| Abstract | Lack-of-fit testing is often essential in many applications of statistical/machine learning. Despite the availability of large datasets, in many applications, collecting labels for all data points is impossible due to measurement constraints. We propose a design-adaptive testing procedure to check a model when only a limited number of responses can be accessed. To select a small subset of covariates from a large pool of given design points, we derive an optimal sampling strategy, the structure-adaptive-sampling, with which the proposed test possesses the asymptotically best power. Numerical results on both synthetic and real-world data confirm the effectiveness of the proposed method. |
