Tractable continuous approximations for constraint selection via cardinality minimization
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Miju Ahn
A Generalized Formulation for Group Selection via ADMM
This paper studies a statistical learning model where the model coefficients have a pre-determined non-overlapping group sparsity structure. We consider a combination of a loss function and a regularizer to recover the desired group sparsity patterns, which can embrace many existing works. We analyze the stationary solution of the proposed formulation, obtaining a sufficient condition … Read more
Iteratively Reweighted Group Lasso based on Log-composite Regularization
This paper addresses supervised learning problems with structured sparsity, where subsets of model coefficients form distinct groups. We introduce a novel log-composite regularizer in a bi-criteria optimization problem together with a loss (e.g., least squares) in order to reconstruct the desired group sparsity structure. We develop an iteratively reweighted algorithm that solves the group LASSO … Read more
Consistency Bounds and Support Recovery of D-stationary Solutions of Sparse Sample Average Approximations
This paper studies properties of the d(irectional)-stationary solutions of sparse sample average approximation (SAA) problems involving difference-of-convex (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. … Read more
Structural Properties of Affine Sparsity Constraints
We introduce a new constraint system for sparse variable selection in statistical learning. Such a system arises when there are logical conditions on the sparsity of certain unknown model parameters that need to be incorporated into their selection process. Formally, extending a cardinality constraint, an affine sparsity constraint (ASC) is defined by a linear inequality … Read more