Tractable Post-Selection Maximum Likelihood Inference for the Lasso
Tractable Post-Selection Maximum Likelihood Inference for the Lasso
复制标题
Lasso 的易于处理的选择后最大似然推断
DOI：
10.2957/kanzo.62.681
复制
发表时间：
2017
期刊：
影响因子：
--
通讯作者：
M. Drton
中科院分区：
文献类型：
--
作者：
Amit Meir;M. Drton
在模型选择后应用标准统计方法可能会产生效率低下的估计和假设检验，无法达到名义I类错误率。主要问题是数据的选择后分布与原始分布不同。特别地，所观察到的数据被约束为位于由所选择的模型确定的原始样本空间的子集中。这通常使得观测数据的后选择似然性难以处理，并且最大似然性推理困难。在这项工作中，我们得到周围的棘手的可能性，通过生成噪声无偏估计的后选择得分函数，并使用它们在随机上升算法，产生正确的后选择最大似然估计。我们将所提出的技术估计的套索选择的线性模型的问题。在渐近分析中，所得到的估计是一致的所选参数，并有一个有限的截断正态分布。构造的置信区间的渐近分布的基础上获得接近标称覆盖率在所有的模拟设置考虑，和点估计被证明是上级的套索估计时，真正的模型是稀疏的。
Applying standard statistical methods after model selection may yield inefficient estimators and hypothesis tests that fail to achieve nominal type-I error rates. The main issue is the fact that the post-selection distribution of the data differs from the original distribution. In particular, the observed data is constrained to lie in a subset of the original sample space that is determined by the selected model. This often makes the post-selection likelihood of the observed data intractable and maximum likelihood inference difficult. In this work, we get around the intractable likelihood by generating noisy unbiased estimates of the post-selection score function and using them in a stochastic ascent algorithm that yields correct post-selection maximum likelihood estimates. We apply the proposed technique to the problem of estimating linear models selected by the lasso. In an asymptotic analysis the resulting estimates are shown to be consistent for the selected parameters and to have a limiting truncated normal distribution. Confidence intervals constructed based on the asymptotic distribution obtain close to nominal coverage rates in all simulation settings considered, and the point estimates are shown to be superior to the lasso estimates when the true model is sparse.
影响因子：
5.8
作者：
Friedman, Jerome;Hastie, Trevor;Tibshirani, Rob
通讯作者：
Tibshirani, Rob
影响因子：
4.5
作者：
Lockhart R;Taylor J;Tibshirani RJ;Tibshirani R
通讯作者：
Tibshirani R
影响因子：
5.7
作者：
Leeb, Hannes;Poetscher, Benedikt M.;Ewald, Karl
通讯作者：
Ewald, Karl