论文标题
Fanok：线性时间的仿制
FANOK: Knockoffs in Linear Time
论文作者
论文摘要
我们描述了一系列算法，该算法有效地实施高斯模型X仿型，以控制大规模特征选择问题上的错误发现率。确定仿冒分布需要解决一个大规模半决赛程序，我们得出了几种有效的方法。一个人处理通用协方差矩阵，其复杂性比例为$ o（p^3）$，其中$ p $是环境维度，而另一个则假设在协方差矩阵上的等级$ k $ factor模型，以减少这种复杂性绑定到$ o（pk^2）$。我们还为估计因子模型和样品仿型协变量而得出有效的程序，并在维度上有线性。我们在$ P $ $ 500,000 $的问题上测试我们的方法。
We describe a series of algorithms that efficiently implement Gaussian model-X knockoffs to control the false discovery rate on large scale feature selection problems. Identifying the knockoff distribution requires solving a large scale semidefinite program for which we derive several efficient methods. One handles generic covariance matrices, has a complexity scaling as $O(p^3)$ where $p$ is the ambient dimension, while another assumes a rank $k$ factor model on the covariance matrix to reduce this complexity bound to $O(pk^2)$. We also derive efficient procedures to both estimate factor models and sample knockoff covariates with complexity linear in the dimension. We test our methods on problems with $p$ as large as $500,000$.
