论文标题
可变选择的正规损失最小化的持续减少
Persistent Reductions in Regularized Loss Minimization for Variable Selection
论文作者
论文摘要
在通过多面体仪表进行正规化损失最小化的背景下，我们表明，对于一类广泛的损失功能（可能是非平滑损失和非convex），并且在输入数据上的简单几何条件下，可以有效地确定在所有最佳解决方案中具有最佳解决方案的损失函数的最佳解决方案的范围，从而有效地识别出所有问题的范围。此过程是独立的，仅将数据作为输入，并且不需要任何呼叫损失功能。因此，我们将此程序称为上述规范损失最小化问题类别的持续减少。可以通过应用于数据点形成的多面体锥的极端射线识别子例程来有效实现此减少。我们采用现有的输出敏感算法来实现极端射线识别，这使我们的保证和算法适用于超高维问题。
In the context of regularized loss minimization with polyhedral gauges, we show that for a broad class of loss functions (possibly non-smooth and non-convex) and under a simple geometric condition on the input data it is possible to efficiently identify a subset of features which are guaranteed to have zero coefficients in all optimal solutions in all problems with loss functions from said class, before any iterative optimization has been performed for the original problem. This procedure is standalone, takes only the data as input, and does not require any calls to the loss function. Therefore, we term this procedure as a persistent reduction for the aforementioned class of regularized loss minimization problems. This reduction can be efficiently implemented via an extreme ray identification subroutine applied to a polyhedral cone formed from the datapoints. We employ an existing output-sensitive algorithm for extreme ray identification which makes our guarantee and algorithm applicable in ultra-high dimensional problems.
