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首页> 外文期刊>International Journal of Data Science and Analysis >Penalized Poisson Regression Model Using Elastic Net and Least Absolute Shrinkage and Selection Operator (Lasso) Penality
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Penalized Poisson Regression Model Using Elastic Net and Least Absolute Shrinkage and Selection Operator (Lasso) Penality

机译：基于弹性网和最小绝对收缩与选择算子（Lasso）罚分的惩罚性Poisson回归模型

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摘要

Variable selection in count data using Penalized Poisson regression is one of the challenges in applying Poisson regression model when the explanatory variables are correlated. To tackle both estimate the coefficients and perform variable selection simultaneously, Lasso penalty was successfully applied in Poisson regression. However, Lasso has two major limitations. In the p n case, the lasso selects at most n variables before it saturates, because of the nature of the convex optimization problem. This seems to be a limiting feature for a variable selection method. Moreover, the lasso is not well- defined unless the bound on the L1-norm of the coefficients is smaller than a certain value. If there were a group of variables among which the pairwise correlations are very high, then the lasso tends to select only one variable from the group and does not care which one is selected. To address these issues, we propose the elastic net method between explanatory variables and to provide the consistency of the variable selection simultaneously. Real world data and a simulation study show that the elastic net often outperforms the lasso, while enjoying a similar sparsity of representation. In addition, the elastic net encourages a grouping effect, where strongly correlated predictors tend to be in the model together.
机译：当解释变量相关时，使用惩罚性泊松回归在计数数据中选择变量是应用泊松回归模型的挑战之一。为了同时处理估计系数和同时执行变量选择，Lasso罚分已成功应用于Poisson回归中。但是，套索有两个主要限制。在p> n的情况下，由于凸优化问题的性质，套索在饱和之前最多选择n个变量。这似乎是变量选择方法的限制功能。此外，除非系数的L1范数上的界限小于某个值，否则套索的定义不明确。如果存在成对相关性非常高的一组变量，则套索趋向于仅从该组中选择一个变量，而不关心选择哪个变量。为了解决这些问题，我们提出了解释变量之间的弹性网方法，并同时提供了变量选择的一致性。现实世界的数据和模拟研究表明，弹性网在表现类似的稀疏性的同时，通常表现优于套索。另外，弹性网鼓励分组效应，其中高度相关的预测变量倾向于一起出现在模型中。

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