Permuted Inclusion Criterion: A Variable Selection Technique
Permuted Inclusion Criterion: A Variable Selection Technique
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排列包含标准：变量选择技术
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发表时间：
2009
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通讯作者：
Shaun Lysen
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作者：
Shaun Lysen
我们引入了一种新的变量选择技术，称为列出的纳入标准（PIC），基于用XPI表示的permuded版本增强预测器空间X。我们采用对P变量进行n个观察结果的线性回归设置。因此，我们的增强空间具有P实际预测因子和P置换预测指标。对于可变选择，这具有许多理想的属性。例如，这保留了变量之间的关系，例如正方形和相互作用，等同于x和xpi的力矩和协方差结构。更重要的是，XPI缩放X的大小。我们通过远期选择激发了这个想法。我们第一次从XPI中选择一个预测变量时，我们停止。由于这取决于置换，我们多次模拟并创建模型和停止点的分布。这具有量化我们对停止的确定性的额外好处。变量选择通常会以预定金额惩罚每个附加变量。我们的方法使用数据自适应惩罚。我们将此方法应用于模拟数据，并将其预测性能与其他广泛使用的标准（例如CP，RIC和LASSO）进行比较。将PIC视为贪婪算法的选择方案，我们将PIC扩展到广义线性回归（GLM）以及分类和回归树（CART）。学位类型学位学位名称哲学博士（PHD）研究生群体统计第一顾问Andreas Buja
We introduce a new variable selection technique called the Permuted Inclusion Criterion (PIC) based on augmenting the predictor space X with a row-permuted version denoted Xpi. We adopt the linear regression setup with n observations on p variables. Thus, our augmented space has p real predictors and p permuted predictors. This has many desirable properties for variable selection. For example, this preserves relations between variables, e.g. squares and interactions and equates the moments and covariance structure of X and Xpi. More importantly, Xpi scales with the size of X. We motivate the idea with forward selection. The first time we select a predictor from Xpi, we stop. As this depends on the permutation, we simulate many times and create a distribution of models and stopping points. This has the added benefit of quantifying how certain we are about stopping. Variable selection typically penalizes each additional variable by a prespecified amount. Our method uses a data-adaptive penalty. We apply this method to simulated data and compare its predictive performance to other widely used criteria such as Cp, RIC, and the Lasso. Viewing PIC as a selection scheme for greedy algorithms, we extend the PIC to generalized linear regression (GLM) and classification and regression trees (CART). Degree Type Dissertation Degree Name Doctor of Philosophy (PhD) Graduate Group Statistics First Advisor Andreas Buja