基于套索主成分的特征显著性检验
Testing significance of features by lassoed principal components
摘要：
我们认为，在高维设置的功能的意义测试的问题。特别是，我们在微阵列实验中测试差异表达的基因。我们希望确定与某种类型的结果相关的基因，例如生存时间或癌症类型。我们提出了一个新的程序，称为Lassoed主成分（LPC），建立在现有的方法，可以提供一个相当大的改进。例如，在两类数据的情况下，标准（虽然简单）方法可能是计算每个基因的双样本$t$统计量。LPC方法涉及将这些常规基因得分投影到基因表达数据协方差阵的特征向量上，然后应用$L_1$罚分以便对所得投影去噪。我们提出了一个理论框架下，LPC是识别显着基因的逻辑选择，我们表明，LPC可以提供一个显着减少错误发现率在传统的方法上的真实和模拟数据。此外，这种灵活的程序可以应用于各种类型的数据，并可用于改进许多现有的方法，用于识别显着的功能。
英文摘要：
We consider the problem of testing the significance of features in high-dimensional settings. In particular, we test for differentially-expressed genes in a microarray experiment. We wish to identify genes that are associated with some type of outcome, such as survival time or cancer type. We propose a new procedure, called Lassoed Principal Components (LPC), that builds upon existing methods and can provide a sizable improvement. For instance, in the case of two-class data, a standard (albeit simple) approach might be to compute a two-sample $t$-statistic for each gene. The LPC method involves projecting these conventional gene scores onto the eigenvectors of the gene expression data covariance matrix and then applying an $L_1$ penalty in order to de-noise the resulting projections. We present a theoretical framework under which LPC is the logical choice for identifying significant genes, and we show that LPC can provide a marked reduction in false discovery rates over the conventional methods on both real and simulated data. Moreover, this flexible procedure can be applied to a variety of types of data and can be used to improve many existing methods for the identification of significant features.
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