Quantile universal threshold
Quantile universal threshold
复制标题
分位数通用阈值
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
N. Hengartner
中科院分区：
文献类型：
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作者：
C. Giacobino;S. Sardy;Jairo Diaz;N. Hengartner
在小波去噪、广义线性模型和低秩矩阵估计等各种设置中，人们一直在追求从高维数据中有效地恢复低维结构。通过将某些参数的阈值设定为零，套索、弹性网和子集选择等估计器进行变量选择。一个关键的步骤挑战了所有这些估计器：由阈值参数λ控制的阈值量。如果太大，重要的功能就会丢失；如果太小，则包含不正确的特性。在统一的框架内，我们提出在检测边缘选择λ。为了达到这个目的，我们引入了零阈值函数和零阈值统计量的概念，我们明确地为一大类估计量导出了它们。该方法具有将λ的选择从未知尺度转换为概率尺度的优点。数值结果表明了该方法在模型选择和预测方面的有效性。
: Efficient recovery of a low-dimensional structure from high-dimensional data has been pursued in various settings including wavelet denoising, generalized linear models and low-rank matrix estimation. By thresholding some parameters to zero, estimators such as lasso, elastic net and subset selection perform variable selection. One crucial step challenges all these estimators: the amount of thresholding governed by a threshold parameter λ . If too large, important features are missing; if too small, incorrect features are included. Within a unified framework, we propose a selection of λ at the detection edge. To that aim, we introduce the concept of a zero-thresholding function and a null-thresholding statistic, that we explicitly derive for a large class of estimators. The new approach has the great advantage of transforming the selection of λ from an unknown scale to a probabilistic scale. Numerical results show the effectiveness of our approach in terms of model selection and prediction.