通过最小化可重构性实现强大的仿制品
Powerful Knockoffs via Minimizing Reconstructability
摘要：
Model-X仿制品允许分析师使用几乎任何机器学习算法进行特征选择，同时仍然可以证明控制错误发现的预期比例。要应用X模型的仿制品，必须构造称为仿制品的合成变量，这些变量在特征选择期间有效地充当控制。构建仿制品的黄金标准是最小化特征与其仿制品之间的平均绝对相关性（MAC），但令人惊讶的是，我们证明了这一过程在非常简单的设置中可能无能为力，包括具有相关可交换特征的高斯线性模型。关键问题是最小化MAC在特征和仿制品之间创建了强联合依赖性，这允许机器学习算法使用仿制品部分或完全重建特征对响应的影响。为了提高山寨的力量，我们建议生成山寨，最大限度地减少可重构性（MRC）的功能，我们证明了我们的建议，高斯功能，显示它是计算效率高，鲁棒性强，功能强大。我们还证明，某些MRC敲减最小的自然定义的估计误差在高斯线性模型。此外，在一组广泛的模拟，我们发现许多设置与相关的功能，其中MRC的仿制品显着优于MAC最小化的仿制品和没有设置中，MAC最小化的仿制品优于MRC仿制品超过一个非常轻微的保证金。我们在一个新的开源python包knockpy中实现了我们的方法和大量来自山寨文学的其他方法。
英文摘要：
Model-X knockoffs allows analysts to perform feature selection using almost any machine learning algorithm while still provably controlling the expected proportion of false discoveries. To apply model-X knockoffs, one must construct synthetic variables, called knockoffs, which effectively act as controls during feature selection. The gold standard for constructing knockoffs has been to minimize the mean absolute correlation (MAC) between features and their knockoffs, but, surprisingly, we prove this procedure can be powerless in extremely easy settings, including Gaussian linear models with correlated exchangeable features. The key problem is that minimizing the MAC creates strong joint dependencies between the features and knockoffs, which allow machine learning algorithms to partially or fully reconstruct the effect of the features on the response using the knockoffs. To improve the power of knockoffs, we propose generating knockoffs which minimize the reconstructability (MRC) of the features, and we demonstrate our proposal for Gaussian features by showing it is computationally efficient, robust, and powerful. We also prove that certain MRC knockoffs minimize a natural definition of estimation error in Gaussian linear models. Furthermore, in an extensive set of simulations, we find many settings with correlated features in which MRC knockoffs dramatically outperform MAC-minimizing knockoffs and no settings in which MAC-minimizing knockoffs outperform MRC knockoffs by more than a very slight margin. We implement our methods and a host of others from the knockoffs literature in a new open source python package knockpy.
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