AIC for the Lasso in generalized linear models
AIC for the Lasso in generalized linear models
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DOI：
10.1214/16-ejs1179
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发表时间：
2016
影响因子：
1.1
通讯作者：
Yoshiyuki Ninomiya;Shuichi Kawano
中科院分区：
文献类型：
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作者：
Yoshiyuki Ninomiya;Shuichi Kawano
Lasso是一种流行的正则化方法，可以同时进行估计和模型选择。它包含一个正则化参数，并提出了几个选择正则化参数的信息准则。虽然它们中的任何一个都可以确保模型选择的一致性，但我们没有适当的规则来在这些标准之间进行选择。同时，在高斯回归设置下，提供了对AIC的fiNITE修正。从理论上讲，fiNite校正不是从一致性的角度来保证的，而是从最小化预测误差的角度来保证的，并且不具有上述diffi的缺陷。我们的目的是得到广义线性模型中套索的一个判据。为此，我们从原始的De-fi准则出发，推导出一个判据，即Kullback-Leibler散度的渐近无偏估计。这就是在高斯回归环境下的fiNite修正，因此我们的判据可以看作是它的推广。我们的判据容易获得，需要的计算量比交叉验证少，但模拟研究和实际数据分析表明，它的性能几乎与交叉验证相同或更好。此外，我们的判据被推广到一类其他正则化方法。
: The Lasso is a popular regularization method that can simul- taneously do estimation and model selection. It contains a regularization parameter, and several information criteria have been proposed for selecting its proper value. While any of them would assure consistency in model selection, we have no appropriate rule to choose between the criteria. Meanwhile, a finite correction to the AIC has been provided in a Gaussian regression setting. The finite correction is theoretically assured from the viewpoint not of the consistency but of minimizing the prediction error and does not have the above-mentioned difficulty. Our aim is to derive such a criterion for the Lasso in generalized linear models. Towards this aim, we derive a criterion from the original definition of the AIC, that is, an asymptotically unbiased estimator of the Kullback-Leibler divergence. This becomes the finite correction in the Gaussian regression setting, and so our criterion can be regarded as its generalization. Our criterion can be easily obtained and requires fewer computational tasks than does cross-validation, but simula- tion studies and real data analyses indicate that its performance is almost the same as or superior to that of cross-validation. Moreover, our criterion is extended for a class of other regularization methods.