We propose the conditional predictive impact (CPI), a consistent and unbiased estimator of the association between one or several features and a given outcome, conditional on a reduced feature set. Building on the knockoff framework of Candès et al. (J R Stat Soc Ser B 80:551–577, 2018), we develop a novel testing procedure that works in conjunction with any valid knockoff sampler, supervised learning algorithm, and loss function. The CPI can be efficiently computed for high-dimensional data without any sparsity constraints. We demonstrate convergence criteria for the CPI and develop statistical inference procedures for evaluating its magnitude, significance, and precision. These tests aid in feature and model selection, extending traditional frequentist and Bayesian techniques to general supervised learning tasks. The CPI may also be applied in causal discovery to identify underlying multivariate graph structures. We test our method using various algorithms, including linear regression, neural networks, random forests, and support vector machines. Empirical results show that the CPI compares favorably to alternative variable importance measures and other nonparametric tests of conditional independence on a diverse array of real and synthetic datasets. Simulations confirm that our inference procedures successfully control Type I error with competitive power in a range of settings. Our method has been implemented in an R package, cpi, which can be downloaded from https://github.com/dswatson/cpi.

我们提出了条件预测影响 (CPI)，这是一个或多个特征与给定结果之间关联的一致且无偏的估计器，以减少的特征集为条件。基于 Candès 等人的仿冒框架。(JR Stat Soc Ser B 80:551–577, 2018)，我们开发了一种新颖的测试程序，可与任何有效的仿冒采样器、监督学习算法和损失函数结合使用。可以有效地计算高维数据的 CPI，而没有任何稀疏性约束。我们展示了 CPI 的收敛标准，并开发了用于评估其幅度、显着性和精度的统计推断程序。这些测试有助于特征和模型选择，将传统的频率论和贝叶斯技术扩展到一般监督学习任务。CPI 还可以应用于因果发现以识别潜在的多元图结构。我们使用各种算法测试我们的方法，包括线性回归、神经网络、随机森林和支持向量机。实证结果表明，CPI 与替代变量重要性度量和其他条件独立性的非参数测试相比，在各种真实和合成数据集上具有优势。模拟证实，我们的推理程序在一系列设置中成功地控制了具有竞争力的 I 类错误。我们的方法已经在一个 实证结果表明，CPI 与替代变量重要性度量和其他条件独立性的非参数测试相比，在各种真实和合成数据集上具有优势。模拟证实，我们的推理程序在一系列设置中成功地控制了具有竞争力的 I 类错误。我们的方法已经在一个 实证结果表明，CPI 与替代变量重要性度量和其他条件独立性的非参数测试相比，在各种真实和合成数据集上具有优势。模拟证实，我们的推理程序在一系列设置中成功地控制了具有竞争力的 I 类错误。我们的方法已经在一个R包，cpi，可从 https://github.com/dswatson/cpi 下载。