论文标题
安全筛查规则的广义双稀疏学习
Safe Screening Rules for Generalized Double Sparsity Learning
论文作者
论文摘要
在高维环境中，稀疏模型显示了其在计算和统计效率方面的力量。我们认为变量选择问题具有一定类别的同时稀疏正规化，同时在特征和小组的稀疏性方面执行。该分析利用$εq$ norm在矢量空间中的引入，事实证明，该矢量空间与混合物正则化密切相关，并且自然会导致双重配方。讨论了原始/双重最佳解决方案和最佳值的属性，这激发了筛选规则的设计。我们在一般框架中进行了几项快速安全的筛选规则，这些规则在早期阶段丢弃非活动功能/组的规则保证在精确解决方案中是不活动的，从而导致计算速度的显着提高。
In a high-dimensional setting, sparse model has shown its power in computational and statistical efficiency. We consider variables selection problem with a broad class of simultaneous sparsity regularization, enforcing both feature-wise and group-wise sparsity at the same time. The analysis leverages an introduction of $εq$-norm in vector space, which is proved to has close connection with the mixture regularization and naturally leads to a dual formulation. Properties of primal/dual optimal solution and optimal values are discussed, which motivates the design of screening rules. We several fast safe screening rules in the general framework, rules that discard inactive features/groups at an early stage that are guaranteed to be inactive in the exact solution, leading to a significant gain in computation speed.
