Leave-one-out cross-validation is risk consistent for lasso
Leave-one-out cross-validation is risk consistent for lasso
复制标题
留一法交叉验证对于 lasso 来说是风险一致的
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
D. McDonald
中科院分区：
文献类型：
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作者：
D. Homrighausen;D. McDonald
套索过程遍布统计和信号处理文献，因此是大量理论和应用研究的目标。虽然这项研究的大部分重点是 lasso 所拥有的理想特性——预测风险一致性、符号一致性、正确的模型选择——但这些结果假设调整参数是以预言方式选择的。然而，这在实践中是不可能的。相反，数据分析师必须使用数据两次，一次是为了选择调整参数，另一次是为了估计模型。但只有启发式方法才能证明这种程序的合理性。为此，我们给出了通过交叉验证选择平滑参数时 lasso 的风险一致性的第一个明确答案。我们表明，在设计矩阵的一些限制下，套索估计器仍然与凭经验选择的调整参数风险一致。
The lasso procedure pervades the statistical and signal processing literature, and as such, is the target of substantial theoretical and applied research. While much of this research focuses on the desirable properties that lasso possesses—predictive risk consistency, sign consistency, correct model selection—these results assume that the tuning parameter is chosen in an oracle fashion. Yet, this is impossible in practice. Instead, data analysts must use the data twice, once to choose the tuning parameter and again to estimate the model. But only heuristics have ever justified such a procedure. To this end, we give the first definitive answer about the risk consistency of lasso when the smoothing parameter is chosen via cross-validation. We show that under some restrictions on the design matrix, the lasso estimator is still risk consistent with an empirically chosen tuning parameter.
影响因子：
0.8
作者：
Weiliang Shi;G. Wahba;S. Wright;Kristine E. Lee;R. Klein;B. Klein
通讯作者：
Weiliang Shi;G. Wahba;S. Wright;Kristine E. Lee;R. Klein;B. Klein