A Family of Penalty Functions for Structured Sparsity
A Family of Penalty Functions for Structured Sparsity
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DOI：
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发表时间：
2010-12
影响因子：
3.3
通讯作者：
C. Micchelli;Jean Morales;M. Pontil
中科院分区：
文献类型：
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作者：
C. Micchelli;Jean Morales;M. Pontil
我们研究了稀疏线性回归向量的学习问题，在其稀疏模式结构的附加条件下。我们提出了一个家庭的凸罚函数，这编码先验知识的回归系数的绝对值的一组约束。该族包含li范数，并且足够灵活以包括具有实际和理论重要性的稀疏模式的不同模型。我们建立了这些功能的一些重要性质，并讨论了一些例子，他们可以明确计算。此外，我们提出了一个收敛的优化算法求解正则化最小二乘与这些惩罚函数。数值模拟突出了结构稀疏的好处，我们的方法比Lasso和其他相关方法提供的优势。
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 li 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.