A Goodness-of-Fit Assessment for General Learning Procedures in High Dimensions

• 成果类型: Article; Early Access
• 署名作者: He, Chenxuan; Chen, Canyi; Zhu, Liping
• 署名单位: Renmin University of China; University of Michigan System; University of Michigan
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2025.2529602
• 发表日期: 2025
• 关键词: neural-networks; tests; selection; rates

摘要

Black-box learners have demonstrated remarkable success across various fields due to their high predictive accuracy. However, the complexity of their learning procedures poses significant challenges in evaluating whether a given learner has achieved optimal performance on datasets with unknown data-generating mechanisms. We propose a general goodness-of-fit test for assessing different learning procedures involving high-dimensional predictors, encompassing methods from classical linear regression to advanced neural networks. Our goodness-of-fit test leverages data-splitting, using the test set to evaluate the black-box learner trained on the training set. By examining the cumulative covariance of the residuals, our method can effectively handle high-dimensional predictors. Extensive simulations and three real data analyses validate the effectiveness of our method. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.