图 书 馆
结构稀疏的罚函数族A Family of Penalty Functions for Structured Sparsity |
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| 课程网址: | http://videolectures.net/nips2010_morales_fpf/ |
| 主讲教师: | Jean Morales |
| 开课单位: | 伦敦大学 |
| 开课时间: | 2011-03-25 |
| 课程语种: | 英语 |
| 中文简介: |  我们研究了在稀疏模式结构的附加条件下学习稀疏线性回归向量的问题。我们提出了一系列凸罚函数，这些函数通过对回归系数的绝对值的一组约束对这种先验知识进行编码。该族包含了$ ell_1 $范数，并且具有足够的灵活性以包含稀疏模式的不同模型，这些模型具有实际和理论上的重要性。我们建立了这些函数的一些重要属性，并讨论了一些可以显式计算它们的示例。此外，我们提出了一种收敛优化算法，用这些惩罚函数来求解正则化最小二乘。数值模拟凸显了结构稀疏性的优势，以及我们的方法相对于套索和其他相关方法的优势。 |
| 课程简介: | 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 $ell_1$ 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. |
| 关 键 词: | 惩罚函数; 正则化; 回归向量 |
| 课程来源: | 视频讲座网 |
| 数据采集: | 2021-03-07：zyk |
| 最后编审: | 2021-03-10：zyk |
| 阅读次数: | 53 |