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**1 - 3**of**3**### Regularizers for structured sparsity

- Advances in Computational Mathematics

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### A Family of Penalty Functions for Structured

"... We study the problem of learning a sparse linear regression vector under additional conditions on the structure of its sparsity pattern. We present a family of convex penalty functions, which encode this prior knowledge by means of a set of constraints on the absolute values of the regression coeffi ..."

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We study the problem of learning a sparse linear regression vector under additional conditions on the structure of its sparsity pattern. We present a family of convex penalty functions, which encode this prior knowledge by means of a set of constraints on the absolute values of the regression coefficients. This family subsumes the ℓ1 norm and is flexible enough to include different models of sparsity patterns, which are of practical and theoretical importance. We establish some important properties of these functions and discuss some examples where they can be computed explicitly. Moreover, we present a convergent optimization algorithm for solving regularized least squares with these penalty functions. Numerical simulations highlight the benefit of structured sparsity and the advantage offered by our approach over the Lasso and other related methods. 1

### A Family of Penalty Functions for Structured

"... All in-text references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ..."

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All in-text references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.