparse Sample Average Approximations
Miju Ahn (mijuasmu.edu) Abstract: This paper studies properties of the d(irectional)stationary solutions of sparse sample average approximation (SAA) problems involving differenceofconvex (dc) sparsity functions under a deterministic setting. Such properties are investigated with respect to a vector which satisfies a verifiable assumption to relate the empirical SAA problem to the expectation minimization problem defined by an underlying data distribution. We derive bounds for the distance between the two vectors and the difference of the model outcomes generated by them. Furthermore, the inclusion relationships between their supports, sets of nonzero valued indices, are studied. We provide conditions under which the support of a dstationary solution is contained within, and contains, the support of the vector of interest; the first kind of inclusion can be shown for any arbitrarily given set of indices. Some of the results presented herein are generalization of the existing theory for a specialized problem of $\ell_1$norm regularized least squares minimization for linear regression. Keywords: nonconvex optimization, sparse learning, differenceofconvex program, directional stationarity Category 1: Convex and Nonsmooth Optimization Citation: Download: Entry Submitted: 12/29/2018 Modify/Update this entry  
Visitors  Authors  More about us  Links  
Subscribe, Unsubscribe Digest Archive Search, Browse the Repository

Submit Update Policies 
Coordinator's Board Classification Scheme Credits Give us feedback 
Optimization Journals, Sites, Societies  