Controlling the false discovery rate via knockoffs
通过 Knockoff 变量控制错误发现率AI 解读 ↓
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通过 Knockoff 变量控制错误发现率
- 研究问题
- 在线性模型中筛选大量解释变量时，如何控制入选变量中的预期错误发现比例，同时保持发现真实关联的能力？
- 方法与思路
- 作者构造模仿原变量相关结构的 knockoff 变量，用原变量与其替代变量的统计量比较形成筛选规则。
- 材料陈述的贡献
- 摘要称在观测数不少于变量数的线性模型中实现有限样本 FDR 控制，无需已知噪声水平，并展示结合 Lasso 的结果。
- 阅读关注点
- 应核对线性模型与噪声条件、替代变量的可构造性、统计量要求和筛选阈值，以及功效比较采用的设计。
- 阅读边界
- 仅据版本未注明的索引摘要；完整模型条件和比较数值未提供，FDR 控制也不等于每个入选变量都是真实或因果关联。
原文摘要
In many fields of science, we observe a response variable together with a large number of potential explanatory variables, and would like to be able to discover which variables are truly associated with the response. At the same time, we need to know that the false discovery rate (FDR)—the expected fraction of false discoveries among all discoveries—is not too high, in order to assure the scientist that most of the discoveries are indeed true and replicable. This paper introduces the knockoff filter, a new variable selection procedure controlling the FDR in the statistical linear model whenever there are at least as many observations as variables. This method achieves exact FDR control in finite sample settings no matter the design or covariates, the number of variables in the model, or the amplitudes of the unknown regression coefficients, and does not require any knowledge of the noise level. As the name suggests, the method operates by manufacturing knockoff variables that are cheap—their construction does not require any new data—and are designed to mimic the correlation structure found within the existing variables, in a way that allows for accurate FDR control, beyond what is possible with permutation-based methods. The method of knockoffs is very general and flexible, and can work with a broad class of test statistics. We test the method in combination with statistics from the Lasso for sparse regression, and obtain empirical results showing that the resulting method has far more power than existing selection rules when the proportion of null variables is high.