用神经网络自动判断线性模型中变量重要性，比传统方法更准。
Linear Models, Variable Selection, Artificial Intelligence
- 用ANN学习OLS估计值来判断变量显著性
- 在不同样本量和方差下模拟准确率超传统方法
- 适合处理100个以下变量的高维数据建模
线性回归中的变量选择问题自假设检验诞生以来一直存在。逐步回归法（前向、后向、逐步）通过增删变量构建模型；AIC、BIC等惩罚似然法旨在筛选对似然贡献显著的变量；LASSO与弹性网则通过惩罚小系数，仅保留大系数变量。本文提出一种人工智能方法：训练人工神经网络（ANN）根据普通最小二乘法（OLS）估计值判断变量重要性。模拟研究显示该方法在不同样本量和方差条件下具有较高准确率。进一步对比实验表明其性能优于前向、后向、AIC、BIC和LASSO。方法在世界卫生组织（WHO）关于预期寿命的数据集上得到应用验证。项目提供GitHub链接，包含预训练的可处理最多100个预测变量的ANN模型、原始WHO数据集及本研究使用的子集。
原文摘要 · Abstract (English)
Variable selection in linear regression models has been a problem since hypothesis testing began. Which variables to include or exclude from a model is not an easy task. Techniques such as Forward, Back ward, Stepwise Regression sequentially add or delete variables from a model. Penalized likelihood methods such as AIC, BIC, etc. seek to choose variables that have a significant contribution to the likelihood. Penalized sum of square methods such as LASSO and Elastic Net have been used to penalize small coefficients to only allow variables with large coefficients in the model. This work introduces an Artificial Intelligence approach to model selection where an ANN is trained to determine the significance of the variables based on OLS estimates. A simulation study shows the accuracy across various sample sizes and variances. Furthermore, a simulation study is conducted to compare the performance of the approach against Forward, Backward, AIC, BIC and LASSO. The approach is illustrated using a dataset from the World Health Organization regarding Life Expectancy. A github link is provided to the pretrained ANN that can handle up to 100 predictor variables, the original WHO dataset and the subset used in this work.
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